Oxygen Demand Concepts and Dissolved Oxygen Sag in Streams

IntroductionIn 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.

TheoryBiodegradable 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 CO2) 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.

To balance the equation oxygen is needed.

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 the equilibrium oxygen concentration and the actual oxygen concentration. 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 DevelopmentWe’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 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.

Figure 1. Equilibrium dissolved oxygen concentration as a function of water temperature.

Oxidation of BODWe 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

where L is substrate concentration expressed as oxygen demand or BODL [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

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

to obtain

The rate of oxygen utilization is equal to the rate of substrate utilization (when measured as oxygen demand) and thus we have

where C is the dissolved oxygen concentration [mg/L]. Now we can substitute for L in equation using equation to obtain

RespirationBacteria 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.

where b is the specific endogenous oxygen consumption rate and ke is the endogenous oxygen consumption rate.

Oxygen Transfer CoefficientThe rate of oxygen transfer is directly proportional to the difference between the

actual dissolved oxygen concentration and the equilibrium dissolved oxygen concentration.

where C* is the equilibrium oxygen concentration, C is the actual dissolved oxygenconcentration, and is the is the overall volumetric oxygen transfer coefficient. If reaeration is the only process affecting the oxygen concentration then equation can be integrated to obtain

Oxygen DeficitWe now have equations for the reaction of oxygen with BODL, endogenous

respiration, and for reaeration. Substituting into equation we get

We can simplify the equation by defining oxygen deficit (D) as:

and noting that the rate of change of the deficit must be equal and opposite to the rate of change of oxygen concentration

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

lack of oxygen will limit microbial kinetics and will no longer equal . If we

stick to conditions under which our assumptions are valid then we can substitute equations and into equation to obtain

This is a first order linear differential equation. Integration with initial oxygen deficit= Do @ t = 0 gives:

Application to a RiverWe 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

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

and where (or when) it will occur ( ). This will be the "critical point." If there

are going to be adverse effects (like dead fish) this will be the place.The maximum oxygen deficit occurs when

We can substitute this into the first order differential equation to get

and solve for Dc to get

an equation with unknowns tc and Dc. The Streeter-Phelps equation still holds at the critical point so we also have

also with unknowns xc and Dc. So now we have two equations in two unknowns. We can solve for tc by eliminating Dc.

To find Dc given the kinetic coefficients and the initial oxygen deficit, first find tc

using equation . Then use equation to solve for Dc.

Zero Order KineticsAn 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.

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 ( ).

This equation is only valid when the substrate concentration is greater than K s. 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

and solving for the dissolved oxygen deficit

The substrate concentration is depleted when . Substituting into equation to get

the maximum dissolved oxygen deficit yields

where Dt is the dissolved oxygen deficit at the transition when the substrate is all

utilized. For times greater than there is no longer any substrate and thus k0 = 0

and equation becomes

Separating variables and integrating

Equation is valid for all times greater than . The general shapes of the two types

of sag curves are shown in Figure 2.

6.0

0.01.02.03.04.05.0

800.00.0 200.0 400.0 600.0Time (s)

DO sag

(mg/L)

zero order

first order

Figure 2. Dissolved oxygen sag curves obtained from zero and first order models for substrate utilization.Experimental Objectives

The objectives of this lab are to:1) Illustrate the effects of adding biodegradable compounds to natural waters.2) Evaluate the Streeter-Phelps dissolved oxygen sag model and a zero order

substrate utilization model and compare with laboratory data.3) Explain the theory and use of dissolved oxygen probes.

Experimental MethodsIn 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 time using a dissolved oxygen probe. The apparatus is shown in Figure 3.

The BOD measured using this technique will be lower than the BOD measured using the standard BOD test because a significant fraction of the 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 substrate utilization rate (Ellis et al., 1996).

Probe CalibrationCalibrate the dissolved oxygen probe (see

http://www.cee.cornell.edu/mws/Software/DOcal.htm).

Oxygen Transfer Coefficient1) 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.

Figure 3. Apparatus used to measure dissolved oxygen consumption rates.

Endogenous respiration oxygen requirements1) 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 solution1) 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 Curves1) 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 Questions1) 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 AnalysisThe rate constants can be estimated using Excel. A sample spreadsheet is available

at the course web site.

Oxygen Transfer Coefficient1) Estimate the gas transfer coefficient from equation or by using the spreadsheet

model.2) Graph the dissolved oxygen concentration vs. time along with the theoretical

curve.

Endogenous Decay1) 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 Glucose1) 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 Sag1) 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?

ReferencesEllis, 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. putida1) 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 culture1) 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 4C.

Table 3. 20% PTYG culture media. (Prepare 4 L)

compound mg/L g/4Lpeptone 1000 4tryptone 1000 4

yeast extract 2000 8glucose 1000 4MgSO4 470 1.9

CaCl2·2H2O 70 0.28

Table 1. Reagent list

Description Supplier Catalog number

peptone Fisher Scientific BP1420-100tryptone Fisher Scientific BP1421-100glucose Aldrich 15,896-8

yeast extract Fisher Scientific BP1422-100MgSO4·7H2O Fisher ScientificCaCl2·2H2O Fisher Scientific

KH2PO4 Fisher ScientificK2HPO4 Fisher Scientific

Na2HPO4 · 7H2O

Fisher Scientific

NH4Cl Fisher ScientificFeCl3 · 6H2O Fisher Scientific

Table 2. Equipment list

Description Supplier Catalog number

magnetic stirrer Fisher Scientific 11-500-7SAccumet™ 50

pH meterFisher Scientific 13-635-50

ATI Orion DO probe

Fisher Scientific 13-299-85

6 L container Fisher Scientific 03-484-22250 mL PP

bottleFisher Scientific 02-925D

15 mL PP bottles

Fisher Scientific 02-923-8G

variable flow digital drive

Cole Parmer H-07523-30

Easy-Load pump head

Cole Parmer H-07518-00

PharMed tubing size 18

Cole Parmer H-06485-18

4 prong hypodermic

tubing diffuser

CEE shop

1/4” plug Cole Parmer H-06372-501/4” union Cole Parmer H-06372-50

stainless steel hypodermic

tubing

McMaster Carr

gas diffusing stone

Fisher Scientific 11-139B

Setup1) Prepare the Ps. putida culture

starting 48 hours before lab. 2) Prepare 100 mL glucose stock

solution.3) Attach one Easy-Load pump

head to the pump drives and plumb with size 18 tubing connected to the hypodermic diffuser.

4) Verify that DO probes are operational, stable, and can be calibrated.

5) Mount DO probes on magnetic stirrers. (Use large stirbars.)

6) Use 100 mL plastic beakers containing 50 mL of bacteria suspension. The open tops will result in negligible oxygen transfer during the course of 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: Reference source notfound).

Glucose Stock Solution

C6H12O6 + 6O2 6CO2 + 6H2O

Glucose Dilutions

100 µL in 100 mL will provide 10 mg/L BOD10 µL of stock solution diluted into 100 mL provides 1 mg BOD/L.

Table 4. BOD dilution water stock solutions. Use 10 mL per liter of each of the 4 solutions to prepare 10x BOD dilution water.

phosphate buffer M.W. g/L mg/100 mL

µM

KH2PO4 136.09 8.5 850 62.46K2HPO4 174.18 21.7

52175 124.87

Na2HPO4 · 7H2O 268.07 33.4 3340 124.60NH4Cl 53.49 1.7 170 31.78

Magnesium sulfateMgSO4 120.39 11 1100 91.37

Calcium chlorideCaCl2 110.99 27.5 2750 247.77

Ferric chlorideFeCl3 · 6H2O 270.3 0.25 25 0.925