United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
Research and Development
EPA-600/S2-81 -228 Dec. 1981
Project Summary
Performance of Trickling
Filter Plants: Reliability,
Stability and Variability
Richard Haugh, Salar Niku, Edward D. Schroeder, and GeorgeTchobanoglous
Effluent quality variability from
trickling filters was examined in this
study by statistically analyzing daily
effluent BODs and suspended solids
data from 11 treatment plants.
Summary statistics (mean, standard
deviation, etc.) were examined to
determine the general characteristics
of those data. Distributions of most
effluent data were skewed to the right,
and daily suspended solids data
generally exhibited more variation
than daily BODi data.
Five probability distribution
functions, chosen through experience
and the literature, were tested to de-
termine which would be best used to
describe daily, 7-day average and 30-
day average effluent data distribu-
tions. Three distributions (the two
parameter empirical, the gamma, and
the log normal) were found to be
adequate, with the log normal being
preferred because of ease of applica-
tion.
Daily effluent BODs and suspended
solids data were found to contain both
random and nonrandom components.
Weekly cycles were found in about
half of the plants studied, and signifi-
cant month-to-month variation in
effluent quality was found in every
plant. Effluent BOD and suspended
solids concentrations were higher in
winter than in summer when pooled
data from all plants were examined.
Multiple regression analysis was
used to determine the effects of
various process parameters on efflu-
ent quality. In general, primary
effluent BODs and suspended solids
concentrations and wastewater
temperature had the greatest effect.
Variation due to measurement error
was estimated to be 5 to 78 percent
and 11 to 78 percent for effluent
BODs and suspended solids values.
respectively.
Methods for incorporating statis-
tical concepts into trickling filter
design and operation are discussed.
This Project Summary was develop-
ed by EPA's Municipal Environmental
Research Laboratory, Cincinnati, OH,
to announce key findings of the
research project that is fully docu-
mented in a separate report of the
same title (see Project Report ordering
information at back).
Introduction
As discharge requirements have
become more stringent, it has become
necessary to include concepts of vari-
ability into the theory, design, and
regulation of wastewater treatment
plants. For example, limitations on the
average daily and weekly concentrations
of pollutants have made it necessary not
only to insure that average performance
is within discharge limits, but also to
reduce the amount of variation in
performance.
A number of recent studies have
examined effluent variability in waste-
water treatment plants, but most of
these studies have been concerned
-------
solely with activated sludge plant
performance. The purpose of this study
was to investigate and characterize the
nature and sources of variability of
effluent quality in trickling filter waste-
water treatment plants. Five-day
biochemical oxygen demand (BODs) and
suspended solids (SS) concentrations
are the effluent quality parameters that
are examined.
Most theoretical and laboratory work
on wastewater treatment processes,
and practically all studies of data from
full scale treatment plants, have been
based on deterministic, steady state
concepts. Recently, however, dynamic
and stochastic models have been devel-
oped for both the activated sludge and
trickling filter processes. Laboratory
studies have been done on the activated
sludge process under variable loading
conditions, and treatment plant influent
and effluent data have been studied
using sophisticated stochastic models.
There exists a need to incorporate the
concept of variability in virtually every
area of the wastewater treatment field.
Numerous authors have argued that
stochastic concepts should be included
in wastewater treatment - plant
planning, design, and regulation. In the
following sections, areas in which
consideration of treatment variability is
important are.discussed.
Variability of Trickling Filter
Processes
Discharge Requirements
Effluent variability is implicitly
recognized in current federal secondary
treatment standards plant discharge
limits. The 7-day average maximums
allow for the fact that short term fluctu-
ations tend to be averaged out in the
long run.
However, daily, weekly and monthly
concentration limits are not explicitly
stochastic because they set maximum
values that cannot be exceeded (without
causing a violation). These fixed limits,
especially daily maximums, are concep-
tually inconsistent with the stochastic
nature of wastewater treatment
processes and requirements should be
restated in a probabilistic manner. An
example of a probabilistic standard
would be one in which the daily,com-
posite average BODs concentration
cannot exceed a specific value more
than two times in any consecutive 30-
day period.
Design
Stochastic concepts are also useful in
treatment plant design. Designers must
consider the degree of variability to be
expected, as well as the average
performance, if discharge requirements
are to be met. Currently, most design
techniques are based on steady state
assumptions and average constituent
values are used for design parameters.
One method of accommodating process
variability is to oversize the treatment
units. Another way to allow for process
variability is to determine the expected
effluent variation based on data from
existing treatment plants. Linear
regression models can be developed to
predict the distribution percentiles of
effluent BOD and SS concentrations,
based on the annual mean value of each
parameter. Working backwards,
designers can choose an effluent con-
centration not to be exceeded more than
a prescribed percentage of the time and
then calculate the required average
value. Using these computed average
values as design criteria, traditional
design methods can then be used to size
the treatment units. If the design
averages are achieved, treatment
variability should be within the expected
limits.
Possibly a more cost effective
approach to reducing the occurrence of
high effluent concentrations is to
reduce the variability of treatment
processes rather than improving the
average performance of these proc-
esses. Reducing the variability has the
effect of narrowing the distributions of
effluent values. The use of equalization
chambers and automatic process
control have been proposed for the
purpose of reducing effluent variability.
Equalization of influent flows reduces
loading fluctuations; because the treat-
ment process is operated under loading
conditions that approach steady state
conditions, fluctuations in process
performance are reduced. Effluent flow
equalization before discharge reduces
effluent quality variation directly by
mixing flows from different periods of
process performance. Automatic
control can be used to adjust process
parameters to compensate for changes
in loading conditions and process
efficiently.
Fluctuations in Trickling Filter
Performance
Effluent quality variability in trickling
filter plants is caused by a number of
environmental, operational, and loading
factors. Factors that cause fluctuations
in trickling filter performance are dis-
cussed below.
The wastewater flow rate through the
trickling filter controls the thickness and
velocity of the liquid film on the biolog-
ical slime. An increase in flow rate
increases the film thickness, which in
turn inhibits oxygen transfer through
the film. Higher liquid velocities reduce
the contact ti me for diffusion of organics
from the liquid into the slime. Thus the
overall effect of increased flowrate is a
higher filter effluent BOD concentration
for a given influent BOD concentration.
An increase in the concentration of
organic matter entering the filter
generally causes an increase in the
filter effluent organic concentration.
Increased organic concentration
increases the mass loading rate on the
filter and raises the concentration of
organics in the liquid film. The in-
creased concentration of organics
causes food and nutrients to penetrate
deeper into the slime layer, which
increases the reaction rate per unit area
unless the maximum reaction rate has
been reached or some other factor, such
as oxygen transfer, has become rate
limiting. Although the mass removal^
rate increases, it does not increase as'
much as the increase in mass loading,
and the net result is a higher filter
effluent organic BOD concentration.
Air and wastewater temperature both
affect treatment efficiency. A tempera-
ture increase in the liquid film and bio-
logical slime increases transport and
reaction rates, thus improving treat-
ment efficiency. In conventional filters,
the supply of air (and thus oxygen) to the
microorganisms is controlled by the
relationship between air and waste-
water temperature. The greater the
difference between air and water
temperature, the greater the draft
through the filter.
Other factors that affect filter opera-
tion are wastewater pH and the
presence of toxic substances. The
optimal pH for microbial growth in
conventional biological treatment is
between 6.5 and 8.5. IfthepH isconsid-
erably outside this range, treatment
efficiency will decrease. Toxic sub-
stances in the influent can also retard
biological activity and reduce treatment
efficiency.
Trickling filters are quasi-natural
biological processes, and there is
evidence that slime growth-decaj|
-------
cycles occur locally within the filter,
independent of fluctuations in flow rate,
organic concentration or other param-
eters. It is not known whether these
cycles cause significant variations in
the overall performance of the filter.
Fluctuations in Clarifier
Performance
The most important factors that affect
clarifier performance are the concentra-
tion and composition of incoming
suspended matter and the flow rate
through the tank. An increase in flow
rate decreases the time available for
particles to settle to the bottom of the
tank and thus increases the concentra-
tion of particles in the clarifier effluent.
Density, shape, and size all affect the
settling velocity of particles. An
increase in the settling velocity of the
suspended particles entering the clari-
fier results in an increase in the
percentage of particles removed.
Higher concentrations of suspended
matter in the clarifier influent generally
result in higher effluent concentrations
because there is an increase in the
concentration of particles with settling
velocities too low to be removed.
Flocculation and straining of particles
also affect suspended solids removal in
clarifiers, but these mechanisms cannot
be explained simply in terms of clarifier
influent strength and flow rate.
Other factors can influence clarifier
performance. Improperly operated
sludge scrapers can cause disruptive
currents in the tank, and settled solids
that remain on the bottom of the tank
too long can become anaerobic and
produce gas bubbles that float solids to
the water surface.
Objectives
The purpose of this study is to investi-
gate the characteristics and some
possible sources of variability in final
effluent quality in trickling filter waste-
water treatment plants. Daily perform-
ance data have been obtained from 11
treatment plants and analyzed statis-
tically to investigate the following
questions:
1. How can the distributions of efflu-
ent BOD5 and SS concentrations
from trickling filter plants be char-
acterized?
2. Are trickling filter effluent BOD5
and SS concentrations data
random?
3. If trickling filter plant effluent
BODs and SS data are not random,
do the data follow any annual or
weekly cycles?
4. What are the effects of influent,
environmental, and operational
parameters on effluent variability?
5. What is the effect of measure-
ment error on effluent data vari-
ability?
It would be worthwhile to study the
variability of each process. However,
data from between the trickling filter
and final clarifier are not generally
available. Therefore, in this study only
the variability of the final effluent is
examined.
Procedures
The data base for this study consists
of daily operation and performance
records from 11 trickling filter plants
(Table 1) located in six different states.
Data sets from most of the plants are 1
year in length, but the data from plants 5
and 7 are somewhat longer. All concen-
tration data are flow weighted compos-
ite values.
Characterization of Effluent
Distributions
To characterize the effluent BODs and
SS distributions for the treatment plants
in this study, summary statistics such as
the mean, standard deviation, and skew
coefficient were computed for daily, 7-
day average and 30-day average
effluent concentrations from each
plant. Also, three theoretical and two
empirical distribution functions were
chosen as possible models for effluent
distributions and were tested using the
Kolmogorov-Smirnov goodness-of-fit
test. Details of these procedures are
explained below.
Running Averages
Portions of federal and state dis-
charge requirements for BOD5 and SS
concentrations are stated in terms of
running 7- and 30-day averages. There-
fore, the distributions of these averages,
as well as the distributions of daily
averages, are of interest and will be
investigated in this study. Trickling filter
eflfuent data are not random, and it
cannot be assumed that running aver-
age distributions are approximately
normal. Therefore, the distributions of
Table 1. Trickling Filter Treatment Plants Studied
Location Period of Data
Plant
Number
Type of
Process
Average
Flow (mgd)
1
2
3
4
5
6
7
8
9
10
11
Iowa
Michigan
Wisconsin
Michigan
Ohio
Michigan
Michigan
Oklahoma
Michigan
Michigan
Arkansas
Jan '76
Jan '76
Jan '76
Jan '76
Feb '76
Jan '77
Jan '76
Jan '76
Sept '76
Dec '76
Jan '77
- Dec '76
- Dec '76
- Dec '76
- Dec '76
- July '77
- Dec '77
- Jan '77
- Dec '76
- Aug '77
- Nov '77
- Dec '77
2-stage
1 -stage
2-stage
1 -stage
1 -stage
2-stage
1 -stage
2-stage
1 -stage
1 -stage
2-stage
33.7
0.5
7.6
0.8
15.8
0.9
11.6
12.3
4.0
0.8
6.0
-------
running averages had to be determined
in the same manner as the distributions
of daily averages.
Summary Statistics
The following summary statistics
have been computed for daily, 7-day
average, and 30-day average effluent
BODs and SS concentration data from
each plant:
arithmetic mean
standard deviation
coefficient of variation
skew coefficient
maximum observation
minimum observation
number of valid observations
Examination of these statistics will
provide information on the central
tendencies, ranges and shapes of the
effluent BOD5 and SS concentration
distributions for data from each plant.
Theoretical Distribution
Models
Virtually an unlimited number of
theoretical distribution functions could
be tested for fit with the effluent data.
Practical limitations prevent testing
more than a few. The normal, log-
normal, and gamma distributions are
good candidates because of their sim-
plicity, widespread use, and demon-
strated usefulness in previous studies
of wastewater treatment process
performance.
Empirical Distribution Models
Strong linear relationships between
annual mean and percentile concentra-
tion values have been shown to exist in
previous studies. For example, if one
year's effluent BOD5 data for a group of
plants is placed in ascending order, the
95th percentile value will be approxi-
mately proportional to the plant's
annual mean value.
The set of linear regression equations
developed for the percentile values do
not, by themselves, define a continuous
probability distribution. However, given
the mean value from a set of data, a
finite number of predicted percentile
values can be determined. A continuous
distribution can then be constructed by
linearly interpolating between each of
the predicted percentile values.
Kolmogorov-Smirnov
Goodness-of-Fit Test
The usefulness of each of the five
(proposed) distribution functions for
modeling BODS and SS data from each
plant was examined using the
Kol mogorov-Smi rnov goodness-of-f it
test. The null hypothesis for this test is:
"The observed data were sampled
from an underlying population
which is distributed according to
the hypothesized distribution
function."
It is assumed that if the test hypothesis
is true, any differences between the
observed distribution and the hypothe-
sized distribution are due to the effects
of random sampling.
Randomness of Effluent Data
It was important to determine if trick-
ling filter effluent BODs and SS concen-
tration data were random. If the trickling
filter effluent data are not random, then
distribution models for effluent data are
not random, and distribution models for
effluent concentrations cannot be used
in the classical manner because
probability density functions are usually
assumed to be based on random data.
Another consequence of nonrandom-
ess would be that predictable cycles
might exist in effluent data.
The randomness of trickling filter
effluent BOD5 and SS concentration
data have been tested using the runs
test and a test for serial correlation. In
addition to simply determining if the
data are random, these tests can be
used to determine the relative magni-
tude of nonrandomness in each set of
data and to provide a basis for compar-
ing the relative randomness of different
sets of data.
The runs test is a general purpose test
of the randomness of a data series.
Trend, grouping, and many types of
cyclical movement in the data can be
detected. In some cases, the runs test
fails to detect dependence between suc-
cessive values of a data series. It is
therefore prudent to perform a test for
correlation between consecutive data
pairs (serial correlation) in addition to
the runs test when examining data
randomness.
The test for serial correlation is per-
formed by treating the original data
series as one variable, xt, and treating
the data series shifted forward one
observation as the other variable, xt-i.
The Pearson correlation coefficient, a
measure of association of the strength
of the linear relationship between two
variables, is then computed to test for
correlation between xt and xt-i. If the
data are random, the correlation coeffi-
cient will tend towards zero.
Annual and Weekly Cycles
To the test for the possibi lity of weekly
or annual cycles in trickling filter efflu-
ent data, a two-way analysisof variance
was performed on effluent BODs and SS
concentration data from each plant.
Analysis of variance was not used to
explicitly determine if cycles existed in
the data series, but merely to determine
if effluent concentrations were depend-
ent on the month or day of the week on
which they occurred. However, if efflu-
ent BOD5 (or SS) concentrations from a
treatment plant were found to be
dependent on the day of the week, it was
concluded that a weekly cycle existed in
that data set.
A similar conclusion concerning
annual cycles could not be made for
data that were found to be dependent on
the month. With only 1 year of data from
each plant, there was no way of deter- i
mining if an observed annual sequence
was representative of a repeating
annual cycle or merely part of a random
fluctuation in average monthly perform-
ance. All that could be concluded in this
case was that some variation in the data
was due to significant changes in
average performance from month to
month.
Effects of Various Process
Parameters
The effects of influent, environ-
mental, and operational parameters on
effluent variability were examined by
using multiple linear regression
analysis. This analysis studied the cor-
relations between various process
parameters and effluent BOD5 and SS
concentrations.
The regression analysis has been
conducted in two parts. First, multiple
linear regression equations predicting
effluent BOD5 and SS concentrations
for each plant were constructed using
linear combinations of the following
independent variables:
flow, Q
influent BODs and SS concentra-
tions, BOD,, SS, M
-------
primary effluent BOD5 and SS
concentrations, BODP, SSP
the inverse of the average influent
water temperature, WTEMP"1
the inverse of the average air tem-
perature, ATEMP'1
the deviation from 7.0 of the influ-
ent pH, 7.0-pH
recycle ratio, R
Second, to test the relation impor-
tance of quadratic terms, loading
factors, combinations of terms and
values of parameters from previous
days (lagged variables), regression
equations using the terms above as well
as the following terms were constructed:
quadratic terms: BOD,2, SS,2,
BODp2, SSPZ
loading factors: Q-BOD,, OSS,,
Q-BODp, Q-SSp
combinations of terms: T»va =
(ATEMP + WTEMP)/2, Td =
| ATEMP-WTEMP |
lagged terms: BODi,t-i, SSi,t-i,
BODp,t-i, SSp,t-i, BODi,t-2, SSi,t-2,
BODp,t-2, SSp,t-2, ATEMPt-i
Measurement Error
Any discussion of the causes of varia-
tion in a series of measured quantities
should include consideration of the
effect of measurement error. Like all
laboratory procedures, the BODs and SS
tests have a finite degree of precision.
Thus even if the effluent from a treat-
ment plant was of perfectly uniform
quality at all times, and in addition, the
effluent was always sampled without
error, the measured BODs and SS con-
centrations would still vary from sample
to sample because of the inherent vari-
ability in the methods of analysis.
It is possible to determine how much
variation in trickling filter effluent data
is caused by measurement errors
because the variation due to the limited
precision of the BOD5 and SS tests is
independent of other sources of varia-
tion in the data.
A simplifying assumption has been
made to estimate the variation due to
measurement error. Because the preci-
sion of the BODs and SS tests is a
function of the concentrations being
measured, the precision of these tests
varies from day to day. For simplicity, it
wilt be assumed that the fractional
.standard deviations of the measure-
ment errors are a function of each
plant's annual mean effluent BODs and
SS concentrations.
Results
The characterization of daily, running
7-day average and running 30-day aver-
age effluent BODs and SS concentration
data was conducted in three steps. First,
summary statistics for each type of
effluent data set were computed for
each treatment plant (Tables 2, 3, and
4). Second, coefficients for two empiri-
cal distribution models were computed.
Third, two empirical and three theoreti-
cal distribution models were tested to
determine their usefulness in modeling
effluent data from each plant.
Some general characteristics of trick-
ling filter effluent data can be seen from
these results. For the daily data, the
averages of the mean BODs from all
plants and the mean SS concentration
from all plants are approximately equal.
However, the average standard devia-
tion for SS data is somewhat higher
than the average standard deviation for
BODs data. Thus it may be concluded
that, overall, BOD5 and SS data tend to
be of the same average magnitude but
that SS data tend to be somewhat more
variable.
Comparison of Distribution
Models
Five probability distributions have
been tested for their fit to effluent BODs
and SS data using the Kolmogorov-
Smirnov (K-S) goodness-of-fit test.
Distributions tested were the one- and
two-parameter empirical models and
the normal, log-normal, and gamma
distribution functions.
For any single effluent parameter
(e.g., daily BODs, 7-day average SS, etc.)
the distribution that best fit the data
changed from treatment plant to treat-
ment plant. However, it can be con-
cluded that, in general, the log-normal,
gamma, and two-parameter empirical
distribution functions are equivalent for
the purpose of describing effluent data
distributions.
Randomness of Effluent Data
Using a 5-percent significance level
as the rejection criterion, the hypothesis
of randomness can be rejected for every
set of BOD and SS data on the basis of at
least one of the two tests. It can be
concluded that the BOD data from every
plant and the SS data from every plant
but one are highly nonrandom. For 9 out
of the 11 treatment plants, it can be
concluded that, for most of the treat-
ment plants studied, effluent BODs data
are less random than SS data.
Annual and Weekly Cycles
It may be concluded from the results
of the randomness tests that there are
significant nonrandom patterns in trick-
ling filter effluent data. The existence of
annual or weekly cycles in the data has
been examined by performing a two-
way analysis of variance on BODs and
SS data from each plant and by pooling
normalized data from all the treatment
plants and plotting the averages for
each month and day of the week.
For each treatment plant studied,
effluent BODs and SS concentrations
are in some manner dependent on the
month in which they occur. The ratios of
maximum monthly average to minimum
monthly average and the differences
between monthly averages are of
physical as well as of statistical
significance. Because only 1 year of
data from each plant was used, it may
not be concluded that effluent concen-
trations at these 11 treatment plants
have repeating annual cycles.
The effluent concentrations in eight
sets of data depend on the day of the
week on which they occur. Because
there are 52 weeks in each set of data, it
may be concluded that there is a repeat-
ing weekly cycle in each of these eight
data sets. Existence of any general
weekly or annual patterns in the efflu-
ent data from all the treatment plants
was studied by plotting monthly and
daily averages for pooled data. Effluent
BOD5 and SS concentration data from
each treatment plant were first normal-
ized. Normalized data from all of the
treatment plants were pooled together
and grouped according to the month in
which the data were taken. To study
weekly patterns, effluent data from the
nine treatment plants with daily data
were pooled and then grouped accord-
ing to the day of the week on which the
data occurred. Effluent BODs and SS
data tend to have annual cycles that are
roughly in phase with one another.
Concentrations of both BODs and SS
tend to be higher than average in the
winter months and lower than average
in the summer and early fall.
-------
Table 2.
Summary Statistics for Daily Effluent BODs and Suspended Solids Concentrations
BODs
Plant
Number
1
2
3
4
5
6
7
8
9
10
11
Average
Median
Mean
(g/m3)
33.31
10.73
10.05
58.35
29.24
27.04
23.21
43.09
51.13
21.02
18.31
29.59
-
Sx
(g/m3)
15.28
7.24
7.52
20.83
11.21
6.75
16.93
6.59
19.95
6.22
11.98
11.86
11.21
V,
0.46
0.67
0.75
0.36
0.38
0.25
0.73
0.15
0.39
0.30
0.65
0.46
0.39
Skew
0.92
1.62
1.68
0.10
1.31
0.09
1.62
0.61
0.23
-0.15
2.17
0.93
0.92
Max
102.0
43.0
61.0
107.0
93.0
58.0
100.0
69.0
125.0
33.0
104.0
-
93.0
Min
(g/m3)
8.0
0.0
1.0
22.0
6.0
3.0
1.0
28.0
12.0
8.0
0.0
-
6.0
Valid
Obs
357
365
362
250
492
365
383
365
359
250
355
-
-
Mean
(g/m3)
52.50
21.45
21.04
54.85
18.34
15.09
24.05
34.03
41.08
23.60
16.15
29.29
-
Sx
(g/m3)
31.17
13.35
16.69
15.02
8.81
5.98
15.09
13.63
17.61
14.42
8.85
14.60
14.42
Suspended Solids
Vx
0.53
0.62
0.79
0.27
0.48
0.40
0.63
0.40
0.43
0.61
0.55
0.52
0.55
Skew
2.26
1.15
1.17
0.10
2.16
0.40
0.99
4.56
1.60
1.08
1.09
1.51
1.15
Max
(g/m3)
280.0
80.0
88.0
94.0
84.0
37.0
86.0
172.0
130.0
86.0
64.0
--
86.0
Min
(g/m3)
6.0
1.0
1.0
20.0
3.0
2.0
2.0
12.0
12.0
2.0
1.0
-
2.0
Valid
Obs
356
366
361
250
493
365
386
365
365
250
363
--
--
Effects of Process Parameters
Correlations between influent, opera-
tional, and environmental process
parameters and effluent BOD and SS
concentrations were studied using
multiple linear regression analysis.
Regression equations using combina-
tions of various process parameters as
independent variables were construc-
ted in a stepwise manner. All data used
in constructing the regression
equations were normalized so that the
regression coefficients would be easier
to interpret.
The regression analysis was
conducted in two parts. First, regression
equations were developed using simple
linear combinations of untransformed
variables. In the second part, various
transformations and combinations of
the independent variables used in the
first part were included in the regres-
sion analysis. In both steps, only those
independent parameters that contri-
buted materially to the significance of
the regression equation were included
in the final form of the equation.
It was concluded that primary effluent
BODs concentration is, in general,
highly correlated with effluent BOD5
concentration. Flow rate, influent BODs
concentration, and the reciprocal of
influent wastewater temperature are
also highly correlated with the effluent
BOD5 for most plants where data were
available. Results for the other indepen-
dent parameters are inconclusive,
because there was little correlation, the
correlation varied from plant to plant, or
because data for that variable were not
available from most plants. The regres-
sion equations for effluent SS generally
have somewhat lower coefficients of
determination, indicating that effluent
SS concentrations are not correlated to
other process parameters as highly as
are effluent BOD5 concentrations.
Variation Caused by
Measurement Error
The estimates of variation caused by
measurement error are given in Table 5
for effluent concentration data from 11
trickling filter plants. Variation caused
by the SS test is greater than for the
BODs test for every plant. The standard
deviation of the analytical tests is esti-
mated to be between 1.8 and 7.5 g/m3
for BODs and between 5.3 and 10.7,
-------
Table 3. Summary Statistics for Continuous 7-Day Averages Effluent BOD and Suspended Solids Concentrations
BODS Suspended Solids
Plant
Number
1
2
3
4
5
6
7
8
9
10
11
Average
Median
Mean
(g/m3)
33.12
10.56
9.99
58.31
29.15
27.02
22.87
43.00
51.49
21.01
17.99
-
Sx
(g/m3)
11.52
4.95
4.76
20.17
6.86
3.86
13.32
4.79
17.47
4.59
8.40
9.15
6.86
V,
0.35
0.47
0.48
0.35
0.24
0.14
0.58
0.11
0.34
0.22
0.47
0.34
0.35
Skew
0.15
0.93
0.67
0.07
0.57
-0.39
1.48
0.45
-0.07
0.21
1.28
0.49
0.45
Max
(g/m3)
62.3
25.4
24.6
96.8
53.1
35.7
81.7
54.3
82.9
29.6
48.7
--
53.1
Min
(g/m3)
14.0
3.1
1.7
27.2
14.0
14.4
7.1
34.1
18.3
10.0
4.5
-
14.0
Valid
06s
360
360
360
360
514
359
391
360
359
359
358
-
--
Mean
(g/m3)
52.52
21.22
21.14
54.82
18.41
15.07
23.62
34.04
41.23
23.86
16.11
-
-.
Sx
(g/m3)
18.63
9.18
8.00
12.65
5.26
4.40
9.84
7.17
12.57
9.59
5.07
9.31
9.18
Vx
0.35
0.43
0.38
0.23
0.29
0.29
0.42
0.21
0.30
0.40
0.30
0.33
0.31
Skew
0.38
0.70
0.26
-0.03
0.73
0.04
0.59
1.61
0.73
1.21
0.60
0.62
0.60
Max
(9/m3)
103.6
49.1
41.5
78.8
39.0
27.4
52.3
63.1
80.3
59.2
34.7
--
52.3
Min
(9/m3)
17.6
6.1
5.1
30.0
7.3
6.4
5.9
24.1
18.3
6.4
5.9
-
6.4
Valid
Obs
360
360
360
360
516
359
391
360
359
'359
359
-
--
g/m3 for SS. Although these results are
only approximate, it is apparent that a
significant percentage of the variation
in effluent concentration data is due to
the limited precision of the BOD5and SS
tests.
Discussion
For any given parameter, the distribu-
tion that was best for describing effluent
data was generally different for each
treatment plant. Three distributions (the
two-parameter empirical, log-normal,
and gamma) were generally comparable
and could be used to describe effluent
data better than the other two distribu-
tions tested. These three distributions
can be used to model effluent distribu-
tions adequately, but no single
distribution, empirical or theoretical, is
generally best for modeling effluent
distribution from all trickling filter
plants. The general characteristics of
trickling filter effluent concentration
distributions found in this study are in
agreement with the results of previous
studies on trickling filter and activated
iludge plants.
All of the distributions but the one-
parameter model fit trickling filter efflu-
ent data with roughtly the same degree
of accuracy. Therefore, the choice of
distribution to use in any particular
application can be made on the basis of
the relative ease with which the differ-
ent distributions are calculated. Even
the one-parameter model can be used to
obtain a reasonable, rough estimate of
effluent distributions and may be
preferable in some applications.
The advantage of using the one-
parameter empirical model is that the
distribution standard deviation does not
have to be calculated or estimated.
When the standard deviation must be
estimated, the one-parameter model is
as accurate for predicting effluent distri-
butions as any of the two-parameter
models, unless an unusually good
estimate of the standard deviation is
available.
Percentiles can be calculated easily
for any of the five distributions once the
parameters of the distribution are
specified. The arithmetic mean and
(when required) the standard deviation
are sufficient to specify any of the distri-
butions except the log-normal. To use
the log-normal distribution, the mean
and standard deviation of the
logarithms of the data are required, and
these are not the same as the loga-
rithms of the arithmetic mean and
standard deviation.
If a desired percentile value is
specified and (when required) the
standard deviation is estimated, any of
the five distributions can be used to
compute the implied mean value of the
distribution. If the gamma distribution is
used, an iterative procedure (which is
time-consuming unless performed on a
computer) must be used to calculate the
distribution mean.
Another disadvantage of using the
gamma distribution is that only rela-
tively incomplete tables of gamma
distribution values are available, and
gamma percentiles are difficult to
compute. In contrast, complete tables of
the normal distribution are available.
With some simple conversions, normal
tables can be used for the log-normal
distribution as well. Of course, tables
-------
Table 4. Summary Statistics for Running 30-Day Average Effluent BOD and Suspended Solids Concentrations
BOD5 Suspended Solids
Plant
Number
1
2
3
4
5
6
7
8
9
10
11
Average
Median
Mean
(g/m3)
32.11
10.00
9.77
57.69
29.03
26.78
22.59
42.75
52.94
21.10
17.05
--
-
Sx
(g/m3)
9.91
3.53
3.69
19.85
5.16
2.39
11.63
3.98
15.56
3.48
6.18
7.76
5.16
V»
0.31
0.35
0.38
0.34
0.18
0.09
0.51
0.09
0.29
0.16
0.36
0.28
0.31
Skew
0.15
1.04
0.77
0.11
0.57
-0.74
1.09
0.57
-0.16
0.66
0.84
0.45
0.57
Max
(g/m3)
51.9
20.7
19.6
88.9
42.7
31.0
52.1
51.7
79.0
27.9
34.5
--
42.7
Min
(3/m3)
17.0
5.4
4.2
32.0
20.0
20.2
10.1
36.8
25.1
15.7
7.8
--
17.0
Valid
Obs
337
337
337
337
516
336
368
337
336
336
336
-
-
Mean
(g/m3)
51.59
20.93
21.05
54.30
18.58
14.85
23.22
34.01
41.81
23.99
15.81
-
--
Sx
(g/m3)
15.63
7.66
5.47
11.54
3.81
3.88
7.55
4.50
9.79
6.25
3.44
7.23
6.25
V.
0.30
0.37
0.26
0.21
0.21
0.26
0.33
0.13
0.23
0.26
0.22
0.25
0.26
Skew
0.78
0.93
0.09
-0.02
0.27
-0.05
0.16
'0.07
0.40
0.23
'0.06
0.24
0.16
Max
(g/m3)
88.9
41.1
31.5
72.2
30.5
21.1
38.6
43.1
61.7
39.4
24.9
-
39.4
Min
(g/m3)
29.7
9.5
11.0
37.3
11.2
7.47
11.2
26.0
26.8
11.3
7.9
-
11.2
Valid
Obs
337
337
337
337
516
336
368
337
336
336
336
-
--
are not available for the two empirical
distribution models, but the calculations
involved in using these distributions are
simple.
Effluent Standards
The distributions of effluent concen-
trations must be known if reasonable
and consistent effluent standards are to
be set. A reasonable standard does not
require a level of treatment that cannot
be achieved with available technology.
Two standards are consistent if neither
standard requires a significantly higher
level of treatment than the other.
Of the 11 treatment plants in this
study, two had a mean effluent BOD5
concentration equal to or less than 17.5
g/m3 and three had a mean effluent SS
concentration equal to or less than 18.6
g/m3. U.S. Environmental Protection
Agency (EPA) secondary standards
were attained by a relative minority of
trickling filter plants evaluated in this
study.
The implied mean effluent BOD5
concentration for the 7-day average
standard is 4.8 g/m3 higher than the
implied mean for the 30-day standard.
For effluent SS concentrations, the
implied mean for the 7-day standard is
2.5 g/m3 higher than for the 30-day
standard. From these results, the
conclusion may be made that the 30-
day effluent BOD5 standard is signifi-
cantly more restrictive than the 7-day
standard, and that the 30-day effluent
SS standard is somewhat more restric-
tive than the 7-day SS standard. EPA
secondary standards are therefore not
consistent when applied to trickling
filter treatment plants.
Randomness of Effluent Data
Effluent concentration data in this
study are not randomly generated and
are thus not independent of time and
preceding effluent concentrations. The
probability that an effluent BOOs (or SS)
concentration will be exceeded on any
one day is dependent on which particu-
lar day is of interest. Information
concerning the conditions under which
events occur is not included in distribu-
tion functions, and hence no statement
concerning the probable level of
effluent concentrations on any one day
can be made based simply on the distri-
bution models considered in this study.
Distribution models for effluent
concentrations do provide information
on the long-term behavior of trickling
filter performance and can be used to
estimate the probable frequency of
occurrence of some range of effluent
values over a 1-year period.
Annual and Weekly Patterns
On the basis of the analysis of
variance results and the plots of pooled,
normalized data, the following
conclusions can be made concerning
effluent BOD5 and SS concentrations at
the 11 treatment plants studied. ^
8
-------
1. There are significant month-to-
month fluctuations in average
effluent concentrations for every
treatment plant studied.
2. One cause of these monthly fluc-
tuations is an annual cycle in
effluent concentrations that is
evident when data from all 11
treatment plants is pooled. Efflu-
ent concentrations tend to be
above average in the winter and
below average in the summer.
3. A significant weekly cycle exists in
effluent concentration data from
some of the treatment plants
studied.
4. When data from nine treatment
plants were pooled, weekly cycles
were evident for BOD5 and SS
data, but the amplitudes of these
cycles were less than half the
amplitudes of the annual cycles.
Effluent BOD and SS concentra-
tions tend to be below average on
Sundays, and SS concentrations
tend to be above average on
Wednesdays.
Effects of Process Variables on
Effluent Concentrations
Based on the results of the multiple
regression analyses, it can be con-
cluded that influent, operational, and
environmental process variables are
correlated with effluent BOD5 and SS
concentration data at trickling filter
plants. It has not been proven that
fluctuations in effluent data are caused
by changes in the independent param-
eters because regression analysis alone
cannot be used to prove cause and
effect relationships. Correlations
between two variables conceivably
could be caused by a third, unmeasured
variable. However, the relationships
found are consistent with current theo-
retical models of clarifiers and trickling
filters and provide strong evidence to
support the hypothesis that a significant
percentage of effluent variation in
trickling filter plants is caused by fluctu-
ations in process loading and
temperature.
Variation Due to Measurement
Error
Measurement errors can cause a
.significant percentage of the total
Table 5. Variation Caused by Measurement Error
Effluent BODS
Effluent Suspended Solids
Estimated Percent Standard Estimated Percent Standard
Plant of Variation Caused Deviation of Variation Caused Deviation
Number by Measurement Error (g/m3) by Measurement Error (g/m3)
1
2
3
4
5
6
7
8
9
10
11
10
7
6
13
15
36
5
78
12
28
6
4.7
1.9
1.8
7.5
4.4
4.0
3.6
5.8
6.9
3.3
3.0
11
23
14
51
44
78
21
37
27
15
37
10.5
6.4
6.3
10.7
5.9
5.3
6.8
8.2
9.1
5.5
5.4
variation in effluent concentrations,
especially for SS data. The percentage
of the variation in effluent data caused
by analytical error was estimated to be
greater than 10 percent for BOD5 and
SS concentrations from 7 and 11 plants,
respectively, and was greater than 20
percent for BOD5 and SS data from 3
and 8 plants, respectively.
General Comments
The greater variability and random-
ness found in SS effluent data may, in
part, be due to the fact that measure-
ment errors appear to be somewhat
greater for SS than for BOD5. However,
one reason that measurement errors
were estimated to be greater for SS data
was because of the assumption that
duplicate BOD5 samples were analyzed,
but only one SS sample was used. If this
assu mption is not correct, the esti mated
measurement errors for SS analysis
would be smaller, though they would
still be somewhat larger than the esti-
mated errors for BODS data.
The sum of the percentages of
variance explained by the regression
models and by measurement error is
greater than 40 percent for all but three
sets of data. From these results, it can
be concluded that a large fraction of
effl uent variability iscaused by variation
in process parameters and by measure-
ment error. Because three of the sums
are greater than 100 percent, the
estimates of measurement error are in
some cases too high.
Measurement errors do not affect the
values of running average data as much
as they affect daily data, because the
errors tend to cancel out. For example, if
the standard deviation of a test is 5.0
g/m3, the standard deviations of 7-day
and 30-day averages for the same
parameter would be 1.9 and 0.9 g/m3,
respectively.
Based on the results of this study, it
may be concluded that the magnitude of
variation in effluent data caused by
measurement errors is quite large at
many treatment plants. If a treatment
plant is operating near its discharge
limits, apparent violations of the daily
and 7-day average concentration limits
can be caused by analytical error alone.
To reduce the possibility of discharge
violations caused by measurement
error, more replicates of each sample
can be analyzed. Also, sampling and
laboratory techniques should be
-------
checked to see that all sources of samp-
ling and analytical errors are minimized.
Reliability of Trickling
Filter Process
The uncertainties associated with
plant design and operation should be
recognized in the design of trickling
filters. The best way to accomplish this
is to incorporate stochastic concepts
and procedures in the design process.
To produce an effluent of high quality
and to meet the effluent discharge
requirements at minimum cost, design
engineers must be able to estimate the
average effluent quality and its varia-
tions for a given treatment process.
Uncertainties and their significance on
process performance can be analyzed
systematically using methods of proba-
bility. A probabilistic approach for
design can be used to provide a consis-
tent basis for the analysis of uncertainty
and a theoretical basis for the analysis
of performance and reliability.
Reliability measures are expressed in
probability terms and are defined as the
probability of adequate performance
(i.e., the percent of the timethat effluent
concentrations meet requirements). A
stochastic model and design tables and
graphs have been developed in a related
study predicting achievable effluent
BODs and SS concentrations based on a
proposed coefficient of reliability
(COR).* The COR relates mean constitu-
ent values to the standard and is
achieved on a probability basis and the
log-normal distribution assumption.
The COR was defined mathematically
as:
COR =
(Vx2 + 1 )1'2 exp { -Z ,. [1 n (V«2 + 1 )]1/ZJ
The coefficient of variation (Vx) for
effluent concentration should be
estimated from past experience
and on reasonable expectation of
performance. Values of the coeffi-
cient of variation (Vx) from other
similar treatment plants may be
used as a guidance. Based on cur-
sory examination, coefficient of
variations of 0.50 for BODs and
0.55 for SS concentration would
appear to be suitable values, how-
ever. Reliability as a function of Vx
and COR is shown in Figure 1.
To support the validity of the reliability
model in prediction of performance of
trickling filters, the percent of the time
that effluent concentration exceeded 30
g/m3 was computed for 1 year of data in
all 11 plants (Table 18 in the full report).
This percent of exceedance was also
predicted using the reliability model
based on the log-normal assumption.
The prediction values are very
comparable with the measured values.
To determine the validity of the
theoretical results of the COR, Figure 1
was reconstructed based on the 1 year
of operational data of all 11 plants.
Percentile values of exceedance for
effluent BODS and SS from one year of
daily operational data have been com-
puted to present an empirical distribu-
tion of effluent concentration without
considering whether it follows any
classical distribution function. The
results of COR based on pooled plant
data were highly comparable to the
1.0
0.9
0.8 -
0.7
0.6
§0.5
1
0.4
0.3
0.2
0.1
*Niku, S.,E D.Schroeder, G Tchobanoglous, andF.
J Samaniego, "Performance of Activated Sludge
Plants Reliability, Stability and Variability,"
EPA-600/2-81-227, U.S Environmental Protec-
tion Agency, Cincinnati, OH, September 1981.
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5
Normalized Mean, m^/Xt
Figure 1. Reliability versus normalized mean for different coefficients of
variations. *
10
-------
results of COR based on the log-normal
distribution assumption.
Stability of Trickling Filter
Plants
Stability is a measure of adherence of
the annual mean concentration, and
"standard deviation" is the most appro-
priate measure of stability in waste-
water treatment plants.
In Figures 2 and 3, the mean,
standard deviation, and range of efflu-
ent BOD5 and SS data for all 11 trickling
filter plants are shown. Examination of
these descriptive statistics results in the
conclusion that a stability cut-off point
of 10 g/m3 can be used. That is, a
distinct difference exists between the
statistical characteristics of the plants
operating below and above the standard
deviation of 10 g/m3. The maximum
daily concentrations of effluent BODs
and SS in stable plants with a standard
deviation of less than or equal to 10
g/m3 are usually less than 70 g/m3;
whereas in unstable plants, maximum
concentrations are usually greater than
90 g/m3 and 80 g/m3, respectively.
The full report was submitted in
fulfillment of Grant No. R805097-01 by
the University of California under spon-
sorship of the U.S. Environmental
Protection Agency.
I
I
(0
.o
to
I
160
140
120
100
80
60
40
20
Stable
Unstable
Standard Deviation
Range
» Mean
Plant Number
I M
*. is
8 12 16
Standard Deviation (g/m3)
20
24
Figure 2. Variability of effluent BOD as a function of standard deviation.
11
-------
£UU
180
160
«~ 740
c
\
-
c
- Standard Deviation
Drmf*f*
Mean
~
- Plant Number
\
10
-
-
"~ <
\ \ \
-
,
Cy
<
\
<0
0>
^)
O
*^
\
i
IX
,
\
§
X
*0
5
\ \ \ n \ i
-
_
_
-
-
"
-
-
-
-
-
-
8 12 16 20
Standard Deviation (g/m3)
28 32
Figure 3. Variability of effluent suspended solids concentration as a function of
standard deviation.
12
-------
Richard Haugh, Edward D. Schroeder, and George Tchobanoglous are with the
University of California. Davis, CA 95616; Salar Niku is presently with Brown
and Caldwell Consulting Engineers. Pasadena, CA 91109.
Jon Bender is the EPA Project Officer (see below).
The complete report, entitled "Performance of Trickling Filter Plants: Reliability,
Stability and Variability," (Order No. PB 82-108 143; Cost: $ 11.00. 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
13
ft U.S. GOVERNMENT PRINTING OFFICE:1981--559-092/3355
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