Oxygen Demand Concepts and Dissolved Oxygen Sag
in Streams
Introduction
In recent years “biodegradable” has become a popular word. Often it is assumed
that if something is biodegradable, then disposal is not a problem. We know that
throwing non-biodegradable substances into our environment leads to degradation of
our planet. But disposal of biodegradable compounds also can be detrimental to the
environment.
The effects of improper disposal of biodegradable substances became a source of
public outrage in the early 1800's. The flush toilet was becoming popular and sewage
was discharged directly into the nearest waterway. The receiving waters were quickly
polluted. Fish in the receiving waters died and the water had a very offensive odor.
Although there are many reasons why we no longer discharge untreated sewage into
the environment, (including disease transmission, sediment buildup...) one of the
reasons is directly related to the fact that sewage contains much that is biodegradable.
Theory
Biodegradable means that a substance can be converted into simpler compounds by
biologically mediated reactions. The second law of thermodynamics predicts that
oxidation of high energy level organics (relative to low energy level CO 2) is favored.
Oxygen is one of the strongest oxidizing agents found in natural aquatic systems.
Oxidation reactions are thermodynamically favored, but kinetically slow unless
microbially mediated. The end products of complete aerobic biodegradation are CO2
and H2O. Production of CO2 has recently come under fire as a potential cause of
global warming, but that is not the subject of this lab. The problem is not with the
products of biodegradation, the problem is that aerobic biodegradation of a compound
requires another reactant. Let's look at the biodegradation of a simple organic
compound, glucose.
C6 H12 O6 +?  6CO2 +6H 2 O
1.1
To balance the equation oxygen is needed.
C6 H12 O6 +6O2  6CO2 +6H 2 O
1.2
The consumption of oxygen needed for biodegradation can be a problem. Oxygen is
not very soluble in water. The equilibrium concentration of oxygen in water is
approximately 10 mg/L (see Figure 1). That means that the degradation of a few
mg/L of a biodegradable compound in a river could result in the depletion of
dissolved oxygen. Fish have a bad day when oxygen is depleted from their
environment. Some species of fish such as trout begin to suffer when the dissolved
oxygen concentration drops below 5 mg/L.
Oxygen in water is consumed during
aerobic biodegradation of organic
compounds and is replenished from the
atmosphere. The two processes have
different kinetics, but are coupled. As
the
oxygen
is
depleted
by
biodegradation the rate at which
oxygen is transferred into the water
increases because the transfer driving
force increases. The rate at which
oxygen is dissolved into water from the
atmosphere is proportional to the deficit
of oxygen in the water. The oxygen
deficit is simply the difference between
Figure 1. Equilibrium dissolved oxygen
the equilibrium oxygen concentration
concentration as a function of water
and the actual oxygen concentration.
temperature.
These two reactions (reaeration, and
biochemical utilization) are modeled by
the Streeter-Phelps equation. In order to
increase the rate at which the biodegradation occurs, the concentration of bacteria was
increased for use in this laboratory experiment. Bacteria respire and thus consume
oxygen even when no substrate is present. Thus an additional term for bacterial
respiration will be needed to model the oxygen sag results obtained in the laboratory.
Streeter Phelps Equation Development
We’ll begin by developing the oxygen deficit as a function of time in a completely
mixed batch reactor (no inflow and no outflow) with initial concentrations of
Biochemical Oxygen Demand (BODL) and dissolved oxygen. We will include
oxidation of BODL and reaeration from the atmosphere. These effects are coupled in
equation 8.3 where C represents oxygen concentration. The first two terms on the
right are negative since oxidation of BOD and respiration consume oxygen while the
third term is usually positive since reaeration increases the concentration of oxygen
(except in the rare instance where the dissolved oxygen concentration is greater than
the equilibrium dissolved oxygen concentration). Eventually we will make a
comparison between time in a reactor and distance down a river.
Crespiration
Coxidation
Creaeration
C



t
t
t
t
1.3
Oxidation of BOD
We must first develop a relationship for the change in oxygen concentration due to
oxidation of organics. The rate that oxygen is used will be proportional to the rate that
substrate (or biochemical oxygen demand) is oxidized. The rate of substrate
utilization by bacteria is given by the Monod relationship
dL
 kLX

dt
Ks  L
1.4
where L is substrate concentration expressed as oxygen demand or BOD L [mg/L], k is
the maximum specific substrate utilization rate, Ks is the half velocity constant, and X
is the concentration of bacteria. However, the concentration of bacteria is a function
of the substrate concentration and thus application of the Monod equation to a
polluted river is not trivial. Often the bacterial concentration remains relatively
constant. If the half velocity concentration is large relative to the concentration of
substrate we obtain
dL
kXL  kX 


 L  kox L
dt
Ks  L  Ks 
1.5
where kox is a first order oxidation rate constant that includes both the approximation
that the bacteria concentration is roughly constant and that the substrate concentration
is smaller than the half velocity constant.
Separate variables and integrate
L
t
dL
L L = 0 (kox )dt
o
1.6
L  Lo e koxt
1.7
to obtain
The rate of oxygen utilization is equal to the rate of substrate utilization (when
measured as oxygen demand) and thus we have
Coxidation dL
1.8
=
= -k ox L
t
dt
where C is the dissolved oxygen concentration [mg/L]. Now we can substitute for L
in equation 1.8 using equation 1.7 to obtain
Coxidation
= -k ox Lo e koxt
t
1.9
Respiration
Bacteria utilize oxygen for respiration and for cell synthesis. When no substrate is
present the bacteria cease synthesis, but must continue respiration. This continual use
of oxygen is termed "endogenous respiration." Bacteria use stored reserves for
endogenous respiration. We can model this oxygen demand as a constant that is
added to the demand for oxygen caused by substrate utilization. As a first
approximation, we can assume that this oxygen demand is proportional to the
concentration of bacteria. In addition, we will assume that the population of bacteria
is relatively constant throughout the experiment.
Crespiration
1.10
=-bX =-k e
t
where b is the specific endogenous oxygen consumption rate and ke is the endogenous
oxygen consumption rate.
Oxygen Transfer Coefficient
The rate of oxygen transfer is directly proportional to the difference between the
actual dissolved oxygen concentration and the equilibrium dissolved oxygen
concentration.
Creaeration ˆ
1.11
= kv,l  C* - C 
t
where C* is the equilibrium oxygen concentration, C is the actual dissolved oxygen
concentration, and kˆv ,l is the is the overall volumetric oxygen transfer coefficient. If
reaeration is the only process affecting the oxygen concentration then equation 1.11
can be integrated to obtain
C*  C
ln *
 kˆv ,l (t  t0 )
C  C0
1.12
Oxygen Deficit
We now have equations for the reaction of oxygen with BODL, endogenous
respiration, and for reaeration. Substituting into equation 1.3 we get
C
= -k ox Lo e koxt k e + kˆv ,l  C* - C 
t
We can simplify the equation by defining oxygen deficit (D) as:
1.13
D=C* -C
1.14
and noting that the rate of change of the deficit must be equal and opposite to the rate
of change of oxygen concentration
dC
dD
=
1.15
dt
dt
We must remember that the deficit can never be greater than the equilibrium
concentration (D must always be less than C *)! In addition, the BOD model breaks
down if the dissolved oxygen concentration is less than about 2 mg/L because the
dL
lack of oxygen will limit microbial kinetics and
will no longer equal -kox L . If we
dt
stick to conditions under which our assumptions are valid then we can substitute
equations 1.14 and 1.15 into equation 1.3 to obtain
D
 ke  kox Lo e koxt - kˆv ,l D
t
1.16
This is a first order linear differential equation. Integration with initial oxygen deficit
= Do @ t = 0 gives:
D
ke 
k   kˆ t
k L
- kˆ t
  Do e  e v ,l  ox o e koxt - e v ,l 

kˆv ,l  kˆv ,l 
kˆv ,l  kox 
1.17
Application to a River
We are interested in the oxygen deficit as a function of distance down a stream. As
an approximation we can think of a cross section of a river as a completely stirred
reactor that is slowly moving downstream. The relation between time in a batch
reactor and distance down the river is simply
t=
x
u
1.18
where u is the stream velocity and x is distance. The Streeter-Phelps model assumes a
constant input of biodegradable substrate, Lo, at x = 0 and the model is valid under
steady-state conditions.
Of particular concern is the maximum deficit, Dc. We want to know the value of Dc
x
and where (or when) it will occur ( t c = c ). This will be the "critical point." If there
u
are going to be adverse effects (like dead fish) this will be the place.
The maximum oxygen deficit occurs when
D
=0
t
We can substitute this into the first order differential equation 1.6 to get
1.19
0  ke  kox Lo e koxtc - kˆv,l Dc
1.20
ke  kox Lo e koxtc
Dc 
kˆ
1.21
and solve for Dc to get
v ,l
an equation with unknowns tc and Dc. The Streeter-Phelps equation still holds at the
critical point so we also have
ke 
k   kˆ t
k L
- kˆ t
  Do  e  e v ,l c  ox o e koxtc - e v ,l c 
1.22

kˆv ,l 
kˆv ,l 
kˆv ,l  kox 
also with unknowns xc and Dc. So now we have two equations in two unknowns. We
can solve for tc by eliminating Dc.
Dc =



 ke -kˆv ,l Do kˆv ,l -kox
kˆv ,l 

1.23
tc =
ln


kox 
Lo kox2
kˆv ,l -kox


To find Dc given the kinetic coefficients and the initial oxygen deficit, first find tc
using equation 1.23. Then use equation 1.21 to solve for Dc.
1
Zero Order Kinetics
An alternate model can be derived based on the assumptions that the concentration
of bacteria is relatively constant and that the rate of substrate utilization is zero order,
i.e., the concentration of the substrate is greater than the half velocity constant Ks.
dL kLX
=
 -kX =-k0
dt K s  L
1.24
The change of the deficit of dissolved oxygen is equal to the change caused by
microbial degradation (k0) plus change due to endogenous respiration minus the
reaeration ( kˆ D ).
v ,l
dD
= k0 + ke  kˆv ,l D
1.25
dt
This equation is only valid when the substrate concentration is greater than Ks. To
simplify derivation, assume that Ks is very small relative to the initial BOD added to
the system and apply the zero-order model until the substrate is completely oxidized.
When the substrate concentration reaches zero a discontinuity will occur as substrate
oxidation stops. Separating variables and integrating
D
k
Do
t
dD
0
 ke  kˆv ,l D
=  dt
1.26
0
1  k0  ke  kˆv ,l D 
ln 
= t
kˆv ,l  k0  ke  kˆv ,l Do 
and solving for the dissolved oxygen deficit
 tkˆ
k0  ke (k0  ke  kˆv ,l Do )e v ,l
D=
kˆ
1.27
1.28
v ,l
Lo
. Substituting into equation 1.28
k0
to get the maximum dissolved oxygen deficit yields
The substrate concentration is depleted when t =
Dt =
k0  ke (k0  ke  kˆv ,l Do )e
kˆ
  Lo kˆv , l 


 k0 
1.29
v ,l
where Dt is the dissolved oxygen deficit at the transition when the substrate is all
L
utilized. For times greater than t = o there is no longer any substrate and thus k0 = 0
k
and equation 1.25 becomes
dD
= ke  kˆv ,l D
dt
Separating variables and integrating
D

Dt
t
dD
=  dt
ke  kˆv ,l D tt
-1  ke  kˆv ,l D 
ln 
 = t - tt
kˆv ,l  ke  kˆv ,l Dt 
D=
1.30

ke ke  kˆv ,l Dt
e
1.31
1.32
kˆv , l  tt t 
kˆv ,l
Equation 1.33 is valid for all times greater than
1.33
Lo
. The general shapes of the two
k
types of sag curves are shown in
Figure 2.
Experimental Objectives
0.0
1.0
The objectives of this lab are to:
firs t order
DO 2.0
sag
1) Illustrate the effects of adding (mg/L) 3.0
4.0
biodegradable compounds to
zero order
5.0
natural waters.
6.0
2) Evaluate the Streeter-Phelps
0.0
200 .0
400 .0
600 .0
800 .0
dissolved oxygen sag model
Time (s)
and a zero order substrate
utilization model and compare Figure 2. Dissolved oxygen sag curves obtained
from zero and first order models for substrate
with laboratory data.
utilization.
3) Explain the theory and use of
dissolved oxygen probes.
Experimental Methods
In this lab we will examine the
effects of adding a small amount of a
biodegradable compound to a small
batch reactor. We will measure the
dissolved oxygen concentration over
Hypodermic diffuser
time using a dissolved oxygen probe.
DO probe
The apparatus is shown in Figure 3.
The BOD measured using this
100 mL beaker
technique will be lower than the BOD
Water surface
measured using the standard BOD test
because a significant fraction of the
Stirbar
glucose will be converted into cell
material (i.e. used for synthesis
instead of for respiration). This
technique can be used to obtain
kinetic parameters for yield, half
velocity constant and maximum Figure 3. Apparatus used to measure
substrate utilization rate (Ellis et al., dissolved oxygen consumption rates.
1996).
Probe Calibration
Calibrate
the
dissolved
oxygen
http://www.cee.cornell.edu/mws/Software/DOcal.htm).
probe
(see
Oxygen Transfer Coefficient
1) Prepare to monitor dissolved oxygen.
2) Place the dissolved oxygen probe in the reactor.
3) Pour 50 mL of deoxygenated distilled water into the batch reactor.
4) Set the stirrer speed to 5.
5) Set the airflow rate to 50 mL/min.
6) Monitor the dissolved oxygen for 3 minutes (or longer).
7) Save the data as \\Enviro\enviro\Courses\453\oxygen\netid_O2trans. The data will
be used later to estimate the oxygen transfer coefficient.
Endogenous respiration oxygen requirements
1) Pour 50 mL of a bacterial suspension into the batch reactor.
2) Place the dissolved oxygen probe in the reactor.
3) Set the stirrer speed to 5.
4) Set the airflow rate to 250 mL/min to aerate the reactor contents.
5) Prepare to monitor dissolved oxygen.
6) After the dissolved oxygen concentration is close to saturation turn off the air and
monitor the dissolved oxygen for 3 minutes (or longer).
7) Save the data as \\Enviro\enviro\Courses\453\oxygen\netid_endog. The data will
be used later to estimate the endogenous respiration rate.
BOD of glucose solution
1) Set the airflow rate to 250 mL/min and aerate the bacterial suspension used
previously.
2) Prepare pipette to add 75 µL of glucose solution (this will provide a BOD of 15
mg/L when diluted by 50 mL bacterial suspension).
3) Prepare to monitor dissolved oxygen.
4) Turn off the airflow.
5) As quickly as possible, add glucose through the port in the bottle and begin
monitoring the dissolved oxygen concentration.
6) Monitor the dissolved oxygen until the dissolved oxygen concentration reaches
approximately 0 mg/L.
7) Save the data as \\Enviro\enviro\Courses\453\oxygen\netid_BOD. The data will
be used later to estimate the BOD of the glucose solution.
DO Sag Curves
1) Set the airflow rate to 250 mL/min and aerate the bacterial suspension used
previously.
2) Prepare to monitor dissolved oxygen.
3) Reduce the airflow rate to 50 mL/min.
4) Begin monitoring the dissolved oxygen in the reactor. Use 5 second data intervals.
5) After ≈300 seconds of monitoring add 10 mg glucose BOD/L (50 L stock) to the
reactor.
6) Observe the oxygen depletion in the reactor.
7) Continue monitoring until the dissolved oxygen concentration returns to within
90% of the original DO concentration.
8) Save the data as \\Enviro\enviro\Courses\453\oxygen\netid_sag.
Prelab Questions
1) A dissolved oxygen probe was placed in a small vial in such a way that the vial
was sealed. The water in the vial was sterile. Over a period of several hours the
dissolved oxygen concentration gradually decreased to zero. Why? (You need to
know how dissolved oxygen probes work to answer this!)
2) Which assumption is different between the Streeter-Phelps and the zero order
model?
Data Analysis
The rate constants can be estimated using Excel. A sample spreadsheet is available
at the course web site.
Oxygen Transfer Coefficient
1) Estimate the gas transfer coefficient from equation 1.12 or by using the
spreadsheet model.
2) Graph the dissolved oxygen concentration vs. time along with the theoretical
curve.
Endogenous Decay
1) Estimate the endogenous oxygen consumption rate from the slope of the graph or
by using the spreadsheet model.
2) Graph the dissolved oxygen concentration for the bacteria culture in the BOD
bottle without any added BOD vs. time along with the theoretical curve.
BOD of Glucose
1) Use the "DO sag" Excel spreadsheet to estimate the first or zero order oxygen
utilization coefficients, and the BOD exerted by the glucose. Which model fits the
data best?
2) How long did it take for the biodegradation of the glucose to occur?
3) What was the change in dissolved oxygen concentration during that time?
4) How much BOD did the glucose solution exert expressed as a fraction of the
BOD of the glucose added.
5) Graph the dissolved oxygen concentration vs. time for the glucose solutions along
with the theoretical curves. Identify the regions where biodegradation of the
glucose was occurring.
Dissolved Oxygen Sag
1) Use the previous estimates of the oxygen transfer coefficient, endogenous
respiration rate, and fraction of BOD exerted (note that a different amount of
BOD was added for the sag curve than for the BOD measurement!) to plot zero
and first order model predictions of the dissolved oxygen sag curve. Discuss any
discrepancies.
2) Estimate the first and zero order oxygen utilization coefficients and the BOD
exerted using the spreadsheet models by minimizing the RMSE using both
models with your data. Use the endogenous respiration rate and the reaeration rate
estimated previously. Which model (zero or first order) fits the data best? Are the
fit parameters significantly different than those obtained in the BOD of glucose
analysis? Include the estimated parameters in your report.
3) Graph the dissolved oxygen concentration vs. time for the dissolved oxygen sag
curve along with the theoretical curves.
4) On the graph indicate maximum dissolved oxygen sag and compare with the BOD
added.
5) Why is the dissolved oxygen sag less than the BOD added?
References
Ellis, T. G.; D. S. Barbeau; B. F. Smets and C. P. L. J. Grady. 1996. “Respirometric
technique for determination of extant kinetic parameters describing
biodegradation” Water Environment Research 68(5): 917-926.
Lab Prep Notes
Bacterial stock preparation using
20% PTYG
Grow 4 liter culture of Ps. putida
1) Heat 1 L of distilled water and
dissolve media for 4 L of 20%
PTYG.
2) Dilute to 4 L in 6 L container
containing aeration stone and
stirrer.
3) Thaw one cryovial containing Ps.
putida and transfer into PTYG
media.
4) Stir and aerate for 24 hours.
Wash/enumerate Ps. putida culture
1) Centrifuge 4 L culture in 250 mL
bottles to obtain concentrated
stock (5000 rpm for 10 minutes).
2) Resuspend total culture in 500
mL using 10x BOD dilution
water (pH control is essential for
bacterial growth and trace
nutrients are required).
3) Refrigerate at 4C.
Table 3. 20%
PTYG
culture
media.
(Prepare 4 L)
compound
peptone
tryptone
yeast extract
glucose
MgSO4
CaCl2·2H2O
mg/L
1000
1000
2000
1000
470
70
g/4L
4
4
8
4
1.9
0.28
Table 1. Reagent list
Description
Supplier
peptone
tryptone
glucose
yeast extract
MgSO4·7H2O
CaCl2·2H2O
KH2PO4
K2HPO4
Na2HPO4 ·
7H2O
NH4Cl
FeCl3 · 6H2O
Fisher Scientific
Fisher Scientific
Aldrich
Fisher Scientific
Fisher Scientific
Fisher Scientific
Fisher Scientific
Fisher Scientific
Fisher Scientific
Catalog
number
BP1420-100
BP1421-100
15,896-8
BP1422-100
Fisher Scientific
Fisher Scientific
Table 2. Equipment list
Description
Supplier
magnetic stirrer
Accumet™ 50
pH meter
ATI Orion DO
probe
6 L container
250 mL PP
bottle
15 mL PP
bottles
variable flow
digital drive
Easy-Load
pump head
PharMed tubing
size 18
4 prong
hypodermic
tubing diffuser
1/4” plug
1/4” union
stainless steel
hypodermic
tubing
gas diffusing
stone
Fisher Scientific
Fisher Scientific
Catalog
number
11-500-7S
13-635-50
Fisher Scientific
13-299-85
Fisher Scientific
Fisher Scientific
03-484-22
02-925D
Fisher Scientific
02-923-8G
Cole Parmer
H-07523-30
Cole Parmer
H-07518-00
Cole Parmer
H-06485-18
CEE shop
Cole Parmer
Cole Parmer
McMaster Carr
H-06372-50
H-06372-50
Fisher Scientific
11-139B
Setup
1) Prepare the Ps. putida culture
Table 4. BOD dilution water stock solutions.
starting 48 hours before lab.
Use 10 mL per liter of each of the 4
2) Prepare 100 mL glucose stock
solutions to prepare 10x BOD dilution
solution.
water.
3) Attach one Easy-Load pump
head to the pump drives and phosphate buffer M.W. g/L mg/100
µM
plumb with size 18 tubing
mL
connected to the hypodermic
136.09 8.5
850
62.46
KH2PO4
diffuser.
174.18 21.7
2175
124.87
K2HPO4
5
4) Verify that DO probes are
3340
124.60
Na2HPO4 · 7H2O 268.07 33.4
operational, stable, and can be
53.49
1.7
170
31.78
NH4Cl
calibrated.
Magnesium
5) Mount DO probes on magnetic
sulfate
stirrers. (Use large stirbars.)
120.39 11
1100
91.37
MgSO4
6) Use 100 mL plastic beakers
containing 50 mL of bacteria Calcium chloride
110.99 27.5
2750
247.77
CaCl2
suspension. The open tops will
result in negligible oxygen
Ferric chloride
transfer during the course of
270.3 0.25
25
0.925
FeCl3 · 6H2O
the experiments.
7) Prepare 1 L of deoxygenated distilled water right before class using the
techniques outlined in the gas transfer lab (see page Error! Bookmark not
defined.).
Glucose Stock Solution
C6H12O6 + 6O2  6CO2 + 6H2O
10gO2
L
10 gO2 moleO2 1moleC6 H12 O6 180 gC6 H12 O6



 0.1 L = 0.9375 g C6 H12 O6 in 100 mL
L
32 gO2
6moleO2
moleC6 H12 O6
Glucose Dilutions
10 mg BOD
L

 100 mL  100  L
L
10000 mg O2
100 µL in 100 mL will provide 10 mg/L BOD
10 µL of stock solution diluted into 100 mL provides 1 mg BOD/L.