SEPA
United States
Environmental Protection
Agency
Municipal Environmental Research
Laboratory
Cincinnati OH 45268
Research and Development
EPA-600/S2-81 -227 Dec. 1981
Project Summary
Performance of Activated
Sludge Processes: Reliability,
Stability and Variability
Salar Niku,
Samaniego
Edward D. Schroeder, George Tchobanoglous, and Francisco J.
was to stat
formance of
sludge pro
sludge pro
From an am
found that
not distribi
generally the
Using th<
probabilistic
and graphs
The objective of this research study
tically analyze the per-
large number of activated
esses and to develop
methods and procedures for intro-
ducing reliab ility and stability concepts
into design and operation of waste-
water treatr lent plants. Variations in
the daily effli ent quality of 43 activated
esses were examined.
ysis of the data, it was
e effluent variables are
ed symmetrically, and
distributions are skewed
right than to the left of
quent value. The log-
further to th
the most fi
normal distiibution was found to fit
the observed effluent biochemical
oxygen dem
solids (SS) (
nd (BOD) and suspended
ta most consistently.
lognormal distribution
and a coeffit ient of reliability (COR), a
model and design tables
ave been developed for
predicting achievable effluent BOD
and SS concentrations. Mean con-
stituent values are correlated to
selected standards with the COR. The
proposed model can be used in the
design of a treatment process expected
to perform at a certain reliability
and/or to estimate the reliability of an
operating treatment plant. Validity of
the reliability model in prediction of
effluent quality performance has been
verified.
The stability of various activated
sludge processes was examined using
several statistical measures. Stability
is defined as a measure of the daily
variations from the annual mean. The
standard deviation was found to be
the most appropriate indicator of
stability. A standard deviation of 10
g/m3 was selected as stability cut-off
point on the basis of a qualitative
examination of the data. Plants with
effluent values below 10 g/m3 are
considered stable; plants with values
greater than 10 g/m3 are considered
unstable. The effect of plant size and
process type on stability was also
examined.
Correlation and regression analyses
have been used to investigate the
causes of effluent quality variability
and to identify the extent of the
factors contributing to this variability.
The contribution of several variables
to the observed effluent BOD and SS
variations were examined. No single
variable or group of variables was
found that could be used to char-
acterize the variability of effluent
quality for all plants in general.
However, the method may be applied
to data from each individual plant to
determine the principal factors re-
sponsible for effluent quality varia-
tions.
The appropriateness of effluent
standards as they are currently stated
was discussed, and the use of the
geometric mean as a measure of
central tendency of daily effluent
quality data was recommended for
setting discharge standards. This
recommendation is based on the fact
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that effluent concentration values are
distributed lognormally and that the
geometric mean of lognormal data has
known probabilistic behavior and a
meaningful interpretation.
Design procedures and/or discharge
requirements should be based on a
recognition of the variability of process
performance; that is, they should be
stochastic in character. An approach
is presented that can be used to design
a process stochastically when the
effluent standards are deterministic in
nature.
This Project Summary was devel-
oped by EPA's Municipal Environ-
mental Research Laboratory, Cincin-
nati, 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).
Introduction
In recent years regulatory agencies
have become more aware of the need to
continually examine the performance
characteristics of wastewater treatment
plants. Since 1970, explicit performance
standards have been placed on most
biological treatment processes in the
United States. The Federal Water
Pollution Control Act Amendments of
1972 (P.L 92-500) were written with
the intent of restoring and maintaining
the chemical, physical, and biological
integrity of the Nation's water. To
achieve these objectives, the U.S.
Environmental Protection Agency (EPA)
has set a minimum standard of effluent
quality as that attainable by the applica-
tion of biological treatment processes.
The standards for secondary treatment
were to be met by 1977, and Best
Practicable Waste Treatment Technology
is to be achieved by 1983. Compre-
hensive standards have not been
established because of the lack of
information on the performance capa-
bilities of operating plants.
It must be recognized that effluent
biochemical oxygen demand (BOD) and
suspended solids (SS) concentrations
from biological treatment processes are
highly variable. Input loads, environ-
mental conditions, operational param-
eters, and human factors may affect or
be the cause of this variability. All of
these factors are themselves subject to
fluctuations in magnitude, composition,
and simultaneous occurrence.
Most wastewater treatment facilities
are designed with limited information
as to the nature and magnitude of these
variations. The usual procedure is that
the flow records, if existing, are
analyzed and some peak flow rate
established. An estimate is made of the
corresponding BOD and SS mass
loadings (with little or no rational basis
for the decision other than experience).
Design parameters such as mean cell
residence time, sludge wastage, and
sludge recycle rate are established on
the basis of past experience and
intuition. The process is then designed
based on empirical models in which
steady state conditions are assumed,
with kinetic coefficients obtained from
the literature.
Kinetic models currently available are
based on mean values and variations in
performance cannot be predicted using
these models. Seldom, if ever, is the
stochastic nature of these variables and
parameters incorporated into the design
process. This is because techniques for
incorporating information on perform-
ance variability into the design and also
in the setting of discharge standards
have not yet been implemented.
Objective
The basic purpose of this study was to
develop information that can be used by
the designer and operator of a waste-
water treatment plant in evaluating and
predicting the performance of a bio-
logical treatment process with respect
to effluent quality and by the regulatory
agencies in preparing reasonable,
effective, and technically sound dis-
charge requirement orders.
Four subjects were studied in this
report:
1. Performance of a large number
of activated sludge processes
was analyzed and the reliability
of each was determined. A
reliability model was developed
that can be used to predict
process performance of plants
under design or currently under
operation.
2. Stability of activated sludge
processes based on statistical
measures was studied with the
objective of introducing a method
that can be used to define and
compare the stability of plants
within and among each.
3. For the reliability and stability
study, each treatment plant was
considered as a "black box";
meaning, all variables affecting
process performance were con-
sidered to be uncontrolled and
unknown. Reliability and stability
models were developed based
only on discharge effluent data.
In this part of the study the effect
of various factors on effluent
quality was studied with the
objective of determining the
nature, sources, and the extent
of the variability in effluent
quality and to identify factors
contributing to this variability
through statistical analysis of
operating data.
4. Appropriateness of effluent
discharge standards as they are
currently established was ex-
amined and discussed. An al-
ternative approach of using
geometric mean as opposed to
arithmetic mean is recommend-
ed for defining the central
tendency of effluent BOD and
SS concentrations and for setting
effluent discharge standards.
General Appraoch
The scope of this project included
collection and analysis of performance
and operational data from 43 activated
sludge wastewater treatment plants
located throughout the United States.
Evaluation of the performance of these
processes in terms of reliability, stability^
and variability was based on th"
analysis of these data. The results of
this study for activated sludge processes
are reported in this summary report.
Location by state, process type, and
plant size are shown in Table 1. The
selected treatment plants represent a
range of geographic locations and
environmental conditions throughout
the United Statesandrange inflowfrom
less than 1 mgd to more than 200 mgd.
Reliability of Activated
Sludge Processes
Reliability Concept
Reliability of a system can be defined
as "the ability to perform the specified
requirements free from failure" or "the
probability of adequate performance for
a least specified period of time under
specified conditions." A treatment plant
is completely reliable if process per-
formance response has no failure (e.g.,
discharge requirement violations).
Failure of a treatment process is
realized when the required effluent
discharge satndards are exceeded, i.e.,
"Failure" = effluent concen-
tration > effluent requirements
-------
Table 1. Activated Sludge Treatment Plants Studied
Plant
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
23
30
31
32
33
34
35
36
37
38
39
40
41
42
43
Plant
Location
Michigan
California
California
Wisconsin
Illinois
Illinois
Illinois
Maryland
New York
Alabama
Michigan
Virginia
Alabama
Illinois
Illinois
California
California
California
California
Illinois
Illinois
Illinois
Illinois
Michigan
Michigan
Michigan
Michigan
Michigan
Michigan
Michigan
Connecticut
California
Ohio
Nevada
Kansas
Washington
California
Michigan
Michigan
Michigan
Michigan
Wisconsin
Wisconsin
Year
76
7-75/6-76
76
76
76
76
76
76
77
6-76/5-77
10-76/9-77
76
7-76/6-77
76
76
75
76
76
76
76
76
76
76
73
74
75
76
77
77
77
76
76
76
75
76
76
76
10-76/10-77
77
12-76/11-77
01-77/10-77
76
76
Type of
Process
Complete mix
Conventional
Complete mix/contact stab.
Contact stabilization
Step feed
Conventional
Conventional
Step feed
Complete mix
Aerated lagoon
Complete mix
Conventional/ step feed
Conventional/ step feed
Conventional
Step feed
Step aeration
Step aeration
Step aeration
Step aeration
Conventional
Conventional
Conventional
Step feed
Conventional
Conventional
Conventional
Conventional
Conventional
Conventional
Conventional
Conventional
Plug flow/Kraus
Contact stabilization
Conventional/tapered
Contact stabilization
Conventional/ step feed
Complete mix/ step feed
Step feed
Conventional/contact stab.
Extended aeration
Conventional
Conventional
Conventional
Average
Flow (mgd)
14.2
100.0
16.2
23.7
69.7
66.2
69.1
15.2
18.6
23.6
0.74
15.8
10.5
2.2
3.3
6.3
2.4
29.0
7.1
209.0
189.0
188.0
185.0
1.9
2.1
2.1
2.3
2.1
9.5
9.5
3.8
47.1
2.8
17.0
10.4
30.8
13.9
17.3
33.3
0.56
26.9
81.6
54.0
Because of numerous uncertainties
underlying the design and operation of a
wastewater treatment plant, there is
some risk of failure (discharge require-
ment violation) that is unavoidable. This
risk should be recognized and waste-
water treatment plants ought to be
designed on the basis of an acceptable
measure of risk (of violation).
In a technical definition, the essential
concept of reliability is "probabilty of
success" or "probability of adequate
performance"; i.e., the percent of the
time that effluent concentration meets
the requirements.
Reliability = 1 - P(failure) =1 -
P (effluent concentration >
requirements)
The probability of failure is extremely
sensitive to the distribution function of
effluent concentration. Thus, to develop
a reliability model, first the distribution
of effluent concentration should be
modeled. Assuming the distribution of
effluent concentration is known, then,
the reliability of the plant can be
computed.
The designer of a treatment process
should first select an appropriate level
of process performance; that is, he must
decide how large a probability of failure
he can accept. The classical approach to
this question is to apply statistical-
economic decision theory. Plant costs
(both capital and operating) rise with
increasing performance requirements.
On the other hand, lower expectations
in water quality or acceptance of a
higher probability of violations will
result in adverse effects on water
quality downstream. Thus, the level of
reliability and the effluent discharge
standards directly affect plant eco-
nomics. The degree of reliability (proba-
bility of adequate performance) should
be selected in such a way that these
costs are minimized.
Effluent Concentration
Distribution
Statistical analyses of the data
summarized in the full report show that
the performance of the plants on an
annual basis is quite variable. Effluent
concentration of BOD and SS varied
significantly among the plants. Mean
effluent BOD and SS for plants studied
ranged from 1.9 to 85.6 g/m3 and 2.5 to
80.1 g/m3, respectively. On the average,
effluent SS concentration and its
variation was greater than the cor-
responding effluent BOD values.
Histograms of the effluent BOD and
SS data were plotted, and the data
distributions were analyzed. The data
were generally not symmetrical and
were all skewed to the right (positive
skewness coefficient). It was found that
in most plants, effluent BOD and SS
data are not normally distributed,
whereas a lognormal distribution con-
sistently fits the observed effluent BOD
and SS data.
The lognormal probability distribution
is one commonly used in civil engineer-
ing practice and seems to have been
adopted originally to produce a better fit
to skewed data by using this simple
transformation of the familiar normal
distribution. The lognormal distribution
has an important justification from the
normal distribution, in that, fluctuations
from the mean are proportional rather
than additive. All currently used kinetic
models for the activated sludge process
result in multiplicative expressions for
effluent BOD. It is thus not unreasonable
to expect effluent BOD to have a
lognormal distribution.
The Kolomogorov-Smirnov (K-S) test
was used to test the goodness-of-fit of
the data to lognormal distribution. It was
concluded that the hypothesized log-
-------
normal model should not be rejected for
more than two-thirds of the plants at
significant levels of 1 percent. Generally,
the results of the K-S test (not reported
in this summary report) suggest that a
lognormal distribution provides a
reasonable description of the effluent
BOD and SS data.
Process Reliability
Reliability of a treatment plant is
based on knowledge of process be-
havior. Because of variations in per-
formance, a treatment plant should be
designed to produce an average effluent
concentration below the discharge
standards. The question is, what mean
value should be used to guarantee an
effluent concentration consistently less
than a standard with a certain reliability?
A coefficient of reliability (COR) may be
introduced that relates mean constituent
values (i.e. the design values) to the
standard that must be achieved on a
probability basis. For example, if a 30-
g/m3 standard is to be achieved 90
percent of the time, the process must be
designed to achieve a particular mean
effluent concentration. The mean
constituent value, mx, is then obtained
from Equation 1:
mx = (COR)Xs (1)
where Xs= a fixed standard.
Suppose that for some probability of
failure a between zero and one but
presumably near zero, a process is to be
designed for which the observed log-
normal variable X has the property that
where
P(X1)-l/2 1
Ln
(5)
and reliability is determined using the
standard normal table (e.g.. Table 2).
For example, the reliability of a plant
operating with a mean value of 0.6 Xs
and a Vx = 0.70 is 87 percent. In other
words, in a long-run operation, about 13
percent of the observed effluent vari-
ables would exceed 30 g/m3 in a plant
operating with a mean value of 18g/m3
and standard deviation of 12.6 g/m3 (Vx
= 0.70). Figure 1 may be used instead of
Equation 5.
Verification of Results
To support the validity of the model in
prediction of effluent quality, the
percent of the time that effluent
concentration exceeded 30 g/m3 was
computed for 1 year of data in all plants.
This percent of exceedance was also
predicted using the reliability model
(Equation 4, or Figure 1) based on the
lognormal assumption. The predicted
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Table 2. Cumulative Probabilities of
the Standard Normal
Distribution
Cumulative
Probability
1-a
1-a
99.9
99
98
95
92
90
80
70
60
50
3.090
2.326
2.054
1.645
1.405
1.282
0.842
0.525
0.253
0
values (not included in the summary
report) were very comparable with the
measured values.
Stability of Activated
Sludge Processes
Conventional criteria and design
procedures employed in the design of
municipal and industrial wastewater
processes are based on the simplified
assumption of steady-state conditions.
In practice, activated sludge systems
are seldom operated under steady state
conditions. Effluent quality depends on
nput loads, environmental conditions,
in-plant biological and operational
variables as well as many other unex-
pected perturbations beyond operational
control. Designing a treatment process
is thus a multivariate problem. Fluctua-
tions in input loads and environmental
conditions, nature of the wastewater,
introduction of toxic materials, and
mechanical failure of the system as well
as human factors may frequently cause
process upset and instability that may
have adverse effects on quality.
Stability Measure
Stability may be thought of as the
property of adherence to a reference or
norm. In the case of wastewater
treatment, the best reference value for
stability appears to be the annual mean
constituent concentration. One com-
plete cycle of weather and a monitoring
period long enough to damp the effects
of short term variations is reflected in
the annual mean value. Variations from
the mean on a day-to-day (or week-to-
week or month-to-month) basis then
provide a measure of stability.
Since stability is a measure of
variation from the mean, a standard
quantitative measure of variation
1.0
0.9
0.8
0.7
0.6
$0.5
"B
DC
0.4
0.3
0.2
0.1
i i i i
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, mx/X8
Figure 1. Reliability versus normalized mean for different coefficients of
variations.
(stability indicator) is of special interest.
The stability indicator may be used as a
tool to evaluate and compare the
relative of different plants and to
examine the effects that various design
and operation procedures may have on
process stability. Several such indicators
are available.
Among those available stability
indicators, standard deviation has been
selected as the most appropriate
indicator of wastewater treatment plant
stability. This is because the standard
deviation is theoretically a measure of
dispersion, and practically it is the most
familiar and simplest term among all
other measures of stability.
Stability is usually defined in relative
terms. For example, in comparing the
stability of two treatment plants, the
plant with less effluent quality variation
is considered more stable. Stability may
also be defined in absolute terms where
a valid time deterministic model is
available. For instance, if the monthly
variance of effluent quality of a plant
continuously increases each month (or
any other time period), then, that plant is
an unstable one in absolute terms.
When variance changes randomly, the
-------
plant may or may not be absolutely
unstable. A major factor would be the
amount of the variance. Other alternatives
are that the plant may be unstable for
short periods of time or may simply be
less stable than other plants with better
performance characteristics.
Stability Cut-Off Point
The stability cut-off point may be
defined as a standard deviation value
below which plants are considered
stable and above which plants are
considered unstable. In Figures 2 and 3,
the mean, standard deviation, and
range of effluent BOD and SS data for a II
43 treatment plants are shown. Exam-
ination of these descriptive statistics
leads to the conclusion that plants
having a standard deviation of less than
10 g/m3 for both effluent BOD and SS
may statistically be considered as stable
plants. The 10 g/m3 value has been
selected as the stability cut-off point
because a distinct difference exists
between the statistical characteristics
of the plants operating below and above
this value. This cut-off point can be
visualized clearly by examining Figures
2 and 3. Stable plants usually operate
with mean effluent BOD values less
than 17 g/m3 and mean effluent SS
values less than 15 g/m3. Two-thirds of
the time their effluent BOD and SS
concentrations are less than 25 and 20
g/m3, respectively. The daily concen-
tration of effluent BOD and SS in these
plants rarely exceeds 60 g/m3.
Plants with a standard deviation of
greater than 10 g/m3 for both effluent
BOD and SS maybe considered unstable.
Mean effluent BOD and SS values for
these plants are generally greater than
for the plants labeled stable, but some
overlap occurs. Unstable plants have
annual mean BOD and SS valuesas low
as 16 and 10 g/m3, respectively. The
maximum daily BOD and SS concentra-
tions of these plants are usually much
greater than stable plants and exceed
90 and 130 g/m3, respectively.
Examination of the results .of this
analysis also leads to the conclusion
that generally, effluent SS shows more
variation than effluent BOD and is
expected to be a more significant factor
in determining instability. Process
upsets may happen more often due to
high values of SS than to high values of
BOD in the final effluent. To achieve the
same level of stability for both BOD and
SS, a plant should be designed to
produce an average effluent SS less
than effluent BOD.
200
180
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140
120
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Figure 2.
24
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4 8 12 16 20
Standard Deviation (g/m3)
Mean, standard deviation, and range of effluent BOD concentration in
different treatment plants.
The Effect of Plant Size on
Stability
Correlations between annual mean
flow (as an indication of plant size) with
annual mean and standard deviation of
effluent BOD and SS were determined
to examine the significance of plant size
on effluent quality and stability. Correla-
tion coefficients of r = 0.19 and 0.17
were determined between annual mean
flow with annual mean effluent BOD
and SS, respectively; and coefficients of
r = 0.23 and 0.16 were determined with
standard deviations of effluent BOD and
SS, respectively. The conclusion from
these results is that there is poor
correlation between plant size and
effluent quality; that is larger plants do
not necessarily produce better quality
effluent than smaller plants. Generally,
there appears to be no relationship
between plant size and stability.
-------
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Standard Deviation (g/m3)
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Figure 3.
Mean, standard deviation, and range of effluent suspended solids
concentration in different treatment plants.
The Effect of Process Type
on Stability
Activated sludge processes are flexible
systems and have been adopted to a
number of different flow schematics.
Ideally, the most appropriate process
design will reduce the variability of
effluent quality significantly.
To examine that relationship between
process type and stability, activated
sludge treatment plants under study
were grouped by process modification
type and then were compared with each
other. The data set included 18 con-
ventional 13 step-feed and step-aeration,
5 complete-mix, 4 contact-stabilization,
1 extended-aeration, 1 kraus, and 1
aerated lagoon. The average (X) and
standard deviation (Sx) of the annual
means, standard deviations, and co-
efficients of variation of each type of
process were computed. Results of the
analysis are presented in Table 3 and
can be used for comparison of the
various modifications of the activated
sludge process in terms of performance
and stability.
Generally, step-feed or step-aeration
modifications of activated sludge give
the best year-round results for BOD
removal, whereas the conventional
activated sludge gives the best year-
round results for SS removal. In terms of
combined BOD and SS removal, step-
feed and conventional activated sludge
processes give similar year-round
results. The complete-mix modification
of activated sludge has somewhat lower
performance characteristics, and the
contact-stabilization process appears to
have considerably lower performance
characteristics than the other three
systems. The other process types were
not included since data for only one
plant was available in each case.
Examination of the results for each
process leads to the conclusion that
conventional and step-feed processes
generally produce effluent BOD and SS
concentrations below average, and that
the complete-mix and contact-stabili-
zation processes produce effluent BOD
and SS concentrations greater than
average when all plant data are pooled.
Stability Based Design of
Activated Sludge Processes
Analysis of data has resulted in the
conclusion that plants having a standard
deviation of less than 10 g/m3 for both
effluent BOD and SS concentrations
may be statistically considered as stable
plants. The question is, what mean
value of effluent BOD and SS concen-
tration may result in a stable process
while considering variations in effluent
quality? Variations in effluent quality
are described by the coefficient of
variation, Vx. This coefficient may be
estimated for each process type using
the results of Table 3.
To produce a stable effluent quality
(i.e., a process with a standard deviation
of equal to or less than 10 g/m3), the
process should be designed for a mean
value equal to or less than X = Sx/Vx,
where Sx = 10 g/m3. These values for
different process types are shown in
Table 4. To achieve stability, activated
sludge processes should be designed
for an efflulent BOD concentration
equal to or less than 13 to 15 g/m3 and
an effluent SS concentration equal to or
less than 10 to 12 g/m3.
-------
Table 3. Statistics of the Annual Effluent BOD and SS Concentration Data for Different Process Types
Process Type Mean Standard Coef. of
fjn nf Deviation Variation
Plants X Sx X
Sx X S«
BOD
Conventional 18 12.80 6.85 9.54
Complete-mix 5 16.82 6.67 13.24
Step-feed/aeration 13 10.84 7.68 8.28
Contact stabilization 4 38.38 32.08 28.17
Extended aeration 1 14.41 5.31
Kraus 1 24.02 9.85
Aerated lagoon 1 30.35 11.61
All plants 43 15.76 13.43 11.28
SS
Conventional 18 14.92 10.53 16.02
Complete-mix 5 19.88 14.19 19.65
Step-feed/aeration 13 16.23 16.65 16.83
Contact stabilization 4 40.88 26.75 37.66
Extended aeration 1 8.82 5.28
Kraus 1 24.12 9.26
Aerated lagoon 1 58.79 18.71
All Plants 43 19.40 17.03 18.35
Table 4. Recommended Design Values for Effluent BOD and SS Concentrations
in Order to Produce Stable Process
Process BOD< SS<
Type (g/m3) (g/m3)
Step-feed/aeration 14.70 12.05
Conventional 14.50 11.63
Complete-mix 13.00 10.00
Contact stabilization 13.16 11.11
Variability of Activated 1 . Influent variables
Sludge Processes 2 Environmental conditions
Variations in the effluent quality from «f- Biological and operational parameters
activated sludge processes are the 4- Settling characteristics and clarrfier
result of a number of internal and _ Design
external factors. In recent years, a 5. Size of plant and type of process
considerable research effort has been °- J.'me effects
directed toward examining process Human factors
performance variations. Both experi- 8- lnherent Process variability
mental and analytical research studies Distributional characteristics and
have been conducted; however, most of statistical data of these variables were
the experimental studies have been determined for the plants studied.
carried out under laboratory rather than Correlation analysis has been used to
field conditions. Thus the results investigate the extent to which varia-
reported do not necessarily reflect tions in effluent quality are linked to
conditions encountered in full-scale variations in the other variables.
operations. Regression analysis techniques have
. , been used to evaluate the contribution
Nature and Sources of of a specifjc variable or set of variables
Effluent Variability in the effluent BOD and SS variations.
Several factors contribute to the Selected groups of variables were
perturbations observed in effluent studied, both individually and in combi-
quality. The following factors have been nation, to determine the individual
identified as being important. linear effect as well as combined effect
7.99 0.69 0.25
6.51 0.77 0.13
7.56 0.68 0.25
20.92 0.76 0.14
0.37
0.41
0.38
10.49 0.70 0.23
18.61 0.86 0.38
16.92 1.00 0.51
23.89 0.83 0.34
26.18 0.90 0.14
0.60
0.38
0.32
20.60 0.84 0.37
of each group of variables on effluent
fluctuations. Detailed results of statistics
as well as coefficient or correlations and
regression a nalyses of the data are sum-
marized in the main report. Only the
summary results of the coefficient of
determination for each regression study
for some of these plants are given in this
summary report (Tables 5 and 6). The
coefficient of determination, R2 (which
is the square of correlation coefficient)
is used to describe the proportion of
variation in one variable that can be
.explained by the other.
In Tables 5 and 6, the most significant
variables, those that explain at least 5
percent of effluent variations have been
shown in parentheses. Other variables
have less than a 5-percent effect on
effluent variability. In those plants that
have one or more missing variables in
their data reports, regression analysis
cannot be carried out because the
variable group is incomplete; thus
results are shown as blanks in these
tables. The meaning of the coefficient of
determination in Tables 5 and 6 is best
explained by an example.
For instance, in Plant No. 1, only 3
percent of effluent BOD changes can
be explained by input variables (Flow,
BOD,). Neither flow nor influent BOD,
has notable effect on effluent BOD.
Wastewater temperature accounts
for 38 percent of the variation.
-------
Table 5. Regression Analysis Coefficient of Determination, R2, for Effluent BOD and Selected Groups of Variables'
Plant
Number
1
2
3
4
5
6
7
8
16
17
18
19
31
33
34
38
39
40
41
42
43
Input*
0.03
0.03
0.05
0.1 6 (BOD 'J
0.30 (BODJ
0.25 (BODJ
0.1 7 (BODJ
0. 1 1 (BODJ
0.34 (BOD,. Flow)
0.37 (Flow)
0. 12 (Flow)
0.01
0
0. 19 (BODJ
0
0.07
0.1 2 (BODJ
0.14(BODJ
0. 10 (BODJ
0.07 (BODJ
0.03
WTEMP
0.32
0.01
0.14
0.15
0.01
0
0.02
0.30
0.38
O.01
0.12
0
0.07
0.01
0.16
0.02
0.03
0.13
0.07
Bio. & Oper.c
0.09 (On)
0.29 (QnJ
0.25 (MCRT)
0.2 / (Xn)
0.02
0.16(MLSS)
0.05
SVI
0
0.27
0
0.12
0.10
0.11
0.04
0.03
0.11
0.08
0.08
0.04
0
0.05
0.06
0
0.01
0.01
0.01
0
Time
0.22
0.03
0.07
0.13
0.15
0.13
0.02
0.06
0.04
0.40
0
0.29
0
0.08
0.02
0.14
0.01
0.20
0.04
0.08
0.07
All Variables"
0.48 (WTEMP)
0.42 (SVI, MLSS)
0.21 (WTEMP)
0.43 (MCRT, WTEMP, BODJ
0.40 (WTEMP)
0.61 (WTEMP, Time)
0.27 (Flow, Time)
0.40 (Time)
0.32 (BOD,, SVI)
0.32 (WTEMP)
0.34 (BODi, Time)
0.1 3 (BODJ
"Values in parentheses are the most important variable (greater than 5% significance) in explaining the total variation.
'"Input loads: Flow, BOD,.
^Biological and operational variables: MCRT, MLSS, Xn, QR.
"All variables: Flow, BOD,, WTEMP, MCRT. MLSS, SVI, Time.
Symbols: BOD, - influent BOD.
MCRT - mean cell residence time.
MLSS - mixed liquor suspended solids.
XR = return sludge concentration.
QR = return sludge flow.
WTEMP = water temperature.
SVI = sludge volume index.
Qw = wastage flowrate.
Biological and operation parameters
can be used to explain only 9 percent
of effluent BOD fluctuations, where
return flow QR, is the most important
operational variable in this plant.
Other biological or operational pa-
rameters do not contribute to the
dispersion of effluent quality signif-
icantly. In Plant No. 1, SVI measure-
ment does not account for the effluent
BOD variations at all. Time of the year
can be used to explain 22 percent of
changes in effluent quality, which
most probably is due to temperature
deviations. A combination of all
groups of variables can be used to
describe 48 percent of effluent
perturbations; and among all vari-
ables, wastewater temperature is the
most important factor. The remaining
variation (i.e., 52 percent) in this plant
is not explained by the available set of
data. The unexplained variation may
be caused by other variables not
included in the regression list, such
as inherent variability and human
factors. Similar explanations will hold
for all other plants.
Discussion
The contribution of each group of
variables to effluent quality variations
can be derived from Tables 5 and 6 as
discussed below.
Input Variables - Considering all
plants studied, input variables ac-
counted for a maximum of 37 percent of
the effluent BOD fluctuations, and in
most cases, their contribution was less
than 17 percent. In a number of plants,
influent BOD and flow were not the
causes of the fluctuations in effluent
BOD at all. Generally, the effect of
influent BOD was more notable than
flow, and with three exceptions, flow
usually was not the responsible factor
for effluent BOD variations.
The coefficient of determination
between effluent SS and influent
variables was generally low. For Plant
No. 17 the R2 value was 0.29, but all
other R2 values were below 0.18. Flow
was found to be be a more important
factor than influent SS in describing
effluent SS deviations. This result may
be due to flow related effects on clarif ier
performance. In most cases, input
variables were more responsible for
effluent BOD variations than for effluent
SS.
Wastewater Temperature - it
was found that up to 38 percent of the
effluent BOD variation and up to 27
percent of the effluent SS variation was
caused by fluctuations in wastewater
temperature. In many plants, tempera-
ture changes did not have any effect on
effluent quality. The contribution of
wastewater temperature in effluent
variability was not dependent on the
geographical area of the plant.
Biological and Operational
Variables - Biological and operational
variables (MCRT, MLSS, XR, QR, Qw)
generally were not found to be signif-
icant factors in explaining the effluent
quality variations. The total contribution
of these variables to effluent BOD
variations was less than 30 percent and
in some cases, was close to zero. Their
effects on fluctuations in effluent SS
was generally greater than effluent
-------
Table 6. Regression Analysis Coefficient of Determination, R2, for Effluent SS and Selected Groups of Variables*
Plant
Number
1
2
3
4
5
6
7
8
16
17
18
19
31
33
34
38
39
40
41
42
43
Input*
0.05
0
0.01
0.10 (SS,)
0.02
0.01
0.05
0.05 (Flow)
0. 13 (Flow)
0,29 (Flow)
0. 18 (Flow)
0
0.07 (SS,)
0.11
0.03
0.06 (Flow)
0.01
0.12
0.07 (Flow)
0.03
0.05
WTEMP
0.04
0.03
0.26
0.12
0.01
0
0.05
0.01
0.14
0.27
0
0.04
0.02
0.03
0.13
0.05
0.12
0.05
0.05
Bio. & Oper.c
0.11 (QR)
0.1 7 (Qn)
0.36 (MCRT)
0.16(Qd
0.20 (MCRT, Xn)
0.17 (MLSS)
0. 7 7 (Qn, MLSS)
sw
0.01
0.18
0.11
0.14
0.04
0.03
0.03
0.04
0.32
0.04
0.18
0.01
0.02
0
0.03
0.02
0
0.07
0.02
0
Time
0.01
0.03
0.06
0.17
0
0
0
0.03
0.25
0.21
0.17
0
0.03
0
0.05
0.13
0.01
0.16
0.10
0.02
0.05
All Variables"
0.21 (Flow, SS,)
0.22 (SVI, MLSS)
0.41 (WTEMP, SVI)
0.52 (MCRT, SVI)
0.52 (SVI, Time)
0.33 (Flow)
0.44 (WTEMP, Flow)
0.05
0.26 (MCRT, Flow)
0.37 (MLSS, Time, MCRT)
0.36 (Time, Flow)
0.22 (WTEMP. Flow)
^Values in parentheses are the most important variable (greater than 5% significance) in explaining the total variation.
"Input Loads: Flow, SS,.
^Biological and operational variables: MCRT, MLSS, XH, QR.
"All variables: Flow, SS,, WTEMP, MCRT, MLSS, SVI, Time.
Symbols: SS, = influent suspended solids.
MCRT - mean cell residence time.
MLSS - mixed liquor suspended solids.
XR = return sludge concentration.
QR = return sludge flow.
WTEMP = water temperature.
SVI = sludge volume index.
Qw = wastage flowrate.
BOD and was in the range of 11 to 36
percent.
Sludge Settleability - Sludge
volume index (SVI) was generally
reported as a measure of sludge
settleability. Changes in SVI would be
expected to be reflected in effluent
quality variations, and this was true to
some extent. Twenty-seven percent of
the effluent BOD fluctuation was
explained by SVI variation in Plant No. 2,
but the R2 values were less than 0.12 in
all other plants. In a number of plants,
there was no correlation at all between
these two variables. Similar statements
can be made about the correlations
between SVI and effluent SS.
Combination of Variables -
When the effects of all the input,
environmental, and operational variables
were summed, between 13 and 61
percent of the effluent BOD and between
5 and 52 percent of the effluent SS
fluctuations (depending on the plant)
were explained. The remaining variations
were unexplained (i.e., inherent or
human factors as defined here).
From these results, it is clear that the
variables that affect plant performance
vary from plant to plant. Any single
variable or group of them may account
for the fluctuations in effluent quality in
different plants. For example, in Plant
No. 1, wastewater temperature was the
most important variable, whereas in
Plant No. 2, SVI and MLSS contributed
the greatest amount to fluctuations in
effluent BOD. The contribution of the
remaining variables was less than 5
percent.
Examination of the results presented
in Tables Band 6 leads to the conclusion
that there were only a few variables that
contributed significantly to the changes
in effluent quality. Among all variables,
wastewater temperature was the most
notable variable in describing effluent
variations. Other variables found to be
significant (minimum significance of 5
percent) included time of the year, flow,
SVI, influent BOD, MCRT, MLSS, and
influent SS
The overall results of this phase of the
study are insufficient to generalize
about the variability of process per-
formance. Inclusion of additional data,
however, is unlikely to alter this
conclusion, for a large dispersion exists
among the plants that have been
studied. Therefore, analysis of data
must be carried out at each specific
plant to identify the main causes of
variation.
Sources of Effluent Variation
Unexplained by the Available
Data - Many causes of performance
variation exist that cannot be explained
on the basis of analysis of the available
data. Included among these variables
are true inherent variability such as
presence of toxic materials, nature of
biota in the system, human factors
including system design, operation and
maintenance procedures, loading fac-
tors, systems control capability, and
sampling techniques. These causes of
variation were not analyzed because
data were not available. Considering the
results obtained from the analysis of the
available data, it is reasonable to
conclude that little additional informa-
tion would be gained from further study.
10
-------
Process Control
Evaluation of the results presented
here provides insight into the main
sources of variation at a particular plant.
To reduce fluctuations in effluent
quality, for example in Plant No. 2,
sludge settleability must be improved. In
Plant No. 17, flow equalization might be
used to reduce the perturbations
observed in the effluent quality; in Plant
No. 41, improvement of unidentifiable
variables, such as human factors, might
reduce effluent quality variations.
In practical applications, regulation of
wastewater temperature and influent
flow and concentration is difficult;
consequently, improvement of opera-
tional procedures and those parameters
related to the sol ids separating facilities
appear to be the most promising and
practical parameters available for
process control.
Effluent Discharge Standards
The objective of this section is to
examine and discuss the appropriate-
ness of effluent discharge standards as
they are currently established and to
compare the current approach using
arithmetic mean to an alternative
approach using the geometric mean
concentration value (GM) for setting
effluent discharge standards.
Use of the Geometric Mean
As mentioned at the beginning of the
summary, effluent BOD and SS data
have a lognormal distribution. For a set
of data that are lognormally distributed,
the sample arithmetic mean X, cannot
represent the central tendency of the
data. The best measure of central
tendency for the lognormal data is the
geometric mean, which is defined as:
GM = (
(7)
Where: II represents the product of all
sample values, and Xi repre-
sents a sample of independent
observations Xi, Xj, ..., Xn.
Present EPA standards for discharge
effluent BOD and SS are based on
arithmetic 7- and 30-day averages.
These average values do not adequately
represent the central tendency of a
lognormally distributed data set. The
geometric mean of the 7- and 30-day
effluent quality data are a more appro-
priate measure of central tendency than
the arithmetic mean and it is recom-
mended to be used in setting discharge
standards.
Stochastic Based Design
and Standards
In view of the uncertainties in process
design and operation, the performance
of a given process will be uncertain to
some degree. Therefore, design pro-
cedures should be based on a recognition
of the uncertainties.
The best way to accomplish this is to
incorporate probabilistic concepts and
procedures in the design process and in
setting discharge requirements. Use of
probabilistic methods in setting dis-
charge standards precluded the rational
setting of parameter values that can
never be exceeded. For example, setting
maximum allowable values of BOD or
SS for any single sample has no
meaning if a measure of random
variation in these parameters exists.
Current EPA effluent discharge stan-
dards should be restructured based on
stochastic concepts to permit individual
parameter values to exceed the desig-
nated standard value a given number of
times in a specified time period.
Probabilistic procedures can be
formulated in such a manner as to
provide a probabilistic basis for design,
even with a deterministic standard.
Given the natural variability of plant
performance, it should be possible to
determine what true average effluent
quality must be maintained such that a
standard can be met with some high
(and predetermined) probability. In
other words, the requirements should
be rephrased to permit the parameter to
exceed the designated value, say, one
time in 3 years or one in 10 years. The
required plant performance can then be
calculated, using the reliability model
developed in this study. It must be
recognized that standards stated in this
manner reflect actual performance
characteristics and are not less restric-
tive than deterministic standards.
Design examples and operational appli-
cation of the results of this study are
given in the main report.
The full report was submitted in
fulfillment of Grant No. R805097-01 by
the University of California under
sponsorship of the U.S. Environmental
Protection Agency.
Salar Niku is presently with Brown and Caldwell Consulting Engineers,
Pasadena, CA 91109; Edward D. Schroeder, George Tchobanoglous, and
Francisco J, Samaniego are with the University of California, Davis. CA 95616.
Jon,Bender is the EPA Project Officer (see below).
The complete report, entitled "Performance of Activated Sludge Processes:
Reliability, Stability and Variability," (Order No. 82-109 604; Cost: $14,00,
subject to change) will be available only from:
National Technical Information Service
5285 Port Royal Road
Springfield, VA22161
Telephone: 703-487-4650
The EPA Project Officer can be contacted at:
Municipal Environmental Research Laboratory
U.S. Environmental Protection Agency
Cincinnati, OH 45268
11
*U.S. GOVERNMENT PRINTING OFFICE:1981--559-093/3354
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