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CEE 263A Final Project Report (Winter 2013)
Reaeration in Rivers and Streams
Kevin Qi

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Abstract
Dissolved oxygen levels in rivers and streams are an essential measure of water quality.
Changes in dissolved oxygen heavily affect river and stream organisms, both aquatic plants and
fish. Oxygen is needed for aerobic respiration in these organisms. Sometimes, dissolved oxygen
levels will be depleted below acceptable levels as a result of “biodegradation of carbonaceous
and nitrogenous wastes discharged into the streams or deposited in the streambed sediment.”
(Melching 1) Reaeration is a natural process that counteracts oxygen depletion. It is the exchange
of gases between the atmosphere and water and helps maintain oxygen at its saturation
concentration.
Introduction
The objective of this paper is to examine the theory, measurement, and prediction of reaeration
in flowing bodies of water while also discussing deoxygenation and the Streeter-Phelps equation.
The U.S. Environmental Protection agency defines reaeration as “a natural physical process. It is
the net rate of transfer of oxygen from the atmosphere to a body of water with a free surface.” A
more updated description described reparation as “the introduction of air into the lower layers of
a reservoir. As the air bubbles form and rise through the water, the oxygen dissolves into the
water and replenishes the dissolved oxygen. The rising bubbles also cause the lower waters to
raise the surface where they take the oxygen from the atmosphere.”
Notes
 The transfer occurs at the air/water surface.
 Reaeration is at a minimum of zero when the dissolved oxygen concentration is at
saturation and it is at a maximum when the dissolved oxygen concentration is zero.
 Sometimes called surface reaeration.

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 The transfer rate is dependent on the turbulence of the surface water. Turbulence at the
surface water is affected by water velocity, depth, and wind speed. This will be discussed
in further detail later.
 dDO/dh (rate of change of dissolved oxygen) decreases as depth increases.
 When a river or stream is stratified, reaeration is limited to the surface. Stratification
limits exposure to reaeration due to a warm layer isolating the top surface layer.
The Effect of Oxygen-Demanding Wastes on Rivers
Dissolved oxygen is necessary for life forms inside water. It is a common measurement of how
healthy a river or stream is. Once the dissolved oxygen drops below 4 or 5 mg/L, the number of
life forms capable of living in the water is greatly reduced.
The rate of reaeration is equivalent to the rate at which oxygen is replenished. It is assumed to be
proportional to the dissolved oxygen deficit (saturated value of dissolved oxygen minus the
actual dissolved oxygen at a given location downstream) and the reaeration constant. This
process is given by the equation below.
Rate of Reaeration= krD *Equation 1
where
kr= Reaeration constant (time-1)
D= Dissolved oxygen deficit= (DOs-DO)
DOs= saturated value of dissolved oxygen (mg/L)
DO= actual dissolved oxygen at a given location downstream (mg/L)
The reaeration rate kr is dependent on the condition of the river or stream. High velocity water
bodies will have much higher reaeration rates than a slow one.

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There is not set universal equation for the relationship between key river and stream parameters
and the reaeration constant. The most commonly used formula is given as:
kr= (3.9u.5)/(H1.5) *Equation 2
where
kr= reaeration coefficient at 20°C (day-1)
u= average stream velocity (m/s)
H= average stream depth (m)
O’Connor and Dobbins developed this generalized empirical equation in 1958 to estimate the
reaeration constant based on characteristics of the stream and the molecular diffusion of oxygen
into water.
Typical values of the reaeration constant for various bodies of water are given in the table below
(Masters 213)
Table 1: Typical Reaeration Constants for Various Bodies of Water
Water Body Range of kr at 20°C (day-1) (base e)
Small ponds and backwaters 0.10-0.23
Sluggish streams and large lakes 0.23-0.35
Large streams of low velocity 0.35-0.46
Swift streams 0.46-0.69
Rapids and waterfalls >1.15
These ranges of kr are based on constant temperatures at 20°C. The reaeration rate constant can
be adjusted to other temperatures by using the following equation:
kT= k20θ(T-20) *Equation 3
where
kT= the reaction rate at a different temperature T
k20= reaction rate constant at the standard 20°C laboratory reference temperature
θ= temperature coefficient. Equal to 1.024 in cases of reaeration

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T= Temperature (°C)
Relationship of Water Temperature and Reaeration
Higher water temperatures reduce dissolved oxygen concentrations because the increase in
temperature reduces oxygen’s solubility in water. The following table from the American Public
Health Association gives an example of a sample of a river taken in 1989.
Table 2: Saturated Dissolved Oxygen Concentrations in the
San Joaquin River at Various Temperatures
Temp (°C)
Approx. Temp
(°F)
DO Concentration (mg/L)
10 50 11.5
15 59 10.2
20 68 9.2
25 77 8.4
30 86 7.7
As seen from the table, dissolved oxygen levels are higher in the winter and lower in the summer
due to the temperatures.
Stratification (surface heating) increases the temperature and therefore lowers the reaeration rate.
Flow Velocity and Reaeration
Increased flow velocity increases the mixing which therefore increases the reaeration rate. This
increased flow velocity comes from ‘releases from reservoirs, flow from tributaries, groundwater
discharge, agricultural and other water returns, storm water runoff, and discharges from
wastewater treatment plants and other urban and industrial sources.” (Reed 16)
Other Empirical Reaeration Equations
Members of the U.S. Geological Survey Database team from ASCE provided another empirical
formula on the reaeration coefficient in a report written in 1999, 30 years after the discovery of
the most commonly used O’Connor and Dobbins reaeration equation. They discovered similar

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relationships as know before. Examples are how kr increases with velocity and decreases with
depth. The study produced four equations that were divided into subgroups based on flow regime
and stream scale.
1. Pool and Riffle streams that have a low flow of Q < 0.556 m3/s
kr= 517(VS).524Q-0.242
2. Pool and Riffle streams that have a high flow of Q > .556 m3/s
kr= 596(VS).528Q-0.136
3. Channel-control streams with low flow of Q < 0.556 m3/s
kr= 88(VS).313D-0.353
4. Channel-control streams with high flow of Q > 0.556 m3/s
kr= 142(VS).524W-0.243D-0.66
where
VS= Rate of energy dissipation over reach
Q= Reach average discharge
D= Reach average flow depth
W= Reach average flow top width
These equations were determined to have a “semi empirical, energy-dissipation form [that]
provided reliable estimates of kr for a wide range of stream flow conditions. These equations are
reliable for estimates of kr for waste-load-allocation studies with financial constraints.”
(Melching 4)
Deoxygenation
The purpose of reaeration is to counteract the deoxygenation that occurs in rivers and streams.
The rate of deoxygenation at any point in a river or stream is given by the following equation:

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Rate of deoxygenation= kdLt *Equation 4
where
kd= the deoxygenation rate constant (day-1)
Lt= the BOD (Biological Oxygen Demand) remaining t (days) after the wastes enter the river,
(mg/L)
The amount of oxygen demand after time t is given as:
Lt= L0e-kt *Equation 5
where
Lt= the amount of oxygen demand left after time t
L0= ultimate carbonaceous oxygen demand
k= BOD reaction constant (time-1)
Combining equation 4 and 5, the following equation is obtained:
Rate of deoxygenation= kdL0e-k
d
t *Equation 6
Oxygen Sag Curve (Streeter-Phelps)
Deoxygenation caused by microbial decomposition of wastes constantly removes oxygen from a
river or stream. Oxygenation by reaeration does the exact opposite. These two processes occur
simultaneously in streams and rivers.
Combining the equations from the deoxygenation and reaeration sections above gives the
following equation for the rate of increase or decrease of the oxygen deficit in a river or stream:
Rate of increase of the deficit= Rate of deoxygenation-Rate of reaeration
dD/dt= kdL0e-k
d
t - krD or
D= (kdL0)(e-k
d
t-e-k
r
t)/(kr-kd) + D0e-k
r
t *Equation 7

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If the values of the streams speed and distance downstream is known and the stream or river has
a constant cross-sectional area, the equation
x= ut *Equation 8
can be used.
where
x= distance downstream
u= stream speed
t= elapse time between discharge point and distance x downstream
Therefore, equation 7 can be written as
D= (kdL0)(e-k
d
(x/u)-e-k
r
(x/u))/(kr-kd) + D0e-k
r
(x/u)
The expression for dissolved oxygen is the difference between the saturation value of dissolved
oxygen and the actual value:
DO= DOs - D
Combining the above two equations, the Streeter-Phelps oxygen sag equation is obtained:
DO= DOs – ((kdL0)(e-k
d
t-e-k
r
t)/(kr-kd) + D0e-k
r
t) *Equation 9
This equation was first obtained in 1925 by Streeter and Phelps. It models dissolved oxygen in a
river or stream along specific distances by degradation of biological oxygen demand.

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Figure 1: Streeter-Phelps oxygen sag curve
Source: http://www.sciencedirect.com/science/article/pii/S0048969703000627
Figure one is the Streeter-Phelps oxygen sag curve that plots distance and time versus the
dissolved oxygen and BOD levels. The dissolved oxygen behavior can be seen in the figure as
the bolded black line. The dissolved oxygen drops rapidly initially until it reaches a critical point
downstream. At this point, the dissolved oxygen is lowest and the river or stream conditions are
worst. After that point, reaeration occurs faster than decomposition.
The time to the critical point can be found by differentiating the oxygen deficit equation
(equation 7), setting it equal to zero, and solving for t using base e values for kr and kd:
tc= (1/(kr – kd)(ln((kr/kd)(1- (D0(kr – kd)/(kdL0))) *Equation 10
where
tc= critical time
When kr= kd
tc= (1/kd)(1-(Da/La))
Also, the denominator in equation goes to zero, so the equation must be re-derived to
D= (kdL0t + D0)e-k
d
t *Equation 11

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The Streeter-Phelps curve can be explained intuitively. At the outfall of the stream or river, there
is more organic matter being degraded from deoxygenation than that can be returned by
reaeration. This causes the big dissolved oxygen drop. The amount of organic matter decreases
further downstream which causes the dissolved oxygen to decrease too. Finally, at the critical
point, the rate of deoxygenation equals the rate of oxygen by reaeration. Reaeration overcomes
deoxygenation beyond this point so the dissolved oxygen increases back up to saturation value.
When the amount of BOD in a river is excessive and the Streeter-Phelps curve drops below an
acceptable level, aquatic plant and fish levels will decrease. Fish need dissolved oxygen water in
the water to live and will die or go elsewhere if the dissolved oxygen levels are too low. Other,
less desirable forms will take over, including fungi, filamentous bacteria, sludge, and blood
worms that cover the bottom. If dissolved oxygen levels reaches zero, then the water or stream
will be a lifeless, anaerobic stretch of water. Toxic gases such as hydrogen sulfide and ammonia
will be released.
Other Relationships of Reaeration
Reaeration and Residence Time
Increasing the rate of residence time will increase the rate of reaeration. Residence time is the
amount of time spent inside the body of water. Therefore, a higher residence gives more time to
let reaeration occur in the water.
Reaeration and Photosynthesis
As photosynthesis rates increase toward saturation levels, the rate of reaeration decreases.
Photosynthesis that occurs in aquatic plants contributes to the levels of dissolved oxygen.

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Photosynthesis releases oxygen (dissolved oxygen in this case), which in turn increases the
saturation levels. This leads to a decrease in the rate of reaeration.
Reaeration and Imported DissolvedOxygen Concentration
High imported dissolved oxygen concentration will reduce the dissolved oxygen deficit which in
turn decreases the reaeration rate.
Channel Geometry and Reaeration
Reaeration increases with river or stream channels that are wider and shallower. Wider channels
have more surface area, which in turn increases the rate of reaeration. Shallower depths allow
larger changes in dissolved oxygen for a given rate of reaeration. Weirs or riffles in channels
increases turbulence which in turn increases reaeration too.
Measuring Reaeration
The measurement of reaeration is an ongoing area of study. The three different methods for
measuring the reaeration coefficient of streams and rivers are the dissolved-oxygen balance,
disturbed equilibrium, and tracer techniques. The tracer technique is the only method that does
not need any measurements of dissolved oxygen in the river or stream. All three methods provide
different results and progress is currently being made to determine which method is the most
accurate for predicting reaeration coefficients in streams and rivers.

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Works Cited
Bacchus,, Technologist A. "FIELD MEASUREMENTS OF STREAM REAERATION
COEFFICIENT." Water Resources 13 (1981): 1-43. Ministry of the Environment. Web. 15 Mar.
2013.
Davis, Mackenzie Leo, and David A. Cornwell. Introduction to Environmental Engineering.
Dubuque, IA: McGraw-Hill Companies, 2008. Print.
"Definition of Reaeration." Reaeration Definition by Babylon's Free Dictionary. N.p., n.d. Web.
15 Mar. 2013.
Ice, George G. Reaeration in a Turbulent Stream System. Diss. Oregan State University, 1978.
N.p.: n.p., n.d. Scholars Archive@OSU. Web. 11 Mar. 2013.
Masters, Gilbert M., and Wendell Ela. Introduction to Environmental Engineering and Science.
Upper Saddle River, NJ: Prentice Hall, 2008. Print.
Melching, Charles C., and Hala E. Flores. REAERATION EQUATIONS DERIVED FROM U.S.
GEOLOGICAL SURVEY DATABASE. Diss. ASCE, 1999. N.p.: n.p., n.d. Print.
Reed, Rhonda. "Basic Concepts Related to Primary and Secondary Drivers." DO Concentrations
in Stockton Deep Water Ship Channel. N.p., n.d. Web. 11 Mar. 2013.