Determination of BOD Kinetic Parameters

DETERMINATION OF BOD KINETIC PARAMETERS AND
EVALUATION OF ALTERNATE METHODS
A Thesis submitted to
THAPAR INSTITUTE OF ENGINEERING & TECHNOLOGY, PATIALA
in partial fulfillment of the requirements
for the award of degree of
MASTER OF ENGINEERING
in
ENVIRONMENTAL ENGINEERING
by
BALWINDER SINGH
Under the supervision of
Dr. ANITA RAJOR Dr. A. S. REDDY
DEPARTMENT OF BIOTECHNOLOGY & ENVIRONMENTAL SCIENCES
THAPAR INSTITUTE OF ENGINEERING & TECHNOLOGY
(DEEMED UNIVERSITY)
PATIALA – 147 004
June, 2004

CERTIFICATE
This is to certify that the thesis entitled, “ Determination of BOD Kinetic Parameters
And Evaluation of Alternate Methods” submitted by Balwinder Singh in partial
fulfillment of the requirements for the award of Degree of MASTER OF
ENGINEERING in ENVIRONMENTAL ENGINEERING to Thapar Institute of
Engineering & Technology (Deemed University), Patiala, is a record of student’s own
work carried out by him under our supervision and guidance. The report has not been
submitted for the award of any other degree or certificate in this or any other
university or institute.
(Dr. Anita Rajor) (Dr. A. S. Reddy)
Department of Biotech. & Env. Sciences,
Thapar Institute of Engg. & Tech.,
Patiala – 147004
Lecturer (Selection Grade)
Patiala – 147004
(Dr. Sunil Khanna) (Dr. D. S. Bawa)
Professor & Head,
Patiala – 147004
Dean (Academic Affairs),
Patiala – 147004

DECLARATION
I here by declare, that the thesis report entitled, “Determination of BOD Kinetic
Parameters And Evaluation of Alternate Methods” written and submitted by me to
Thapar Institute of Engineering & Technology (Deemed University), Patiala, in
partial fulfillment of the requirements for the degree of MASTER OF
ENGINEERING in ENVIRONMENTAL ENGINEERING. This is my original
work & conclusions drawn are based on the material collected by me.
I further declare that this work has not been submitted to this or any other university
for the award of any other degree, diploma or equivalent course.
BALWINDER SINGH

ACKNOWLEDGEMENT
I wish to express my deep gratitude to Dr. A. S. Reddy, Lecturer (Selection Grade),
Department of Biotech. & Environmental Sciences, Thapar Institute of Engg. &
Technology, Patiala for his invaluable guidance, inspiration, valuable suggestions,
encouragement during the entire period of present study. I will not hesitate to express
sincere thanks to Dr. Anita Rajor for providing the constant encouragement and
making the lab work possible under her able guidance.
I am highly thankful to Dr. Sunil Khanna, Head, Department of Biotech. &
Environmental Science for granting permission for the use of departmental labs.
Lastly, I am thankful to my colleagues, friends and family members for bearing with
me and providing me all moral help during the entire period of my work.
BALWINDER SINGH

CONTENTS
CONTENTS PAGE. NO.
Certificate i
Acknowledgement ii
Declaration iii
List of tables iv
List of Figures v
Chapter: 1 Introduction
1.1 Background information and objectives of the study
1.2 Overview of the contents of the report
1.3 Importance of the study
1 – 5
Chapter: 2 Literature Review 6 – 11
Chapter: 3 Materials and Methods 12 – 33
3.1 Introduction
3.2 Sampling
3.3 Serial BOD testing
3.4 Estimation of BOD kinetic parameters
3.4.1 Method of Moments
3.4.2 Least Squares Methods
3.4.3 Thomas Graphical Method
3.4.5 Iteration Method
3.4.6 Fujimoto Method
3.5 comparison of different methods of estimation

CONTENTS PAGE. NO.
Chapter: 4 Results & Discussion
4.1 Introduction
4.2 Results
4.3 Evaluation of methods
4.4 Discussion
4.5 Conclusion
34 - 61
Chapter: 5 Conclusion 62 - 63
References 64 - 66

LIST OF TABLES
Table Name Page No.
2.1 Typical values of k and L0 of various waters 9
4.1 BOD results of River Satluj sample (SAT-7) 35
4.2 BOD results of East Bein River (EB-4) 35
4.3 BOD results of Treated Municipal Sewage 36
4.4 BOD results of Treated Distillery Effluents 36
4.5 BOD results of Treated Dairy Effluents 37
4.6 BOD results of Treated Textile Effluents 37
4.7 Duration of lag observed in serial BOD test 38
4.8 BOD kinetic parameters values for SAT-7 40
4.9 BOD kinetic parameters values for EB-4 41
4.10 BOD kinetic parameters values for Treated Municipal
Sewage
42
4.11 BOD kinetic parameters values for Treated Distillery
Effluents
43
4.12 BOD kinetic parameters values for Treated Dairy
Effluents
44
4.13 BOD kinetic parameters values for Treated Textile
Effluents
45
4.14 Sum of absolute differences between observed and
expected BOD values
47
4.15 Results discarded from the method evaluation 49
4.16 Suitability of methods for different samples 50

LIST OF FIGURES
Figure No. Name Page No.
1.1 Fate of biodegradable organic matter, during BOD test 2
3.2 Moore’s diagram for n=7 days 18
3.3 Thomas method for SAT-7 (IV) 24
3.4 Daily Difference method for SAT-7 (IV) 27
3.5 Fujimoto method for SAT-7 (IV) 32
4.1 - 4.4 Method comparison for SAT-7 (sample I – IV) 52 – 53
4.5 - 4.8 Method comparison for EB-4 (sample I – IV) 54 – 55
4.9 - 4.11 Method comparison for Sewage (sample I – III) 56 – 57
4.12 - 4.14 Method comparison for Distillery Effluent (sample I –
III)
57 – 58
4.15 - 4.17 Method comparison for Dairy Effluent (sample I – III) 59 – 60
4.18 - 4.20 Method comparison for Textile Effluent (sample I – III) 60 - 61

CHAPTER: 1
Introduction
1.1 Background information and objectives of the study:
Biodegradable organic matter is one of the important pollution parameter for water
and wastewater. Being heterogeneous (suspended colloidal and dissolved forms) and
being composed of a wide variety of compounds, it is very difficult to have a single
direct method for estimating its organic matter concentration in any water or
wastewater sample. Because of this reason, indirect methods, like BOD, COD, etc.
are dependent upon for the measurement of organic matter concentration. These
methods measure the organic matter concentration through estimating the amount of
oxygen required for its complete oxidation.
Methods like COD are quite accurate and take very less time for estimating the
organic matter concentration. But they cannot differentiate biodegradable organic
matter from non-biodegradable organic matter. Further, COD is not capable of
accurately estimating volatile organic matter and organic matter with nitrogen bases.
Because of these reasons, BOD is preferred over COD.
In the BOD test microorganisms are used for bio-oxidation of the organic matter in
the presence of oxygen. The amount of oxygen utilized in the bio-oxidation process is
measured and expressed as organic matter concentration in terms of oxygen. This
method actually estimates the amount of biodegradable organic matter rather than the
total organic matter present in water or wastewater sample. In this method, the sample
is diluted to appropriate level, seeded with sufficiently acclimatized microbial
populations, aerated and then filled in the air proof BOD bottles and incubated under
favaourable conditions. Through measuring the initial and final dissolved oxygen
present in the incubated sample, the amount of oxygen consumed in the bio-oxidation
process is estimated. Fig.1.1 shows the fate of biodegradable organic matter during
the incubation in the BOD test.

Microorganism
Biodegradable
Organic Matter
CO2 + H2O + Metabolic energy
Fig. (1.1): Fate of the biodegradable organic matter, during incubation in the BOD
test.
Organic Matter
Non-Biodegradable
Organic Matter
Synthesized
microbial biomass
Residual biomass
CO2+H2O+NH3+Metabolic
energy
NO3
O2
Microorganisms
O2
Auto oxidation by
microorganisms
O2
Bio-oxidation
Biosynthesis

The bio-oxidation process is rather slow and complete bio-oxidation takes a quite
long time (over 25 days). This necessitates incubation of the sample for quite long
time for getting the total biodegradable organic matter concentration. In practice,
incubating the sample, for such a long time, is not feasible and even if feasible, since
the results cannot be real time measurements; their utility is very limited. To avoid
this long incubation period a compromising approach is followed. In this approach
the sample is incubated for relatively short period of 5 days for getting major portion
of the organic matter bio-oxidized. The obtained results are extrapolated through
using a mathematical model [BOD kinetics model, y = L0 (1-e-kt)]. Use of this BOD
kinetics model requires prior knowledge of the BOD kinetic parameters (k & L0). The
required kinetic parameters for the water or wastewater in question are obtained
through laboratory experimentation (through conducting serial BOD test, wherein the
BOD exerted of the incubated sample is measured at regular intervals). Results of the
serial BOD test are used in estimating kinetics parameters with the help of one of the
multitude methods available.
Accuracy and reproducibility of BOD testing is not very satisfactory. Hence
estimation of the kinetic parameters which uses serial BOD test results is prone to
become much more inaccurate. For getting satisfactory results selection of
appropriate method of calculation of kinetic parameters is very important. Present
study is actually concerned with evaluation of the commonly used alternative
methods of kinetic parameters estimation. In the present study the following six
methods have actually been evaluated:
1. Method of Moments
2. Method of Least Squares
3. Thomas Graphical Method
4. Daily Difference Method
5. Iteration Method

6. Fujimoto Method
For evaluating these methods, results are obtained from serial BOD testing for 7 days,
of the following samples have been used:
1. Satluj river water sample
2. East Bein river water sample
3. Treated Municipal sewage sample
4. Treated Distillery effluent
5. Treated Dairy effluent
6. Treated Textile effluent
1.2 Overview of the contents of the report:
This M.E. dissertation includes five chapters. Chapter 1 is introduction. In this
chapter after giving brief background information on BOD and BOD kinetics,
objective of the study is introduced. This chapter also includes overview of the
contents of the thesis and importance of the present study.
In Chapter 2, review of published literature on BOD, BOD kinetics and methods for
BOD kinetic parameters estimation is presented.
In the Chapter 3, the approach followed for achieving the objective of the study is
presented. In addition to this, this chapter also includes a brief overview on the
commonly used methods of BOD kinetic parameters estimation.
Chapter 4 includes the results of the study and discussion. The results mainly include
three components, the serial BOD test results, the estimated BOD kinetic parameters,
and results of evaluation of the alternate methods of kinetic parameters estimation. In
the discussion, it has been shown, which of the method is most appropriate and why.

The report concludes with Chapter 5, wherein the study is summarized, limitations of
the study are highlighted and scope for further study is brought forward.
1.3 Importance of the study:
Design, operation and control of biological treatment units require knowledge of
ultimate BOD whereas the BOD test gives 5 days BOD value or 3 days BOD value.
BOD tests are usually conducted at 20ºC, whereas temperature in the biological
treatment units can be different. These situations make BOD kinetics and BOD
kinetic parameters estimation very important. Very few laboratories actually perform
BOD kinetic parameters studies and ultimate BOD is found through thumb rules,
which is undesirable. In the light of these, the present study proves very important.
The study brings about the fact that all methods of kinetic parameters estimation
cannot be appropriate for all conditions. One has to sensibly select appropriate
methods for estimating the kinetic parameters.

CHAPTER: 2
Literature Review
An attempt has been made to review the available literature on BOD, BOD kinetics
and available methods for kinetic parameters estimation. In the nineteenth century the
performance of sewage treatment plants was measured mainly by the chemical
analysis related to the determination of various forms of nitrogen; as an index of the
state and progress of the oxidation of organic matter. Frankland, 1868 as referred by
William (1971) first observed that depletion of dissolved oxygen in the wastewater
containing organic matter was due to chemical reactions. He observed that depletion
of oxygen was dependent on the time of storage. Dupret 1884 as referred by William
(1971) recognized that oxygen depletions were due to the activity of microorganisms.
The classical equation for expressing the BOD process is:
Substrate + bacteria + O2 + growth factors 22 . H2O + increased
bacteria + energy -------------------------------------------------------------(2.1)
The royal commission on Sewage Disposal, 1912, chose an incubation period of five
days for the BOD test because that is the longest flow time of any British river to the
open sea. An incubation temperature of 20oC was chosen because the long-term
average summer temperature in Britain was 18.3oC (Nesarathnam,1998).
Adeney 1928 as referred by Jenkins (1960) defined the absolute strength of sewage as
the amount of dissolved oxygen required for its complete biochemical oxidation.
Winkler’s method was mostly used to determine the dissolved oxygen content in
water (Standard Method 1995). Bruce et.al, (1993) suggested headspace biochemical
oxygen demand (HBOD) test having three main advantages: the test does not require
sample dilution, oxygen demand determined with in a shorter period of time (24-
36hrs) that can be used predict 5-day BOD value and the experimental conditions
used in the HBOD test, more accurately reproduce the hydrodynamic and culture

conditions. Booki et.al, (2004) suggested the use of fibre optic probe to obtain oxygen
demands in 2 or 3 days in respirometric tests, and then 5-day BOD can be predicted
from the results.
While a standard BOD test procedure developed for certain effluents has been widely
accepted, disagreements regarding the basic mechanisms and kinetics of the test
continue to persist. In fact, a review of the history of the BOD test and the related
mathematical procedures leads to the conclusion that the only universally accepted
concept is that the basic reactions involved are biochemical in nature. The
controversies about BOD kinetics arises largely due to the fact that the distinction
between BOD as a test and BOD as a microbial metabolic process is frequently
overlooked. (The term process is used to refer to the series of cellular enzymatic
reactions, which bring about the conversion of given reactants to final products under
the constraints of the prevalent environmental constraints and factors)(William
E.1971).
Phelps (1953) has presented the developmental history of BOD test and its kinetics.
He after studying the simplified reaction system associated with eq. 2.1 suggested that
the velocity of the reaction varied directly as the concentration of the bacterial food
supply (substrate). The concentration of the substrate was rated in terms of oxygen
equivalents as indicated by the test. Nonetheless, Phelps realized the limitations of his
empirical monomolecular law and delineated them quite clearly. In essence, he
concluded that though there was no actual reason why BOD reaction should be
monomolecular, the approximation was sufficient for practical applications. He also
noted that there were instances where the approach was not applicable. Despite its
stochastic nature, the first order approach has been applicable under some
circumstances, and it is apparently an acceptable approximation of a more general
deterministic expression or expressions.
The BOD test is designed to determine the quantity of oxygen required by the biota of
the system to completely oxidize the biologically available organic material William,
(1971). The quantity of oxygen required is the sum of oxygen consumed by:

1. The bacteria of the ecosystem with in the confines of the BOD bottle as they
utilize the organic material (substrate) to support synthesis and respiration.
2. The consumers (protozoa) as they ingest the bacteria as a food source to support
their growth and respiration.
3. The process of auto destruction of bacterial and protozoan biomass produced as a
result of the preceding two processes.
During the initial phase of the BOD process, substrate is assimilated by bacteria under
aerobic conditions and a major portion of the substrate is converted to biomass. When
bacterial production has reached a maximum, i.e. when the substrate concentration
has been reduced to essentially zero concentration, the bacteria will either enter the
auto destruction phase, or if protozoa are present, they will start utilizing the bacteria
as a food source. When essentially all the bacteria have been so consumed the
protozoa will enter an auto destruction phase. Conceptually then, the BOD test is
terminated when the concentration of bacteria and protozoa have returned to their
respective concentration which prevailed at the start of the test.
Gaudy (1972), Le Blanc (1974), Stones (1981) and Shrivastava (1982) have also
reviewed the BOD test. Studies of streeter and Phelps, 1925 as referred by Gaudy
(1972) led to the following first order equation (BOD kinetic model).
dL/dt = - kL
In integrated form
Lt = L0 e-kt
In other form BODt = L0(1 – e-kt) -------------------------------------------(2.2)
Where,
BODt = BOD exerted in ‘t’ days of incubation.
Lt = BOD exerted at any time ‘t’

L0 = Oxygen demand yet to be exerted at t=0 i.e. ultimate
BOD.
k = BOD reaction rate constant and its units are time-1.
t = Time of incubation.
Analysis of the above first order equation indicates two variables, rate constant k and
ultimate BOD, L0 are dependent on each other. If the rate of biochemical oxidation is
very high, the value BOD5 is essentially equal to the ultimate BOD. (Ramallho,
1983). Maity and Ganguly (2002) observed that experimental ‘k’ value is always
greater than the theoretical ‘k’ value by 18% and 24%, when the sample is tested at
20oC and at 27oC respectively. Shrivastava (2000) studied the effect of sewage and
indigenous seed on BOD exertion and found that with indigenous seed the BOD
values are observed more and kinetic study revealed that with indigenous seed the
ultimate BOD is more and value of rate constant is higher in both first order and
second order equations with sewage seed. Typical values of k and L0 are listed in
table 2.1 (Peavy, 1985)
Table: 2.1 Typical values of k L0 for various waters.
Water Type K (Day-1) L0 (mg/l)
Tap water 0.1 0 – 1
Surface water 0.1 – 0.23 1 – 30
Weak municipal waste water 0.35 150
Strong municipal waste water 0.40 250
Treated effluent 0.12 – 0.23 10 – 30

Reddy reported that kinetics of BOD exertion pattern involves the following:
(i) Mathematical modeling of the oxygen demand pattern of the sample being
incubated
(ii) Using such a mathematical model for extrapolating the results obtain and
finding out the rate constant and ultimate BOD.
There are different methods of estimation of kinetic parameters k L0. Before an
estimate of k L0 can be made a set of progressive long-term (10 to 15 days) BOD
data must be obtained (Merske et.al, 1972). The work of Berthouex et.al, (1971)
showed that the estimation of BOD constants is most accurate when longer BOD test
data, with the addition of nitrification inhibitors, are considered. To calculate k L0
from given series of BOD measurements is fundamentally a curve-fitting problem.
Reed et.al, (1931) published a paper on the statistical treatment of velocity data, that
is recognized as the most comprehensive and accurate approach to the estimation of
the velocity constants of the first order model for the BOD kinetics. However as this
method requires laborious calculations and therefore one is discouraged from
estimating k L0 (Merske et.al, 1972).
Fair (1936) proposed the log-difference method for the solution of the BOD equation,
but was difficult to be solved. The method involved the plotting of daily difference
between the BOD values versus time. Thomas (1937) developed the slope method
(graphical) and for many years this was the most used method for computing the
kinetics parameters. Thomas (1950) proposed a simple graphical approximation for
evaluation of the constants of BOD curve, which is based on similarity function.
Moor et.al, (1950) developed the method of moments, which became the most used
technique of solving BOD kinetics parameters. The method involves constructing of
Moore’ s diagram of åBOD/L0 versus k and åBOD/åBOD.t versus k for the
particular number of days for which the BOD data is available. Remo Navone (1960)
published a new method for calculating BOD constant for sewage. This method
simplified the calculation of these parameters. The least squares method involves

fitting a curve through a set of data points, so that sum of the squares of the difference
between the observed value and the value of the fitted curve must be minimum
(Metcalf Eddy, 2003). Fujimoto (1961), suggested an arithmetic plot between
BODt+1 versus BODt, and the intersection of this plot with line of slope 1 corresponds
to the ultimate BOD(L0).
Gurjar (1994) suggested a new simple method to determine first stage BOD constants
(k L0). Guillermo Cutrera et.al, (1999), compared the three methods (non linear
fitting, linear fitting Thomas method) for estimation of k L0 and found that non-linear
method of least squares results in smallest error.
Rai (2000) suggested a simplified method for determination of BOD constants. He
suggested the iteration method for estimation of k L0. Riefler and Smets. (2003)
compared the type curve method with least square error method to estimate biofilm
kinetic parameters observed that more accurate and precise estimates were
obtained with least square error method.

CHAPTER: 3
Materials And Methods
3.1 Introduction
In the study, serial BOD testing for BOD kinetics was conducted on six different
types of samples (treated municipal sewage, treated distillery effluent, treated textile
effluent, treated dairy effluent, water sample collected from river Satluj near village
Sangowal and water sample collected from river East Bein, a tributary to river satluj,
at Malsian village). The experiments were conducted in triplicate. Samples of the
river Satluj and the river East Bein were analyzed for BOD kinetics, during June to
Sept. 2003, and the samples from other four sources were studied during Oct. to Dec.
2003. Results of the serial BOD tests were used in evaluating different methods used
for estimating the BOD kinetics parameters (k and L0). Evaluation of the methods
was done through calculating and comparing the sum of the absolute differences
between the observed BOD and exerted BOD.
3.2 Sampling
Grab samples were collected from each of the six sources, once a month for three
months. In case of river water samples the sampling was done for four months. The
collected samples were brought to the laboratory in an insulated box. For avoiding
deterioration of the samples during transportation, the box containing the sample was
filled with ice cubes. In the laboratory the samples were retained in a refrigerator and
used in the BOD kinetics experimentation within 2 days time from the day of
collection.

3.2 serial BOD testing
For estimating the BOD kinetics parameters, k and Lo, serial BOD measurements for
the first 7 days were made for the prepared samples incubated at 20C. That is, BOD1,
BOD2, ---and BOD7 were measured for the sample in question. BOD bottle method
described in Standard Method, 1995 Method No. 5210B, was used for these
measurements.
24 BOD bottles were used in the experiment for facilitating daily DO measurement in
triplicate, as a part of the BOD test. Dilution factor approximating to COD/6 was used
for diluting the sample. Aerated distilled water containing 1 ml per liter each of ferric
chloride solution, magnesium sulphate solution, phosphate buffer solution and
calcium chloride solution was used as dilution water. These solutions and the
solutions used in COD measurements and DO measurements were prepared as per the
procedure and strengths indicated in the Standard Method, 1995 under the
corresponding methods. In case of industrial effluents 1 ml per liter of acclimatized
seed was also added to this dilution water. Supernatant of settled secondary sludge
from the ETP of the same industry was used as acclimatized seed.
The sample in question was first tested for COD using the method given in Standard
Method, 1995 Method No. 5220-C. On the basis of the COD dilution factor was
found out and used in the preparation of the diluted sample for serial BOD test. 12
liter of diluted sample was prepared and after sufficient aeration the sample was
transfered into the 24 BOD bottles. While analyzing 3 of the bottles for initial DO,
rest of the bottles were incubated in a BOD incubator at 20oC for 7 days. Every day 3
of the incubated bottles were taken out and tested for DO while using the technique
given in Standard Method, 1995 Method No. 4500-O.C. BOD of the sample was
estimated by using the following expressions:
BODt at 20oC = DF [(DOis-DOfs)-(DOib-Dofb)(1-1/DF)]-----------------(3.1)

Where,
BODt = BOD exerted in ‘t’ days of incubation.
DOis = DO of the diluted sample immediately after preparation,
mg/l.
DOfs = DO of the diluted sample at particular day of
incubation, mg/l.
DOib = DO of seed control before incubation, mg/l.
DOfb = DO of seed control after incubation, mg/l.
DF = Dilution factor.
3.4 Estimation of BOD kinetic Parameters: Using the results obtained from serial
BOD test, BOD and time were plotted and through extending the smooth curve
passing through the data points to the x-axis time lag involved in the test was
estimated (fig. 3.1). On the basis of the lag obtained the first order BOD kinetic
equation was corrected as below:
BODt = L0 (1-e-k . (t-lag time))
The corrected kinetics equation was used in all the calculations, except in case of
method of moments, the original BOD kinetic equation and nomograph for n = 7days
was used. Using the results obtained from the serial BOD tests, BOD kinetics
parameters (k and L0) were estimated by the following six different methods, which
are commonly used:
(i) Method of Moments (Ramallho, 1983)
(ii) Least Squares Method (Metcalf Eddy, 2003)
(iii) Thomas Graphical Method (McGhee, 1991)

(iv) Daily Difference Method (Ramallho, 1983)
(v) Iteration Method (Rai, R.K., 2000)
(vi) Fujimoto Method (Metcalf Eddy, 2003)

4000
3500
3000
2500
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8
Time(days)
Fig. 3.1: Lag of 0.9 day in Textile sample-III
BOD(mg/l)

3.4.1 Method of moments (Ramallho, 1983): This method involves use of Moore’ s
diagram which is actually a nomograph showing relationship between k , åBOD/L0
and åBOD/åBOD.t. From the series of BOD measurements for 7-days,
åBOD/åBOD.t was calculated and ‘k’ value and å BOD/L0 value corresponding to
this åBOD/åBOD.t value were read from the Moore’ s diagram specific to 7-days.
From the åBOD/L0 value obtained, L0 was calculated.
Moore’ s diagrams (fig. 3.2) are constructed through the following equations:
åBOD/L0 = n – [10-k(10-nk – 1)/(10-k-1)] ------------------------------------------(3.2)
åBOD/åBOD.t =
- - -
å å 10
[10 (10 1) /(10 1)]
ik
k nk k
i - n
i i
n
-
- - -
´
=
-
i - n
=
i 1
i 1
-----------------------------(3.3)
Where,
BODt = BOD exerted in time ‘t’ days of incubation.
n = No. of days of incubation for the serial BOD test.
k = BOD rate constant
L0 = Ultimate BOD.
The above expressions have been used for calculating åBOD/L0 and åBOD/åBOD.t
values for n = 7 days. These calculated values have been used for constructing the
required Moore’ s diagram.

0.258
0.238
0.218
Fig. 3.2 : Moore’s diagram for n=7 days
8
7
6
5
4
3
2
1
0
0 0.4 0.8 1.2 1.6 2
k(day-1)
BOD/L0
0.198
BOD/BOD.t
BOD/Lo
BOD/BOD.t

Sample calculation: The kinetic parameters k and L0 of the River Satluj’ s fourth
sample [SAT-7 (IV)] were calculated as given below.
Step:1
Determination of åBOD and åBOD/åBOD.t values:
Dilution factor: 1:2 Incubation period:7days Incubation temperature:20oC
Incubation time
(days)
DO (mg/l) BODt (mg/l) BOD . t
0 8.2 --- ---
1 7.4 1.6 1.6
2 6.7 3.0 6.0
3 6.27 3.86 11.58
4 5.83 4.74 18.96
5 5.63 5.14 25.7
6 4.77 6.86 41.16
7 4.33 7.74 54.18
åBOD=32.94 åBOD.t=159.18
åBOD/åBOD.t = 0.207
Step:2
Reading k value and åBOD/L0 value corresponding to the åBOD/åBOD.t value
from the Nomograph.
k = 0.05/day
åBOD/L0 = 2.465

Step 3:
Estimation of L0 value
L0 = åBOD/(åBOD/L0) = 2.465/32.94 = 13.36 mg/l
3.4.2 Least Squares Method (Metcalf Eddy 2003): According to first order kinetics
dL/dt = - kLt
where,
Lt = L0 - yt
yt = BODt
dy/dt = k (L0 – yt)
dy/dt = kL0 – kyt
This is a linear equation. Through use of least squares method k L0 values in the
above linear equation can be found out. In the calculations the following equation are
used:-
Sxx = n åyt
2 – (å y)2 -----------------------------------------------(3.4)
Sxy = nåyt(dy/dt) – (åyt) (ådy/dt) ---------------------------------(3.5)
Slope (-k) = Sxy / Sxx ---------------------------------------------------------(3.6)
Intercept (kL0) =å (dy/dt)/n + kå(yt)/n -----------------------------------------------(3.7)
L0 = Intercept/(-slope) ----------------------------------------------(3.8)
Sample calculation:
The kinetic parameters k L0 of the river Satluj’ s fourth sample [SAT-7(IV)] were
estimated as follows:

Step 1:
Constructing the following table:
Time yt dy/dt = (yt+1 – yt-1)/2¨W yt
2 yt.dy/dt
1 1.60 1.50 2.56 2.40
2 3.00 1.13 9.00 27.0
3 3.86 0.87 14.90 3.34
4 4.74 0.63 22.47 4.88
5 5.14 1.07 26.42 5.50
6 6.86 1.30 47.06 8.92
7 7.74*
Sums 25.20 6.50 122.42 26.55
* Value not included in total and n = 6 is used.
Step 2:
Substituted the value computed in Step 1 in eq. (3.4) and (3.5).
Sxx = 99.48
Sxy = - 4.5
Step 3:
Calculated k and L0 by using eq. (3.6), (3.7) and (3.8).
k = 0.045/day
L0 = 28.17 mg/l

3.4.3 Thomas Graphical Method (McGhee 1991): This is an approximate method.
It is based on the following equation:
(t/y)1/3 = 1/(2.3 kL0)1/3 + [(2.3 k)2/3/6 L0
1/3] . t --------------------------(3.9)
Plot of (t/y)1/3 versus t gives slope as (2.3 k)2/3/6 L0
1/3 and intercept as 1/(2.3 kL0)1/3.
The kinetics parameters are calculated as follows:
k = 2.61(slope/intercept) - -------------------------------------------------- (3.10)
L0 = 1/(2.3 k. intercept3) ----------------------------------------------------- (3.11)
Sample calculation:
The kinetic parameters k L0 of the river Satluj’ s fourth sample [SAT-7 (IV)] were
Step 1:
Time (t) BODt (y) (t/y)1/3
0 0.00 ---
1 1.60 0.855
2 3.0 0.873
3 3.86 0.919
4 4.74 0.945
5 5.14 0.991
6 6.86 0.956
7 7.74 0.967

Step 2:
Plotted (t/y)1/3 versus ‘t’ (fig. 3.3) and found slope and intercept as given below:
Slope = 0.0205
Intercept = 0.8474
Step 3: From equation (3.10) and (3.11), obtained k and L0:
k = 0.063/day
L0 = 11.34 mg/l

y = 0.0205x + 0.8474
Fig. 3.3: Thomas’ Method for SAT-7(IV)
1
0.98
0.96
0.94
0.92
0.9
0.88
0.86
0.84
0.82
0.8
0 1 2 3 4 5 6 7 8
Days
(t/y)1/3

3.4.4 Daily Difference Method (Ramallho,1983):
According to first order equation:
y = L0 (1- 10-kt)
dy/dt = L0 (-10-kt )(ln10)(-k)
log(dy/dt) = log(2.303 kL0) – kt -----------------------------(3.12)
Plotting log (dy/dt) versus time (midinterval value of ‘t’ ) gives slope as –k and
intercept as log(2.303 kL0). Ultimate BOD (L0) can then be obtained by the following
equation:
L0 = 10(intercept) / 2.303 (k). -----------------------------(3.13)
Sample calculation:
Step 1:
Time (t) y (mg/l) dy/dt log dy/dt Midinterval value
of t
0 0 --- --- ---
1 1.60 1.60 0.204 0.50
2 3.00 1.40 0.146 1.50
3 3.86 0.86 - 0.066 2.50
4 4.74 0.88 - 1.056 3.50
5 5.14 0.40 - 0.398 4.50
6 6.86 1.72 0.236 5.50
7 7.74 0.88 - 1.056 6.50

Step 2:
Plotted Log (dy/dt) versus midinterval of time as shown in fig. (3.4) and obtained
slope and interval as follows:
Slope = - 0.033
Intercept = 0.1182
Step 3:
Calculated k and L0:
k = - slope = 0.033
L0 = 10(intercept)/ 2.303 (k) = 17.12 mg/l

y = -0.0333x + 0.1182
Fig. 3.4: Daily difference method for Sat-7(IV)
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5
0 1 2 3 4 5 6 7
Time (Days)
log (dy/dt)

3.4.5 Iteration Method: R.K. Rai (2000) suggested an iteration method for the
analysis of time series of BOD data and found the results very close to that of least
squares method.
Procedure:
(i) Assumed the ultimate BOD (L0) equal to the last BOD value.
(ii) Calculated k from first order equation
y = L0(1 – e-kt) -----------------------------------------------------(3.14)
Using L0 as in step (i) and using first BOD data (y and t).
(iii) Calculated L0 from equation using k from step (ii).
(iv) Calculate k from equation using L0 from step (iii).
Repeated the calculation of k using just calculated value of L0 and the given
BOD data from start and L0 using just calculated value of k and the given
BOD data from last till all the given data are used up. The values of k L0
obtained in the last step are their correct values.
Sample calculation:
Step 1:
Assumed L0 = 7.73 mg/l
Step 2:
Substituted L0 = 7.73 mg/l, y = 1.6 mg/l and t = 1 day in equation 3.13
obtained k = 0.232/day

Step 3:
Substituted k = 0. 232/day, y = 7.73 mg/l and t = 7 in equation 3.13
obtained L0 = 9.628 mg/l
Step 4:
Substituted L0 = 9.628 mg/l, y = 3.0 mg/l and t = 2 days in equation 3.13
Step 5:
Substituted k =0.187/day, y = 6.87 mg/l and t = 6 days in equation 3.13
obtained L0 = 10.19 mg/l
Step 6:
Substituted L0 = 10.19 mg/l, y = 3.87 mg/l and t = 3 days in equation 3.13
obtained k = 0.159/day.
Step 7:
Substituted k = 0.159/day, y = 5.13 and t = days in equation 3.13
obtained L0 = 9.35mg/l
Step 8:
Substituted L0 = 9.35mg/l, y = 4.73mg/l and t = 4 days in equation 3.13

Step 9:
The values of BOD constants are, therefore
L0 = 9.35mg/l and k = 0.176/day
3.4.6 Fujimoto method (Metcalf Eddy 2003): Using this method an arithmetic plot
was prepared of BODt+1 versus BODt. The value at the intersection of the plot with a
line of slope 1 corresponds to the ultimate BOD. The rate constant k was determined
from the following equation:
BODt = L0 (1-e-kt)--------------------------------------------- (3.15)
Where,
BODt = BOD exerted in time ‘t’ days of incubation.
L0 = Ultimate BOD
t = time (days)
Sample calculation:
Step 1:
Prepared and arithmetic plot of BODt+1 versus BODt (fig. 3.5) using the following
table:
Sr.No. 1 2 3 4 5 6
BODt
(mg/l)
1.60 3.00 3.86 4.74 5.14 6.86
BODt+1
(mg/l)
3.00 3.86 4.74 5.14 6.86 7.74

Step 2:
Drew a line with slope of 1 on the same plot as constructed in step 1. The value at the
intersection of the two lines corresponds to ultimate BOD, L0 = 27 mg/l.
Step 3:
Determined the k value for 5th day data using equation 3.14.
BOD5 = 5.14 = 27 (1-e-5k)
k = 0.042/day

Fig. 5: Fujimoto Method For SAT7-IV
50
45
40
35
30
25
20
15
10
5
0
0 5 10 15 20 25 30 35 40 45 50
BODt
BODt+1

3.5 Comparison of different methods of estimation: The methods are compared by
plotting observed BOD values and expected BOD values during 7 days for six
different methods against time. Evaluation of different methods was done by
calculating the sum of absolute differences between the observed and expected BOD
values as follows:
D = ™ (oi – ei) /ei
Where, oi and ei are the observed BOD and expected BOD values calculated by using
estimated kinetic parameters by each method.

CHAPTER: 4
Results and Discussion
4.1 Introduction
This chapter includes, the results obtained from the serial BOD tests, the BOD kinetic
parameters estimation by different methods and the evaluation of different methods of
BOD kinetic parameters estimation through sum of the absolute differences between
the observed and expected BOD values during 7 days. Further, the results obtained
are discussed to indicate how far the BOD kinetic parameters estimation methods are
reliable and which of the methods has proved most appropriate in the present study.
4.2 Results
Results obtained from the serial BOD tests for 7 days of incubation and from the
COD tests on the following six different types of samples are presented in the tables
4.1 to 4.6.
1) Satluj river water sample
2) East Bein river water sample
3) Treated Municipal sewage sample
4) Treated Distillery effluent
5) Treated Dairy effluent
6) Treated Textile effluent

Table: 4.1 BOD results of River Satluj (SAT-7).
Days BODt(mg/l)
Sample I Sample II Sample III Sample IV
1 1.02 0.20 0.77 1.60
2 2.70 0.74 1.80 3.00
3 3.80 2.54 2.43 3.86
4 4.00 2.94 2.83 4.74
5 4.42 3.54 3.48 5.14
6 4.80 4.20 3.70 6.86
7 6.56 4.60 4.17 7.74
COD
(mg/l)
16.00 21.00 9.00 25.00
Table: 4.2 BOD results of East Bein river (EB-4).
Days BODt(mg/l)
1 6.60 2.60 5.50 10.00
2 15.20 13.30 23.25 21.50
3 28.20 23.60 31.75 51.50
4 35.00 28.60 38.25 61.50
5 44.60 33.30 49.25 71.50
6 49.33 37.00 57.50 88.50
7 62.00 39.30 62.50 95.00
COD
(mg/l)
176.00 115.00 350.00 727.00

Table: 4.3 BOD results of treated municipal sewage.
Days BODt(mg/l)
Sample-1 Sample-2 Sample-3
1 16.38 73.60 27.30
2 23.73 117.00 55.90
3 27.30 155.60 83.20
4 30.45 162.60 106.60
5 35.70 175.00 140.40
6 36.75 183.00 154.70
7 37.80 188.00 183.30
COD
(mg/l)
125.00 160.00 180.00
Table: 4.4 BOD results of treated Distillery effluent.
Days BODt (mg/l)
1 1400 812.50 3500
2 2130 1125.00 6400
3 2570 1687.50 8700
4 3200 1875.00 10400
5 3600 1937.50 12400
6 4250 2000.00 13900
7 4650 2062.00 14900
COD
(mg/l)
5000 10000 13760

Table: 4.5 BOD results of treated Dairy effluent.
Days BODt (mg/l)
1 45.50 13.39 10.20
2 70.00 28.60 16.80
3 96.25 44.20 22.20
4 127.00 57.20 28.20
5 143.50 70.85 36.60
6 164.50 79.69 37.50
7 178.50 82.00 38.20
COD
(mg/l)
200.00 100.00 80.00
Table: 4.6 BOD results of treated Textile effluent.
Days BODt (mg/l)
1 12.00 777.51 135
2 18.00 1282.81 2040
3 24.00 1527.31 2535
4 30.00 1625.11 2925
5 30.00 1646.30 3255
6 36.00 1680.53 3510
7 38.40 1693.57 3795
COD
(mg/l)
720.00 1300.00 2000.00

The results obtained, from serial BOD tests were checked for involvement of any lag
phase and wherever there is a lag phase its duration was measured. Duration of lag,
obtained in serial BOD tests is given in table 4.7.
Table: 4.7 Duration of lag observed in serial BOD test.
Lag Values (day)
Samples Sample I Sample II Sample III Sample IV
River Satluj
0.5 0.85 0.35 Nil
(SAT-7)
East Bein
River (EB-4)
Nil 0.80 0.75 Nil
Treated
Municipal
Sewage
Nil Nil Nil ----
Treated
Distillery
Effluent
Nil Nil Nil ----
Treated Dairy
Effluent
Nil 0.20 Nil ----
Treated Textile
Effluent
Nil Nil 0.9 ----

BOD kinetics parameters (k and L0) calculated from the serial BOD test results using
the following six different methods of BOD kinetic parameters estimation, for each of
the samples on which serial BOD tests were conducted, are presented in the tables 4.8
to 4.13:
1) Method of moments
2) Least squares method
3) Thomas method
4) Daily difference method
5) Iteration method
6) Fujimoto method
COD values and BOD5 /COD values at 20oC are included in these tables.

Table: 4.8 BOD Kinetic Parameters Values for the Satluj River water (SAT-7)
* ‘k’ values are to base 10.
Kinetic Parameters Values
Methods
K L0 K L0 K L0 K L0
Moments* 0.067 9.27 0.00002 14430 0.067 6.51 0.05 13.36
Least squares 0.221 7.36 0.037 21.83 0.195 5.54 0.045 28.17
Thomas* 0.146 6.39 0.049 9.44 0.421 2.45 0.063 11.34
Daily Difference* 0.051 9.4 0.027 18.46 0.082 5.38 0.033 17.12
Iteration 0.414 5.25 0.160 7.42 0.248 4.75 0.176 9.35
Fujimoto 0.172 8.2 0.170 7.00 0.256 5.00 0.042 27.0
COD (mg/l) 16.0 21.0 9.0 25.0
BOD5/COD 0.276 0.169 0.395 0.206

Table: 4.9 BOD kinetic parameters values for the East Bein River water (EB-4):
BOD Kinetic Parameters Values for the East Bein River water
Methods
K L0 K L0 K L0 K L0
Moments* 0.0001 38000 0.018 91.88 0.018 266 0.000 25372
Least squares 0.023 405.48 0.147 64.87 0.095 135.75 0.047 358.14
Thomas* 0.031 100.40 0.119 49.35 0.127 71.51 0.042 113.9
Daily Difference 0.007 490.58 0.134 46.0 0.073 89.74 0.025 264.65
Iteration 0.071 142.85 0.315 45.18 0.231 72.51 0.074 241.0
Fujimoto 0.022 430.0 0.282 48.0 0.208 84.0 0.136 145.0
COD (mg/l) 176.0 115.0 350.0 727.0
BOD5/COD 0.254 0.290 0.141 0.098

Table: 4.10 BOD kinetic parameters values for the treated Municipal sewage:
Sewage
Sample I Sample II Sample III
Methods
K L0 K L0 K L0
Method of moments* 0.206 38.50 0.212 193.43 0.014 917
Least squares 0.444 39.29 0.475 196.64 0.044 683.10
Thomas* 0.192 40.81 0.186 207.70 0.009 1365.26
Daily difference* 0.182 37.26 0.195 183.45 0.016 785.57
Iteration 0.335 41.22 0.499 188.16 0.092 346
Fujimoto 0.524 38.5 0.485 192 0.049 640
COD(mg/l) 125 160 180
BOD5/COD 0.286 1.094 0.78

Table: 4.11 BOD kinetic parameters values for the treated Distillery Effluent:
Distellery
Methods
K L0 K L0 K L0
Method of moments* 0.1 5578.30 0.192 2183.13 0.078 21384.83
Least squares 0.157 6839.22 0.412 2230.28 0.175 21264.28
Thomas* 0.117 5200.84 0.173 2327 0.077 21239.71
Iteration 0.227 5356.47 0.521 2141.98 0.196 19166.45
Fujimoto 0.082 10700 0.447 2170 0.172 21500.00
COD(mg/l) 5000 10000 13760
BOD5/COD 0.72 0.194 0.901

Table: 4.12 BOD kinetic parameters values for the treated Dairy Effluent:
Dairy
Methods
K L0 K L0 K L0
Least squares 0.081 410.53 0.114 157.39 0.186 54.59
Thomas* 0.070 257.60 0.069 137.56 0.087 53.0
Iteration 0.141 293.88 0.146 134.0 0.170 57.26
Fujimoto 0.094 38.20 0.186 120.0 0.455 3850.0
COD(mg/l) 200 100 80
BOD5/COD 0.718 0.708 0.458

Table: 4.13 BOD kinetic parameters values for the treated Textile Effluent:
Textile
Methods
K L0 K L0 K L0
Least squares 0.228 47.81 0.703 1731.0 0.259 4706.95
Thomas* 0.125 43.41 0.231 1916.46 0.179 4232
Iteration 0.329 41.00 0.83 1686.36 0.528 3631.11
Fujimoto 0.151 56.50 0.096 4300.0 0.455 3850.0
COD(mg/l) 720 1300 2000
BOD5/COD 0.042 1.266 1.628

4.3 Evaluation of Methods
For evaluating the methods used for estimating the BOD kinetic parameters, expected
BOD values against each of the observed BOD values were calculated with the help
of the first order BOD kinetics equation given below:
BODt = L0 (1-exp-kt)
In the above equation the BOD kinetic parameters (k and L0) estimated by the method
in question are used for calculating the expected BOD values. While using the
observed and expected BOD values, the sum of the absolute differences between the
observed and expected BOD values, while using the following equation:
k
D = åi = 1
(oi – ei) /ei
Where,
D = sum of the absolute differences between the
observed and expected BOD values
oi = is the observed BOD
ei = is the expected BOD
k = is the number of terms in the formula
The observed BOD values and expected BOD values for the six different methods
have been plotted against time (t) and shown in Figures 4.1 to 4.20. The chi-square
statistic obtained for each of the methods of BOD kinetic parameters estimation are
given in table 4.14, and are also indicated in the above figures.

Table: 4.14 Sum of absolute differences of observed and expected BOD values:
Methods
Sample
Moments Least
Squares
Thomas Daily
difference
Iteration Fujimoto
SAT-7 (I) 0.83 1.13 0.62 2.98 0.64 1.59
SAT-7 (II) 0.15 0.18 0.37 0.17 0.30 2.59
SAT-7 (III) 0.37 0.52 2.33 0.93 0.47 0.19
SAT-7 (IV) 0.44 0.78 0.41 0.93 0.50 1.43
EB-4 (I) 0.55 0.63 2.50 0.99 0.72 0.62
EB-4 (II) 6.07 1.34 0.17 0.19 0.21 0.12
EB-4 (III) 0.75 1.72 0.45 1.27 1.05 0.66
EB-4 (IV) 0.99 0.92 3.70 1.24 0.94 1.07
Sewage-I 0.32 0.34 0.40 0.67 0.73 0.31
Sewage-II 0.16 0.19 0.26 0.60 0.15 0.11
Sewage-III 0.22 0.22 0.14 0.16 0.41 0.36
Distillery-I 0.49 0.64 0.47 0.96 0.57 1.18
Distillery-II 0.28 0.33 0.38 0.59 0.32 0.27
Distillery-III 0.15 0.09 0.08 0.07 0.20 0.10
Dairy - I 0.38 0.86 0.32 2.03 0.35 0.52
Dairy – II 0.71 0.25 0.70 0.35 0.31 0.56
Dairy – III 0.38 0.36 0.36 0.93 0.37 0.95
Textile-I 0.41 0.54 0.42 0.82 0.42 1.09
Textile-II 0.15 0.18 0.37 0.17 0.30 2.59
Textile-III 1.47 1.37 0.74 1.74 0.73 0.69

4.4 Discussion
For evaluating the methods used for estimating the BOD kinetics parameters, the
following criterion has been used:
Criterion-1: The method, for which the sum of absolute difference between the
observed and estimated BODs (through using first order BOD kinetics equation and
estimated BOD kinetic parameters) is minimum, should be the best method for BOD
kinetic parameters estimation. That is, if this sum is less than or equal to 0.35, then
one can say that the observed values are within the range of 0.95xBODexpected to
1.05xBODexpected.
Criterion-2: Criterion-1 for comparison has however not been applied on:
1. all those cases for which the calculated ultimate BOD (L0) is less than the
observed BOD7
2. all those cases for which the observed COD is less than the observed BOD7 or
calculated ultimate BOD (L0).
Details of the results rejected on the basis of the second criterion are indicated in the
table 4.15.

Table-4.15: Results discarded from the methods evaluation
Sample Methods
Satluj river water sample-1 Thomas method and Iteration method
Satluj river water sample-2 Moments method and Least Squares method
Satluj river water sample-3 Thomas method
Satluj river water sample-4 Least Squares method and Fujimoto method
East Bein river water sample-1 Moments method, Least Squares methods,
Daily difference method and Fujimoto method
East Bein river water Sample-4 Moments method
Treated municipal sewage sample-1 Daily difference method
Treated municipal sewage sample-2 All the six method
Treated municipal sewage sample-3 All the six method
Treated distillery effluent sample-1 All the six methods
Treated distillery effluent sample-2 Daily difference method
Treated distillery effluent sample-3 All the six methods
Treated dairy effluents sample-1 All the six methods
Treated dairy effluents sample-2 All the six methods
Treated dairy effluent sample-3 Fujimoto method
Treated textile effluent sample-2 All the six methods
Treated textile effluent sample-3 All the six methods
Method of Moments, Thomas method and Daily Difference method have used log to
base 10 in the estimations of BOD kinetics parameters. Hence the BOD reaction rate
constant (k) obtained by these methods need correction by multiplying with 2.303 in
order to make them comparable with the k values calculated by other methods.

After evaluating the methods according to the criterion-1 given earlier, suitability of
methods for different samples obtained is shown in the table-4.16.
Table: 4.16 Suitability of methods for different samples:
Sample Level of
Significance
Moments Least
Squares
Thomas Daily
difference
Iteration Fujimoto
95% None of 3 None of 2 None of 2 1 of 4 1 of3 1 of 3
90% 2 of 3 1 of 2 2 of 2 None of 4 2 of 3 None of 3
Satluj river
water (4
samples)
80% 1 of 3 1 of 2 ---- 2 of 4 ---- None of 3
95% None of 2 None of 3 1 of 4 1 of 3 1 of 4 1 of 3
90% 1 of 2 None of 3 1 of 4 None of 3 1 of 4 1 of 3
East bein river
water (4
samples)
80% None of 2 2 of 3 None of 4 2 of 3 2 of 4 1 of 3
95% 1 of 1 1 of 1 None of 1 ---- None of 1 1 of 1
90% ---- ---- 1 of 1 ---- 1 of 1 ----
Treated
municipal
sewage (3
samples) 80% ---- ---- ---- ---- ---- ----
Treated
distillery
effluent (3
samples) 80% ---- ---- ---- ---- ---- ----
95% 1 of 1 1 of 1 None of 1 ---- 1 of 1 1 of 1
90% ---- ---- 1 of 1 ---- ---- ----
95% None of 1 None of 1 None of 1 None of 1 None of 1 ----
90% 1 of 1 1 of 1 1 of 1 None of 1 1 of 1 ----
Treated Dairy
effluent (3
samples)
80% ---- ---- ---- 1 of 1 ---- ----
95% None of 1 None of 1 None of 1 None of 1 None of 1 None of 1
90% 1 of 1 1 of 1 1 of 1 None of 1 1 of 1 None of 1
Treated
Textile
effluent
80% ---- ---- ---- 1 of 1 ---- 1 of 1
The results indicate that iteration method is best for estimating the BOD kinetic
parameters from the serial BOD test results. Daily difference method is worst of all.

4.5 Conclusions
Method of moments has been found erroneous under the following two different
conditions:
ƒ When there is a lag phase in the serial BOD test (lag phase reduces the t value
(from 7 to 7-lag period) where as the nomogram used is specific for t=7 days)
ƒ When the sample is a river water sample or when it is thoroughly treated
effluent sample k value obtained by Method of Moments has been very low
and the L0 value very high (consistently higher than the sample’ s COD)
Results of the serial BOD tests have been observed to be not of that high accuracy
and dependable. Accurate results might have made the study much more useful.
The evaluation approach followed in this study has indicated that Iteration method is
the best and daily difference method the worst among the methods evaluated for
estimating BOD kinetics parameters from the serial BOD test results.

7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.1 Method comparison for SAT-7(I)
BOD(mg/l)
Observed BOD
Moments(0.83)
Least squares(1.13)
Thomas(0.62)
Daily diff.(2.98)
Iteration(0.64)
Fujimoto(1.59)
BOD = 6.56 mg/l
COD = 16 mg/l
Fig: 4.2 Method comparison for SAT-7 (II)
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8
Days
BOD (mg/l)
Observed BOD
Moments(0.15)
Least squares(0.18)
Thomas(0.37)
Daily diff.(0.17)
Iteration(0.30)
Fujimoto(2.59)
BOD = 4.60 mg/l
COD = 21.0 mg/l

5
4.5
4
3.5
3
2.5
2
1.5
1
0.5
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.3 Method comparison for SAT-7 (III)
BOD (mg/l)
Observed BOD
Moments(0.37)
Least squares(0.52)
Thomas(2.33)
Daily diff.(0.93)
Iteration(0.47)
Fujimoto(0.19)
BOD = 4.17 mg/l
COD = 9.0 mg/l
Fig: 4.4 Method comparison for SAT-7 (IV)
9
8
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 8
Days
BOD (mg/l)
Observed BOD
Moments(0.44)
Least squares(0.78)
Thomas(0.41)
Daily diff.(0.93)
Iteration(0.50)
Fujimoto(1.43)
BOD = 7.74mg/l
COD = 25.0 mg/l

Fig: 4.5 Method comparison for EB-4 (I)
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8
Days
BOD (mg/l)
Observed BOD
Moments(0.55)
Least squares(0.63)
Thomas(2.50)
Daily diff.(0.99)
Iteration(0.72)
Fujimoto(0.62)
BOD = 62.0 mg/l
COD = 176.0 mg/l
Fig: 4.6 Method comparison for EB-4 (II)
45
40
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8
Days
BOD (mg/l)
Observed BOD
Moments(6.07)
Least squares(1.34)
Thomas(0.17)
Daily diff.(0.19)
Iteration(0.21)
Fujimoto(0.12)
BOD = 39.4 mg/l
COD = 115.0 mg/l

70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.7 Method comparison for EB-4 (III)
BOD (mg/l)
Observed BOD
Moments(0.75)
Least squares(1.72)
Thomas(0.45)
Daily diff.(1.27)
Iteration(1.05)
Fujimoto(0.66)
BOD = 62.50 mg/l
COD = 350.0 mg/l
Fig: 4.8 Method comparison for EB-4 (IV)
120
100
80
60
40
20
0
0 1 2 3 4 5 6 7 8
Days
BOD (mg/l)
Observed BOD
Moment(0.99)
Least squares(0.92)
Thomas(3.70)
Daily diff.(1.24)
Iteration(0.94)
Fujimoto(1.07)
BOD = 95.0 mg/l
COD = 727.0 mg/l

50
40
30
20
10
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Observed BOD
Moments(0.32)
Least squares(0.34)
Thomas(0.40)
Daily diff.(0.67)
Iteration(0.73)
Fujimoto(0.31)
BOD = 37.8 mg/l
COD = 125.0 mg/l
Fig. 4.9 Method comparison for sewage-I
250
200
150
100
50
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.10 Method comparison for Sewage - II
BOD(mg/l)
Observed BOD
Moments(0.16)
Least squares(0.19)
Thomas(0.26)
Daily diff.(0.60)
Iteration(0.15)
Fujimoto(0.11)
BOD = 188.0 mg/l
COD = 160.0 mg/l

200
180
160
140
120
100
80
60
40
20
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Observed BOD
Moments(0.22)
Least squares(0.22)
Thomas(0.14)
Daily diff.(0.16)
Iteration(0.41)
Fujimoto(0.36)
BOD = 183.0 mg/l
COD = 180.0 mg/l
Fig: 4.11 Method comparison for Sewage-III
5000
4500
4000
3500
3000
2500
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8
Days
Fig. 4.12 Method comparison for Distillery-I
BOD(mg/l)
Observed BOD
Moments(0.49)
Least squares(0.64)
Thomas(0.47)
Daily diff.(0.96)
Iteration(0.57)
Fujimoto(1.18)
BOD = 4650.0 mg/l
COD = 5000.0 mg/l

2500
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.13 Method comparison for Distillery II
BOD(mg/l)
Observed BOD
Moments(0.28)
Least squares(0.33)
Thomas(0.38)
Daily diff.(0.59)
Iteration(0.32)
Fujimoto(0.27)
BOD = 2062.0 mg/l
COD = 10000.0 mg/l
Fig: 4.14 Method comparison for Distillery-III
18000
16000
14000
12000
10000
8000
6000
4000
2000
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Oserved BOD
Moments(0.15)
Least squares(0.09)
Thomas(0.06)
Daily diff.(0.07)
Iteration(0.20)
Fujimoto(0.10)
BOD = 14900.0 mg/l
COD = 13760.0 mg/l

Fig: 4.15 Method comparison for Dairy-I
200
180
160
140
120
100
80
60
40
20
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Observed BOD
Moments(0.38)
Least squares(0.86)
Thomas(0.32)
Daily diff.(2.03)
Iteration(0.35)
Fujimoto(0.52)
BOD = 178.5 mg/l
COD = 200.0 mg/l
Fig: 4.16 Method comparison for Dairy-II
100
90
80
70
60
50
40
30
20
10
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Observed BOD
Moments(0.71)
Least squares(0.25)
Thomas(0.70)
Daily diff.(0.35)
Iteration(0.31)
Fujimoto(0.56)
BOD = 82.0 mg/l
COD = 100.0 mg/l

45
40
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Fig: 4.17 Method comparison for Dairy-III
Observed BOD
Moments(0.38)
Least squares(0.36)
Thomas(0.36)
Daily diff.(0.93)
Iteration(0.37)
Fujimoto(0.95)
BOD = 38.2 mg/l
COD = 80.0 mg/l
50
45
40
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.18 Method comparison for Textile-I
BOD(mg/l)
Observed BOD
Moments(0.41)
Least squares(0.54)
Thomas(0.42)
Daily diff.(0.82)
Iteration(0.42)
Fujimoto(1.09)
BOD = 38.4 mg/l
COD = 720.0 mg/l

2500
2000
1500
1000
500
0
0 1 2 3 4 5 6 7 8
Days
Fig: 4.19 Method comparison for Textile-II
BOD(mg/l)
Observed BOD
Moments(0.15)
Least squares(0.18)
Thomas(0.37)
Daily diff.(0.17)
Iteration(0.30)
Fujimoto(2.59)
BOD = 1693.6 mg/l
COD = 1300.0 mg/l
4500
4000
3500
3000
2500
2000
1500
1000
500
0
-500
0 1 2 3 4 5 6 7 8
Days
BOD(mg/l)
Observed BOD
Moments(1.47)
Least squares(1.37)
Thomas(0.74)
Daily diff.(1.74)
Iteration(0.73)
Fujimoto(0.69)
BOD = 3795.0 mg/l
COD = 2000.0 mg/l
Fig: 4.20 Method comparison for Textile-III

CHAPTER: 5
Conclusions
The present study on the evaluation of six different methods for BOD kinetic
parameters estimation, while using the serial BOD test results for treated industrial
effluents and river waters, has indicated that Iteration method is the best and Daily
difference method is the worst. This conclusion should be seen in the light of the
following limitations of the present study:
1. BOD and COD results indicate that some of the samples used in the study are not
in real sense treated effluents (at the time sampling the treatment plant might not
been working satisfactorily) (sewage samples 2 and 3, distillery effluent sample 3
and textile effluent sample 2 and 3).
2. In quite a few cases the testing has indicated that their BOD7 is greater than COD
– this indicates that the testing of the samples has not been that accurate. For
making the evaluation process acceptable the results of all such samples whose
BOD7 was obtained greater than the COD have not been considered.
3. In some of the cases in the serial BOD test, an initial lag phase was observed
(indicating that the seed used was not sufficiently acclimatized). For taking care
of this problem the BOD kinetic equation used has been appropriately modified.
But this modification has brought in certain errors affecting the evaluation
process.
4. Treated effluent samples have been used and for properly treated effluents k
values, as expected, have been found to be very low and wherever very low k
values are encountered the L0 was found to be higher than COD. Samples with
such cases have also been not considered in the evaluation process.
For the selection of appropriate method for BOD kinetic parameters, study has
indicated that the following aspects may be given due consideration:

ƒ Serial BOD test may be conducted accurately while using properly acclimatized
seed and the results may be crosschecked with COD test.
ƒ For each type of wastewater or water samples the methods may be separately
evaluated and selected on the basis of statistically significant number of serial
BOD tests (at least 7 samples may be tested).
ƒ Incubation period for serial BOD test was chosen as 7 days and this may be
followed because it can allow bio-oxidation of significant fraction of the organic
matter and nitrogenous BOD exertion may still not be significant. However in
case of treated effluent samples for avoiding nitrogenous BOD exertion
appropriate inhibitors may be used.
The present study has clearly indicated that Moments Method of kinetic parameters
estimation is not good for samples from surface water bodies and for thoroughly
treated secondary effluents. Keeping this in mind further work may be planned for
answering the question ‘which method is most appropriate under what conditions?

REFERENCES
1. APHA, AWWA and WPCF (1995), “Standard Methods for Estimation of
Water Waste Water”, 19th addition, 1995, Jointly edited by Eaton, Andrew
D.; Clesceri, Lenore S. and Greenberg, Arnold E..
2. Berthouex, P. M. and Hunter, W.G. (1971), “Problems associated with planning
BOD experiments”. J. San. Eng. Div. Amer. Soc. Civil Engr., 97 (SA4), p. 393-
407.
3. Booki Min; David Kohlar; Bruce E. Logan (2004), “A Simplified HBOD Test
Protocol Based on Oxygen Measurement using a fiber optic Probe”, Water
Environmental Research, Vol. 76(1), p. 29-36.
4. Bruce E. Logan; Gretchen A. Wagenseller (1993),”The HBOD Test: A New
Method for Determining Biochemical Oxygen Demand”, Water Environmental
Research, Vol. 65(7), p. 862.
5. Fair, G.M. (1936) “The Log Difference Method of Estimating the Constants of
the First Stage BOD Curve” Sewage Works Journ., Vol. 8, p. 430 – 434.
6. Fujimoto, Y (1961), “Graphical use of first stage BOD equation”, J. Water
Pollution Control, Vol. 36(1), p. 69.
7. Gaudy, A.F. Jr. (1972) “ Biochemical Oxygen Demand” in water Pollution
Microbiology Ed. Ralph Mitchell, Wiley Interscience N. Y. London, p. 305.
8. Guillermo Cutrera; Liliana Manfredi; Carlos E del Valle and Froilan Gonzalez, J.
(1999), “On the determination of the kinetic parameters for the BOD Test”,
Water SA, Vol. 25 No. 3, p. 377-379.
9. Gurjar, B. R. (1994), “Formulation of a Simple New Method to Determine
First – Stage BOD Constants, (K L)” , Indian J. Environmental Protection,
Vol. 14, No. 6, p. 440-442.

10. Jenkins, D. (1960) “ The use of Manometric Methods in the Study of Sewage
and Trade Wastes” , in Waste Treatment Ed. P.C.G. Issac., p.319.
11. Le Blanc, P.J. (1974) “ Review of Rapid BOD Test Methods” , J. Water
Pollution Control Federation. Vol. 46, p. 2202.
12. Maiti, S.K. and Ganguly Sangeeta (2002) “ Errors in the Performance of
27 and BOD5
BOD3
20 test and its Effect on Determination of Rate Constant”
Indian J. Environmental Protection, Vol. 22 (10), p. 1113 – 1119.
13. Marske, D.M. and L.B. Polkowski (1972), “ Evaluation of methods for
estimating biochemical oxygen demand parameters”. J. Water Poll. Cont.
Fed., 44 (10), p. 1987-2000.
14. McGhee, T.J. (1991) “Water Supply and Sewrage” 6th edition McGraw Hill,
Tokyo.
15. Metcalf Eddy (2003), “Wastewater Engineering”, Tata McGraw Hill
Publication, New Delhi.
16. Moore, E. W.; Thomas; H. A., and Snow, W.B. (1950), “ Simplified Method for
analysis of BOD data”, Sew. Ind. Wastes. 22 (10).
17. Nesarattnam Suresh (1998), “Effluent Treatment”, Pira Environmental Guide
Series, published by Pira International UK.
18. Phelps, E.B. (1953) “ Stream Sanitation” , Wiley, New York.
19. Peavy H.S., Donal R. Rowe, George Tchobanoglous (1985) “ Environmental
Engineering” McGraw Hill, New York p. 43
20. Rai, R. K. (2000), “ Simplified method for Determination of BOD Constants” ,
Indian J. Environmental Protection, Vol. 20, No. 4, p. 263-267.
21. Rai, R. K. (2000), “ Iteration Method For The Analysis Of BOD Data” , Indian
J. Environmental Health. Vol. 42. No. 1 p. 25-27.

22. Ramallho, R. S. (1983), “ Introduction to Wastewater Treatment Process” ,
Academic Publication, (Second Edition), New York.
23. Reddy, A. S., “BOD and BOD kinetics” , Under Publication.
24. Reed, L.J. and Theriault, E.J. (1931), “The statistical treatment of reaction” .
Velocity data – II. J. Phys. Chem., p. 35 – 950.
25. Remo Navone (1960), “A new method for calculating k and L for sewage” ,
Water and Sewage Works, p. 285-286.
26. Shrivastava, A.K. (1982) “ Analytical and Experimental Investigations of BOD
Kinetics in an Aquatic Eco-systems” Ph. D. Thesis submitted to University of
Roorkee, Roorkee.
27. Shrivastva, A.K.: Swaroop Jyoti and Jain Neeraj (2000), “Effect of Indigenous
Seed on Kinetic Equations” , Indian J. Environmental health, Vol.22(2), p. 75-
78.
28. Stone, T. (1981), “A resume of the Kinetics of BOD Test”, Water Pollution
Control 80(4), p. 513-520.
29. Thomas, Jr. H.A. (1937) “The Slope Method of Evaluating the Constants of
the First Stage BOD Curve” Sewage Works J., Vol. 9, p. 425.
30. Thomas, H.A. (1950), “Graphical determination of BOD curve constants” ,
Water Sewage works, Vol. 97, p. 123.
31. William, E. Gates and Sambhunath Ghosh (1971) “ Biokinetic Evaluation of
BOD Concepts and Data” J. Sanitary Engineering Division, SA-3, p. 287 – 307.

Determination of BOD Kinetic Parameters

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