WATER POLLUTION CONTROL RESEARCH SERIES
16050 FOR 01/72
Symposium on
Direct Tracer Measurement
of the Reaeration Capacity
of Streams and Estuaries
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U.S. ENVIRONMENTAL PROTECTION AGENCY
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WATER POLLUTION CONTROL RESEARCH SERIES
The Water Pollution Control Research Series describes the
results and progress in the control and abatement of pollution
in our Nation's waters. They provide a central source of.
information on the research, development and demonstration
activities in the Environmental Protection Agency, through
inhouse research and grants and contracts with Federal, State,
and local agencies, research institutions, and industrial
organizations.
Inquiries pertaining to Water Pollution Control Research
Reports should be directed to the Chief, Publications Branch
(Water), Research Information Division, R&M, Environmental
Protection Agency, Washington, D.C. 20^60.
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PROCEEDINGS
of a
SYMPOSIUM
on
DIRECT TRACER MEASUREMENT
OF THE
REAERATION CAPACITY OF STREAMS AND ESTUARIES
July 7-8, 1970
COSPONSORS
Environmental Protection Agency
and
The Georgia Institute of Technology
School of Civil Engineering
SYMPOSIUM ARRANGEMENT
Ernest C. Tsivoglou, Principal Investigator, GIT
Mark A. McClanahan, Associate Investigator, GIT
Walter M. Sanders, III, Project Officer, EPA
Project #16050 FOR
January, 1972
For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 80402 • Price $1.00
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EPA Review Notic_e_
This report has "been reviewed by the Environmental
Protection Agency and approved for publication.
Approval does not signify that the contents necessar-
ily reflect the views and policies of the Environmental
Protection Agency, nor does mention, of trade names
or commercial products constitute endorsement or
recommendation for use.
ii
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ABSTRACT
A symposium on direct measurement of the reaeration capacity of streams
and estuaries was conducted in July, 1970, under the joint sponsorship
of the Georgia Institute of Technology, School of Civil Engineering,
and the Environmental Protection Agency, for the purpose of making
immediately available the results of current research on this subject
at Georgia Tech. The symposium was designed to make public for the use
of other engineers and scientists all of the available information on
the subject at that time.
The papers presented and included here provide an outline of the fund-
amentals of gas transfer in turbulent systems, the theory and applica-
tion of radiotracers for measuring gas transfer in natural waters, and
the associated field and laboratory procedures. Other papers provide
tracer-observed values of the reaeration capacity of several streams,
and comparisons with computed values obtained from well-known pre-
dictive models. A new theory regarding the relationship between the
reaeration capacity and the hydraulic properties of natural streams
is presented, together with early supporting observed results. The
effects of pollutants on the reaeration capacity, and some observed
results, are discussed in another paper. Invited papers provide the
initial results of tracer measurement of the reaeration capacity of a
small estuary, as well as the oxygen balance for an inland stream using
the tracer-observed reaeration capacity (by Georgia Tech) together with
DO and BOD data obtained independently (by EPA).
These Proceedings thus reflect the state-of-the-art of measuring and
predicting the reaeration capacity of natural streams as of July, 1970.
iii
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Page
CONTENTS
Section
I. Conclusions
II. Recommendations 3
III. Papers
A. Turbulence, Mixing and Gas Transfer
by E. C. Tsivoglou 5
B. Relative Gas Transfer Characteristics of Krypton
and Oxygen
by E. C. Tsivoglou 19
C. Field Tracer Procedures and Mathematical Basis
by J. R. Wallace 31
D. Field Hydraulic Studies
by J. R. Wallace and D. E. Hicks 1*3
E. Laboratory Procedures
by R. J. Velten 55
F. Reaeration Capacity of the Flint,South and Patuxent
Rivers
by E. C. Tsivoglou 67
G. Oxygen Balance of the South River
by A. G. Herndon 83
H. Reaeration Studies of the Chattahoochee River
by J. R. Wallace 89
I. Model Study of Reaeration Capacity of the James River
Estuary (Virginia)
by M. W. Lammering , 93
J. Field Studies in Yaquina River Estuary of Surface Gas
Transfer Rates
by D. J. Baumgartner, M. H. Feldman, L. C. Bentsen,
and T. L. Cooper 115
K. Radiological Safety
by Jon R. Longtin 139
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Page
L. Effect of Hydraulic Properties on Reaeration
by Ed-ward L. Thackston
M. Pollutant Effects on Reaeration
by L. A. Weal 165
N. Observed vs. Calculated Reaeration Capacities of
Several Streams
by J. R. Wallace 179
0. Relationships Between Hydraulic Properties and
Reaeration
by E. C. Tsivoglou
VI
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FIGURES
Paper Ho. Page
A 1. Molecular Diffusion 10
A 2. Gas Transfer in Stagnant Water 12
A 3. Gas Transfer in Turbulent Water 15
h. Basic Reaeration Equation 17
B 1. Reactor I Cchmatic 22
B 2. Open Reactor Experiment 2^
B 3- Typical Radon Test, Open Reactor 25
B ^. Relative Transfer Rates of Kr^5 and Oxygen 26
B 5. Gas Transfer Ratios, All Tests 28
B 6. Gas Transfer, Diffusivity and Molecular Size 30
C 1, Flint River, Krypton Transfer Coefficients 3^
C 2. Flint River Study Locale, Vicinity of Atlanta 36
C 3- Tracer Release Device (manual) 37
C k. Field Sampling Arrangement 39
D 1. Discharge Measurements ^5
D 2. Average Discharge Measured in Flint River
June 12-July 31, 1968 ^6
D 3. Channel Profile, Flint River, June 12-July 31, 1968 kl
D U. Average Discharge Measured in South River
August 5-September 13, 1968 ^9
D 5- Channel Profile, South River, August 5-September 13,
1968 50
D 6. Method of Adjusting Flow 51
vii
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aper No.
E 1. Pressure Pipette (not to scale) 57
E 2. Typical Response Curves 59
E 3. Typical Response Curves 60
E k. Typical Response Curves 6l
E 5. Strontium-85 and Krypton-85 Gama Spectra 63
F 1. Patuxent River Study Locale 68
F 2. Patuxent River, Oxygen Transfer Coefficients 70
F 3. South River Study Locale, Vicinity of Atlanta 71
F k. South River, Krypton Transfer Coefficients 73
F 5. South River, Krypton Transfer Coefficients 1^
F 6. Krypton Transfer Coefficients of South River 75
F 7. Flint River Study Locale., Vicinity of Atlanta 77
F 8. Flint River, Krypton Transfer Coefficients 79
F 9. Flint River (Summer, 19&9) ^
F 10. Flint River (Summer, 1969) ^2
G 1. South River Waste Assimilation 8^
I 1. James River Map 95
I 2. Counting Assembly 98
I 3. James River Estuary Model 1°1
I h. Station 31* 102
I 5. James River Estuary Model 103
X 6. Station 32 I0^
j 7. James River Estuary Model 105
j 8. Station 29 lo6
viii
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Paper No. Page
I. 9» James River Estuary Model 107
I 10. Station 23 108
I. 11. James River Estuary Model 109
I 12. Station 53 HO
J 1. FWPCA Stations, Estuary Diffusion Project,
Yaquina Estuary 118
J. 2. Cross Sections of Estuary at Conductivity Monitoring
Sites, Yaquina Bay, Oregon . 119
J. 3- Reaeration Project Segment, Yaquina River-Mile 15-19 120
J 4. Yaquina River Estuary Reaeration Project Segment,
Depth at Various Sections 121
J 5. Yaquina River Estuary Reaeration Project Segment,
Width at Various Sections 122
J. 6. Yaquina River Estuary Reaeration Project Segment,
Tidal Conditions April 7, 1969 123
J 7. Yaquina River Estuary Gas Transfer Data for
Reaeration Project 126
J 8. Yaquina River Estuary Gas Transfer Data for
Reaeration Project, September 9, 1969 127
J.: 9« Yaquina River Estuary Gas Transfer Data for
Reaeration Project, September 17, 19^9 128
J 10. Yaquina River Estuary Gas Transfer Data for
Reaeration Project, May 26, 1970 129
J 11. Research Vessel Adapted for Gas Transfer Data
and Flourometry 131
J 12. Wind Current Meter Set Up for Reaeration Project,
Station 2, Yaquina River Estuary 132
J 13. Water Current Meter Set Up for Reaeration Project,
Yaquina River Estuary 133
ix
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Paper No. page
^^^^•V^«» M^B^HV »••••• I I
K 1. One Dimensional Dispersion
L 1. Observed Versus Predicted Values of ]%> From Pro-
posed Formula 156
L 2. Observed Versus Predicted Values of ^ From
Churchill Formula 157
L 3- Observed Versus Predicted Values of K2 From
Dobbins Formula 158
L k. Observed Versus Predicted Values of K2 From
O'Connor -Dobbins Formula 159
M 1. Reactor Arrangement (pollutant studies) 168
M 2. Typical Reactor Experiment 170
M 3. Effect of Linear Alkylate Sulfonate (LAS) on the
Reaeration of Water at a Constant Mixing Speed 173
M k. South River Krypton Transfer Coefficients 175
N 1. Observed vs Calculated Reaeration Coefficients 183
G 1. Measured Reaeration Rates, Flint, South, and Pat-
uxent Rivers 192
0 2. Gas Transfer for Patuxent River Studies 193
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TABLES
Paper No. Page
E 1. Transportation Study Using Krypton-85 65
G 1. South River Deoxygenation and Reaeration Coeffi-
cients c"
I 1. Dose Solutions 9^
I 2. Rate Constants for Krypton-85 Loss and Reaeration 112
J 1. Density Distribution Near Station 2, Sept. 2, 1969 12 U
K 1. Reaeration Study of Great Miami River
K 2. Absorption of Krypton-85 Gamma by Various Materials
L 1. Standard Deviation of Prediction by Different Pre-
diction Formulas 155
L 2. Power to Which Each Hydraulic Variable Is Raised in
Various Reaeration Formulas 1°0
M 1. Summary of Alpha Tests on Linear Alkylate Sulfonate
in Distilled Water
M 2. Summary of Alpha Tests on Chattahoochee and South
River Water Samples
N 1. Comparison of Observed and Predicted Results 180
xi
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FOREWORD
This special symposium on tracer measurement of the reaeration capacity
of streams and estuaries was arranged and conducted in the interests of
immediate technology transfer, as an outgrowth of EPA Research Grant
16050 EOT, "Characterization of Stream Reaeration Capacity." During
the course of that research it was decided, together with the project
Officer, Dr. Walter M. Sanders,III, that the results already obtained
and the techniques in use had sufficient scientific and technological
significance to warrant making this information available without de-
lay to engineers and scientists in the field. Accordingly, the sym-
posium was arranged. The material presented here represents all of
the information available as of the date of the symposium. Research
under Project 160^0 EDT continued thereafter, and the complete results
of that research are presented in the subsequent report for that Project.
Ernest C. Tsivoglou,
Principal Investigator
xiii
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SECTION I
CONCLUSIONS
The tracer method for measuring gas transfer in natural streams and
estuaries makes it possible for the first time to obtain independent
field measurements of stream reaeration capacity. The technique is
fully developed and effective for application in nontidal streams.
Initial application in a small estuary has indicated some difficulty
associated with stratification of fresh and salt water flow, and for
such application considerable care must be exercised in locating the
most useful tracer release depth, as the tracer will faithfully reflect
the gas transfer that takes place in those volume elements of water that
are actually dosed.
For highly turbulent streams, it has been shown that much of the real
action of gas transfer may take place in quite short reaches and times,
and for such streams none of the available models for predicting re-
aeration on the basis of hydraulic properties provide predictions that
approach the observed'reaeration coefficients. For less turbulent
streams of smaller slope, several of the available predictive models
yield predicted values more nearly in accord with observed reaeration
coefficients.
A new model relating reaeration capacity directly to energy dissipation
has been proposed, based on the results of current rese.arch at Georgia
Tech. In this model, energy dissipation is evaluated in terms of the
change in water surface elevation between two stream locations and
the time of flow. This model has provided predictions in good agree-
ment with observed results over the entire range of observation, and
current research at Georgia Tech is directed toward further improve-
ment and refinement of this basic model relating reaeration capacity
to measurable stream hydraulic properties.
Studies of the effects of pollutants on the reaeration capacity have
also been conducted, both with specific pollutants in distilled water
and with natural stream samples that contain mixed pollutants. The
initial results of this research indicate that detergents (LAS) de-
cidedly reduce the reaeration capacity, depending upon the concentra-
tion and the degree of turbulent mixing, and have demonstrated that
the addition of partially treated domestic sewage to a stream can
significantly reduce the natural reaeration capacity of the stream.
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SECTION II
RECOMMENDATIONS
As a result of this state-of-the-art review of available information on
measuring the reaeration capacity of natural streams, it is recommended
that current research in this field be directed toward developing im-
proved understanding of the basic relationships between energy dissipa-
tion and reaeration in natural streams, and, specifically, toward the
final development of a fully satisfactory model for predicting stream
reaeration capacity in terms of hydraulic properties that can be mea-
sured directly and with accuracy.
It is further recommended that additional research be conducted on the
important matter of the effects of various pollutants on the reaera-
tion capacity of natural streams. Such research should be directed
toward the development of improved understanding of pollutant effects,
to the point that such effects can be predicted with accuracy and con-
fidence and that the real environmental damages associated with these
effects can properly be evaluated and assigned to the responsible pol-
lution sources.
It is recommended also that a second symposium on natural stream re-
aeration be conducted at an appropriate time when sufficient new in-
formation is available regarding hydraulic models for reaeration ca-
pacity, the effects of pollutants on the reaeration rate coefficient and
on the oxygen saturation limit, and stream oxygen balances based upon
known reaeration capacity.
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SECTION III
PAPERS
Turbulence, Mixing and Gas Transfer
E. C. Tsivoglou
Introduction and Background
Reaeration refers to the ability of a flowing stream, or any other
turbulent water system, to obtain oxygen from the limitless resource
of the atmosphere. Some of you here are very familiar with this sub-
ject and some are not, so that a brief outline of the state of the art
and the principles of gas transfer in turbulent streams appear desirable
before proceeding to a discussion of the results of our research.
Stream self-purification involves two principal processes, namely:
(a) the depletion of dissolved oxygen resources due to bacterial de-
gradation of domestic and industrial organic wastes; and (b) replenish-
ment of the dissolved oxygen resource by absorption of oxygen from the
atmosphere. The second process, reaeration, is a direct function of
turbulence, but we have no way of measuring turbulence independently.
Other natural processes modify the oxygen balance in a polluted stream
or reservoir: the anaerobic decomposition of benthal deposits of
settleable organic matter results in a local demand on stream DO re-
sources j if algae are present in large numbers, they will add oxygen to
the stream during daylight hours by photosynthesis and will consume
DO during the dark hours by respiration; in some streams, prolific
growths of attached bacterial slimes have a great influence on the oxygen
balance in the flowing water; the situation is often further complica-
ted by the presence of multiple sources of pollution and tributary
flows. All of these oxygen-influencing processes occur simultaneously
in a polluted stream, to lesser or greater degree, and in a specific case
any one of them may dominate the total self-purification process.
Stream self-purification is thus a very complex process in any real sit-
uation. Unfortunately, we do not have methods for the independent eval-
uation of each of the above oxygen-influencing processes, and that is why
we have been unable until recently to obtain accurate evaluations of
oxygen uptake from the atmosphere—we do not know how to evaluate turbu-
lent mixing, which controls rea»ration, and we cannot obtain accurate in-
dependent evaluations of some of the other processes such as photosynthe-
sis and bioextraction.
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Indirect ^valuation of Reaeration - Prior to the development of the
tracer method for direct and system-independent evaluation of gas
transfer, in 1966, all estimates of oxygen income by stream reaera-
tion in real situations had to be made by an indirect oxygen balance
procedure. In essence, an attempt is made to evaluate all of the
other processes that have influenced the observed stream DO profile,
£nd~then a calculation is made of what the reaeration oxygen income
must have been in order to produce the observed DO profile. The
I5p7oSch~in^ch the same as that used in estimating the bottom
"roughness" of a stream in calculations related to open channel flow -
one cannot obtain a system-independent direct measure of roughness,
either.
Application of the indirect method of estimating stream reaeration
requires that a mathematical model for the observed DO profile be
available, and, of course, the development of such a model requires
?hat certain simplifying assumptions be made. The earliest such model
was the famous oxygen-sag equation provided by Streeter and Phelps
in 1Q25 (l) This still stands, more than fifty years later, as one of
the greatest single contributions in the field, and is still widely used.
Its logic is clear, simple and faultless. Of course, as with any such
model of natural processes, it is idealized, and the simplifying assump-
tions that were necessary in order to develop the model also limit its
application and effectiveness - and this was recognized by Streeter and
Phelps, as well as by others who came later. Nevertheless, the simple
oxygen-sag model provides the necessary basis for understanding stream
self-purification.
The oxygen-sag model incorporates only the effects of bacterial degrada-
tion of the dissolved organic pollution and reaeration, and neglects
benthal decomposition, photosynthesis, bottom slimes and such secondary
processes. So that it is a little too simplified and idealized for
practical application in many of today's pollution problems. For
example, if an organic sludge deposit is present, and we ignore it in
using the oxygen-sag equation for an indirect estimate of reaeration,
we calculate a reaeration oxygen income that is not quite right. In
addition to such errors of omission, even the process by which the
stream bacteria degrade the dissolved organic pollution may, in some
cases, be more complex than envisioned in 1925 by Streeter and Phelps.
One cannot ignore, either, the real errors of field and laboratory
measurement that creep into any real study of a natural situation.
The net result of such unavoidable errors of assumption, omission and
field measurement is that indirectly calculated estimates of reaeration
income contain an unknown degree of error, small in some cases and
undoubtedly large in others. In point of fact, the reaeration rates
calculated by the indirect method contain an error that simply compen-
sates for all of the other errors of assumption, omission and measure-
ment that have been made. As a result, it has not been possible to
accept such indirect estimates of reaeration as firm or accurate.
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Predictive Models - Because of the above-noted problems of indirectly
evaluating stream reaeration, various investigators have attempted over
the past 60 years to develop rational mathematical models for the re-
aeration process itself. Such models generally attempt to explain
reaeration in terms of turbulence theory and stream hydraulic properties
such as velocity and depth. The first such model was provided in 1911
by Black and Phelps, in a report on the pollution of New York Harbor (2).
That model, which attempted to explain reaeration in terms of molecular
diffusion, stream depth and a "mixing period", is still in use today (3).
Since 1911, other attempts have been made to explain reaeration in terms
of the hydraulic properties that are associated with turbulent mixing.
Some of the better known models include those of Streeter and Phelps
(1925),(l) O'Connor and Dobbins (1956)(4) and Churchill et al. (1962) (5),
all of which consider reaeration (and turbulence) to be directly related
to stream velocity and inversely related to stream depth. Other models
include that of Krenkel and Orlob (6) who attempted to explain reaeration
in terms of longitudinal dispersion, and the Thackston model (7) which
incorporates hydraulic slope as an additional factor.
All such mathematical models for stream reaeration are referred to here
as predictive models, rather than indirect, as their purpose is to pre-
dict reaeration independently in terms of hydraulic factors. In all
cases, their development has been hampered and limited because the only
means of testing the model has been indirect calculation of the real
reaeration income by the questionable oxygen-sag approach. Hence, all
of the predictive models must still be regarded as possible but not
proved.
The predictive models for reaeration will be discussed in greater detail
later. They are regarded as most important, as they represent the neces-
sary direction of development, that is, the explanation of reaeration,
and the ability to predict it, in terms of hydraulic properties. Thus,
although any or all of the predictive models may prove eventually to be
not quite adequate or correct, all of them provide necessary emphasis
and insight into the important relationships between reaeration, gas
transfer, and turbulent mixing in natural streams.
Purposes of This Research - Recognizing the real need for an independent
means of evaluating stream reaeration capacity with accuracy and depend-
ability, in 1964 the Federal Water Pollution Control Administration began
studies to develop such a procedure. The result of those studies has
been the gaseous tracer method that forms the basis of the studies to be
described at this symposium. The tracer method for reaeration was first
demonstrated in the field during 1966, in studies of the pollution and
self-purification of the Jackson River below Covington, West Virginia.
Those field studies demonstrated the techniques and effectiveness of the
reaeration tracer procedure, and produced the first direct and indepen-
dent observations of stream reaeration capacity.
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The research reported at this symposium was begun in 1968, and has been
sponsored by a grant from the Federal Water Pollution Control Administra-
tion to Georgia Tech. It has been conducted through our School of
Civil Engineering by the Sanitary Engineering staff and Georgia Tech
students. The purposes of the research have been:
(l) To evaluate and define the basic relationships between natural
stream reaeration capacity and measurable stream hydraulic proper-
ties, by means of direct field tracer and physical studies in local
streams.
(2) As a part of the research, to evaluate currently available pre-
dictive models for reaeration, in terms of accuracy, range of error,
etc.
(3) As needed, to develop modified predictive models, or additional
models, for predicting stream reaeration capacity on the basis of
measurable hydraulic properties.
(4) To develop a standardized procedure for evaluating the effects of
pollutants on stream reaeration capacity, and to apply this tech-
nique to evaluate the effects of various pollutants such as deter-
gents, oils, municipal wastes, etc.
As an incidental but not negligible purpose, the research program would
also provide useful reaeration data for real pollution problems in the
Atlanta and Georgia Tech vicinity.
Fundamentals of Gas Transfer
Reaeration is a purely physical process that involves: (l) entry of
oxygen molecules from the atmosphere into the water at the air-water
Interface; and (2) subsequent distribution of this dissolved oxygen
throughout the volume and depth of water. The driving force for reaera-
tion (or for the transfer of any other gas) is simply the partial pres-
sure difference of oxygen between the atmosphere and the water. When
the water achieves a partial pressure of dissolved oxygen that is equal
to the partial pressure of oxygen in the atmosphere, the water is said
to be saturated with oxygen, and there will be no further net oxygen
transfer.
The entry of oxygen molecules into the water from the atmosphere, and
their subsequent distribution throughout the water volume and depth
involve: (l) molecular diffusion and (2) dispersion, or mixing.
Diffusion and dispersion are two quite different processes, although
they complement each other, and the technical literature is somewhat
confusing at this point. For instance, the commonly-used terms eddy
diffusion and hydrodiffusion really refer to dispersion or mixing,
rather than to the molecular diffusion process so well known in science,
It is also important to bear in mind throughout this discussion that
8
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the water can obtain additional oxygen only at the air-water inter-
face, or the water surface. Figures 1 through k provide a brief out-
line of the fundamentals of the diffusion and dispersion processes,
and of their respective roles in reaeration and gas transfer.
Molecular Diffusion - Referring to Figure 1, if I could place a
group of dissolved molecules (such as salt, or a gas) at some point
in a beaker of stagnant water, and do this without disturbing the water,
the dissolved molecules would: (a) gradually spread out through the
water, and (b) eventually achieve a uniform concentration throughout
the water in the beaker. They would do this without any movement at
all of the water itself, or in totally quiescent water. They would do
it because of their own inherent kinetic energy. This is the process
referred to as molecular diffusion.
Referring again to Figure 1, all molecules possess inherent kinetic
energy associated with their surrounding temperature, and the average
kinetic energy is just 3/2 kT, where k is the Boltzmann Constant, and
T is the absolute temperature. In terms of mass and velocity, then,
molecules of a specific mass will move about with a specific velocity,
on the average, according to the model KE = 1/2 mv2. The dissolved
salt or gas molecules therefore move about as shown by the arrows in
Figure 1, and this motion is entirely random and takes place in random
directions. It is this movement due to inherent kinetic energy that
allows the dissolved molecules to spread out and achieve uniform con-
centration in the beaker of water, by molecular diffusion.
Pick's first law of diffusion places molecular diffusion on a quantita-
tive basijg. Referring to Figure 1, J is the net flux of molecules
(in mg/cm /sec) across any plane within the volume of water; dc/dr refers
to the concentration gradient across the plane (dc represents the dif-
ference in concentration of dissolved material on the two sides of the
plane, and dr represents the infinitesimal distance from one side of the
plane to the other), and is the driving force for diffusion; Dm is
referred to as the coefficient of molecular diffusion, and its magnitude
depends upon the molecular characteristics of both the diffusing mole-
cules and the surrounding medium.
In 1905, Albert Einstein developed an equation for evaluation of the
molecular diffusion coefficient, based upon his studies of the Brownian
motion. Referring to Figure 1, the diffusion coefficient, D^, is seen
to be equal to the product of the universal gas constant, R, and the
absolute temperature, T, divided by Avogadro's number, N , and a "fric-
tion factor", f, related to the ability of the surrounding medium to
impede the progress of the diffusing molecule.
A little later, Stokes further defined the friction factor, f, for
spherical particles falling freely through water, and showed the fric-
tion factor to be directly proportional to the viscosity, T], of the
medium and the radius, r, of the falling sphere. Hence, the diffusion
coefficient, 1^, is seen to be a function of the absolute temperature,
the viscosity of the fluid and the size of the diffusing particle.
9 ,
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• • I •/. «
KE = kT
Fick's First Law:
(rag/cm /sec) = (cm /sec) x
Dm =
RT
N f
o
(Einstein)
f = 6rrT|r
(Stokes)
Hence,
Dm = ffT,1),r)
and
dc
= .driving force for diffusion
FIGURE 1
MOLECULAR DIFFUSION
10
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Now a word about gas molecules, and regarding them as spheres. If we
could take a single oxygen molecule and set it down on a table, and
hold it still, it would not look like a sphere. Presumably, this
diatomic molecule might look something like a dumbbell. However, one
cannot set it down on a table and hold it still long enough to look
at it, because this single molecule is constantly in motion. First,
it has what we call "spin", and it spins like a top about an axis;
secondly, the axis itself "precesses", as though the top were wobbling,
about some other axis; thirdly, the molecule possesses "dipole moments"
and "quadrupole moments" related to the movement of. the atoms with
respect to each other. The combined effect of all of these motions is
to make the molecule behave like a sphere, even though it wouldn't look
like one if it could sit still on a table. Nor will the effective dia-
meter of the operating sphere be the same as the length of the quiet
dumbbell. The effective diameter of the spherical gas molecule is of
the order of angstrom units (1 angstrom = 10 cm).
To summarize, then, molecular diffusion takes place because of the
inherent kinetic energy of the diffusing molecules and in proportion
to the magnitude of the existing concentration gradient; the diffusion
coefficient is a function of the absolute temperature, the viscosity of
the fluid medium and the size of the diffusing molecules.
Figure 2 illustrates the mechanics of gas transfer in completely quies-
cent water. The water is completely still, there being.no temperature
gradients, convection currents, or other motion of volume elements of
vater. (Although such a system might well be impossible to achieve
experimentally, the concept is valid and suitable for our purposes here).
Initially, there is no dissolved oxygen at all in the water, so that
initially oxygen molecules move only into the water from the overlying
atmosphere.
A little later, there will be available dissolved oxygen molecules in
the upper water layer near the water surface; they also are in constant
movement due to their inherent kinetic energy, and they move in random
directions. Some of them escape again to the overlying atmosphere,
while others thus diffuse to deeper water layers. However, oxygen mole-
cules are able to enter the topmost water layer from the overlying atmos-
phere more easily than they are able to diffuse downward through the
fluid medium. As a result, the dissolved gas molecules accumulate fairly
rapidly in the uppermost water layers, and those layers become "satura-
ted."
At any time after the start of the experiment, the net rate of entry of
gas molecules at the air-water interface is just the rate of entry from
above (constant, because the overlying atmosphere has constant oxygen
concentration) minus the rate of escape back to the atmosphere (propor-
tional to the dissolved oxygen concentration in the uppermost water
layer). Because of the relatively rapid accumulation of gas molecules
in the topmost water layer, the net rate of entry (or, reaeration) soon
becomes very small.
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C2
Ah
hi
T
depth
(C. - C ) = AC = very small
= very small
.*. J ~ - Dm () = very small
FIGURE 2
GAS TRANSFER IN STAGNANT WATER
12
-------
As a result, the deeper water layers soon become "starved" for oxygen
molecules. Referring to Figure 2, across any infinitesimal distance
(depth) Ah, the dissolved oxygen concentration difference, Ac =
(c]_ - 02), is infinitesimally small. Hence, at any depth and at any
time, the driving force for molecular diffusion, the concentration
gradient (Ac/Ah), is very small. Referring back, then, to Fick's law,
diffusion of oxygen molecules downward is very slow, and reaeration of
truly stagnant water is a very slow process that requires days or weeks
before the bottom layers of water approach DO saturation. The whole
process is slow because of the blocking action of molecular diffusion,
Turbulent Mixing - Consider now the same beaker of water, but no longer
quiescent. Instead, the water is being mixed by some external force
(perhaps the beaker is sitting on a vibrating platform). We will be
concerned now primarily with volume elements of water, rather than with
molecules of oxygen. We define a volume element to be infinitesimally
small in the calculus sense, but large enough to contain a very large
number of molecules.
Referring to Figure 3, at the start of our experiment the water contains
no dissolved oxygen. Volume element No.l moves up to the water surface
from below and remains there for a definite, if very small, period of
time. Because it contained no dissolved oxygen, the net rate of entry
of gas molecules from the overlying atmosphere is very large - at a
maximum - and the volume element gains a relatively large amount of
dissolved oxygen before it leaves the surface to move downward to a
deeper location. In its downward path it encounters a second volume
element of water, No.2, that has never been at the water surface and so
contains very little or no dissolved oxygen. Thus, the one volume ele-
ment contains quite a large amount of dissolved oxygen compared to the
other, and at the interface between them there is a large concentration
difference, Ac = (c^ - eg). Hence for that moment across that inter-
face, the driving force for molecular diffusion, (Ac/Ar), is relatively
large, and the transfer of dissolved gas molecules from the one volume
element to the other is relatively rapid.
If we now multiply this example by all of the volume elements of water
in the beaker, it is clear that mixing greatly speeds the reaeration
process. The water surface is constantly replaced by volume elements
from below, and hence the blocking action of molecular diffusion is no
longer present. The lower water depths are no more starved for dissolved
oxygen than the upper locations. The average concentration of dissolved
oxygen is at any time the same at all depths and all locations, includ-
ing the surface, in a homogeneously mixed system, and, hence, the net
rate of entry of gas molecules at the water surface remains relatively
large until the whole volume of water approaches the DO saturation con-
centration. Note also that the dissolved oxgyen concentration gradient,
(Ac/Ar), does not now occur in any preferred direction, such as downward.
Instead, there is an average concentration gradient throughout the whole
volume of water, and it is multidirectional.
13 '
-------
It is also clear that the faster the water is mixed, and the surface
replaced, the faster will be the reaeration process. Instead of days
or longer, the water can be saturated with dissolved oxygen in minutes
at high rates of mix. Thus, molecular diffusion keeps up with mixing
in the turbulent system, instead of blocking reaeration. It is also
important to note that in the mixed system the depth of water has
nothing to do with the rate of reaeration except insofar as the depth-
to-volume ratio influences the physical rate of water surface replace-
ment.
So far as reaeration is concerned, then, the term "turbulence" has a
special meaning relating strictly to the rate of water surface replace-
ment and to the dispersion of volume elements of water. Turbulent mix-
ing of the water and consequent dispersion of the dissolved gas mole-
cules takes place due to the application of external forces, such as
the platform vibration, or a mechanical stirrer, etc. It enhances
molecular diffusion and reaeration as outlined above.
Misconceptions - The foregoing outline of the fundamental mechanisms of
gas transfer in turbulent water systems indicates that certain widely
held concepts of gas transfer are not, in fact, correct representations
of the physical facts. In the first place, in a well-mixed system, or
in a turbulent natural stream, the surface water layer is not saturated
with dissolved oxygen - constant surface replacement precludes this.
Also, as indicated above, there is no preferred direction of oxygen
transfer, such as downward, and the physical depth of a watercourse
influences reaeration only to the extent that it influences the rate
of water surface replacement in the hydraulic sense.
In particular, in a homogeneously mixed system no stagnant surface water
"film" can exist for any finite period of time, and, hence, even though
it may be an adequate mathematical convenience in some situations, the
"film theory" of gas transfer is wrong in concept. The film theory
denies the obvious fact of physical surface water replacement, and is
based upon the false supposition that a dissolved oxygen concentration
gradient is not present within a well-mixed system - as has been seen,
such a concentration gradient is the driving force for diffusion, and
must exist everywhere within the unsaturated fluid volume.
A clear distinction must therefore also be made between physically
impossible stagnant surface water films and physically real hydrodyna-
mic upper layers of water in a system that is not homogeneously mixed.
For example, in a stratified reservoir the whole volume of water is
physically or hydrodynamically separated into two distinct regions -
the lower region has little opportunity for reaeration because its
volume elements never reach the air-water interface. In that case,
then, the hydrodynamic situation prevents surface replacement and
reaeration is very slow. However, this has to do with the hydraulic
properties of the system, and has nothing to do with the film theory.
1U
-------
h
" (Ar)
• T — -1
. . J — —J
AC
FIGURE 3
SAS TRANSFER IN TURBULENT WATER
1 5
-------
Basic Reaeration Model - Referring now to Figure 4, the familiar basic
reaeration equation is shown, and states simply that the rate of change
of the dissolved oxygen saturation deficit, D = (C - C), is propor-
tional to the deficit at any time. In that model, Cs is the saturation
concentration of DO in the water, and C is the momentary average DO con-
centration in the water. The proportionality constant, Kp, is the
reaeration rate coefficient. The saturation deficit, then, is the driv-
ing force for reaeration, and is proportional to the oxygen partial
pressure difference between the air and water.
The basic reaeration equation has been derived elsewhere from simple
first principles, (8) where it has also been shown that Kg, the bulk
gas transfer coefficient, is proportional to the rate of surface re-
placement per unit volume, (ny), and that the proportionality constant,
a, is directly related to the molecular diffusion coefficient, Dra. Thus,
the coefficient, a, is a constant for oxygen in clean water at any fixed
temperature, but will be a function of temperature and may also be
modified by the presence of pollutants.
The rate coefficient, KO, is what we are after, and what is measured
in the field by the tracer method to be described in the following dis-
cussions. As indicated in Figure k, it is a function of the water
surface area, A, and the volume, V, and the rate of surface replacement,
n, in new surfaces per unit time. However, it should be noted that the
ratio (A/V) is properly regarded as the reciprocal of the whole depth
of water only if mixing is homogeneous in terms of surface replacement.
Thus, for example, the average whole depth of water in a stratified
reservoir is meaningless as a measure of Kg or reaeration capacity. In
point of fact, it is probable that most natural watercourses are not
homogeneously mixed, and hence the average depth of flow is not a use-
ful measure of the depth that is effective in reaeration, or of the
effective volume.
The purpose of our research, then, has, been to define the hydraulic
properties that determine Kg in real streams; this is tantamount to
attempting to define the rate of surface replacement in terms of
measurable hydraulic properties such as velocity, depth, time of flow,
hydraulic gradient, hydraulic radius, flow, roughness, wetted perimenter;
etc. This research, and its results, will be described in the follow-
ing papers, after the basic tool, the tracer procedure, has been out-
lined.
16
-------
in turbulent water:
dC A . -.v
at = an v (Cs " c)
5 -rr = - K0D ("basic reaeration equation)
C-
where
D = (C - c) = driving force for gas transfer in
turbulent water
= an — = bulk gas transfer coefficient
a = related to diffusion coefficient, Dm
= constant for oxygen in clean water at any one
temperature.
f Ax 2 ^
(n —) = cm of new surface exposed per unit time
and per unit per unit volume
FIGURE k
BASIC REAERATION EQUATION
1 7
-------
Bibliography
1. Streeter, H. W., and Phelps, E. B., A Study of the Pollution and
Natural Purification of the Ohio River. III. Factors Concerned in
the Phenomena of Oxidation and Reaeration, Pub. Health Bull. No.
14b, U.S. Pub. Health Serv., Washington, D.C. (1925).
2. Black, W. M., and Phelps, E. B., The Discharge of Sewage into
New York Harbor , Report to the Board of Estimate and Apportion-
ment, New Jersey City (March, 19Tl) •
3. Velz, C. J., Applied Stream Sanitation , Wiley-Interscience,
John Wiley & Sons, New York, N.Y. , 619 PP- (1970).
4. O'Connor, D. J., and Dobbins, W. E., "The Mechanism of Reaeration
in Natural Streams", Journal Sanitary E_ng« Div., Proc. Amer.
Soc. Civil Engr., 82, No. SA6, 1115 (1956).
5. Churchill, M. A., Elmore, H. L., and Buckingham, R. A., "Prediction
of Stream Reaeration Rates", Jour. San. Eng. Div., Proc. Amer. Soc.
Civil Engr., 88, No.SA^, 1
6. Krenkel, P. A., and Or lob, G. T., "Turbulent Diffusion and the
Reaeration Coefficient", Jour. San. Eng. Div., Proc. Americ. Soc.
Civil Engr., 88, SA2, 53 (March, 1962)7
7, Thackston, E. L., and Krenkel, P. A., "Reaeration Prediction in
Natural Streams", Jour. San. Eng. Div., Proc. Amer. Soc. Civil
Engr., 95, SA1, 65 (19&9)-
8. Tsivoglou, E. C., Tracer Measurement of Stream Reaeration,
Fed. Water Pollution Control Admin ., Washington, D.C. (19&7)j
U. S. Gov't Printing Office, Washington, D.C. (1969).
18
-------
Belative Gas Transfer Characteristics
of Krypton and Oxygen
E. C. Tsivoglou
In a polluted stream, the DO may be simultaneously depleted and
replenished by a number of different natural processes, not all of
which can be evaluated at any moment. Stream self-purification is
quite complex, in that there are too many unknowns. As a result,
despite the numerous attempts to do so over the past 60 years, it
has not been possible to make accurate and dependable evaluations of
stream reaeration capacity on the basis of field measurements of DO.
But stream reaeration is the key to self-purification, and the deter-
mining factor as regards the necessary degree of waste treatment and
resulting costs. Hence, accurate evaluation of stream reaeration
capacity has remained a problem of major importance in water pollu-
tion control.
This is a classical situation for the use of tracers. Specifically,
it is a situation in which a gaseous tracer for oxygen can be used
to circumvent, or evade, problems of measurement that have proved
to be otherwise insurmountable. In order to apply such a tracer tech-
nique successfully we need to:
(a) Select a suitable gaseous tracer for oxygen (one that is
not affected by so many additional natural processes);
(b) Be able to observe the gas transfer behavior of the tracer
in the stream, under field conditions;
(c) Be able to translate this field tracer information to the
corresponding gas transfer behavior of oxygen under the
same field conditions.
This discussion is concerned with the problems of selecting a suit-
able gaseous tracer for oxygen and establishing the necessary rela-
tionships regarding the gas transfer behavior of the tracer gas and
oxygen, or with problems (a) and (c) above. The following paper
will consider the problem of field application, or problem (b) above.
Selection of Tracer
In order to serve as a suitable tracer for oxygen, the tracer gas to
be used must meet a number of specific requirements. In particular,
the gaseous tracer should be:
(a) Chemically and biologically inert, to the extent possible,
at expected temperatures, pressures, etc.
19
-------
(b) Relatively simple to detect and measure, and not subject
to interferences due to the presence of a wide variety of
pollutants.
(c) Measurable at low concentrations.
i
Of course, the tracer should also be relatively easy and safe to
use under both laboratory and field conditions, and should not itself
bring about any effects on the gas transfer characteristics of oxygen
or the hydraulic characteristics of the water.
In regard to the first requirement, the monatomic ("noble") gases such
as argon, neon, krypton, xenon and radon seem most likely to be suit-
able. They have complete outer electron shells and are known to be
chemically and biologically inert as a result. Hence, there should
be no chemical reaction of the tracer gas with naturally present dis-
solved materials or with pollutants. Nor should the monatomic gases
be subject to extraction or degradation by the aquatic biota, even
in the presence of large biological populations of one kind or another.
They are different in that oxygen is a diatomic gas, but as outlined
earlier (behavior of gas molecules as spheres) this should not reduce
their effectiveness as a reaeration tracer. In brief, the monatomic
gases should not be affected by the many chemical and biological
natural processes that affect dissolved oxygen concentration, and
should make excellent reaeration tracers from that standpoint.
If it is to be used effectively as a tracer under real field condi-
tions, the tracer gas must be relatively simple to detect and measure,
and measurable at very low concentrations. As a corollary, a little
must go a long way in field operations, otherwise problems of prepar-
ing and handling large field tracer doses might restrict its useful-
ness to quite small streams. Clearly, the best solution to these
problems of detection and sensitivity is the use of radioactive iso-
topes of the monatomic gases. For the radioisotopes, detection and
measurement techniques and equipment are well-known and readily
available, and are simple and direct. They are also highly sensitive,
and extremely small concentrations of radioactive material can be
measured with great accuracy and dependability. Hence, the most
likely gaseous tracer for stream reaeration appears to be a suitable
radioactive isotope of one of the inert monatomic gases.
Of the monatomic gases, argon appears to be most nearly like oxygen
in molecular characteristics (molecular weight, molecular diameter),
and would probably be the most suitable tracer from that standpoint.
However, no suitable radioactive isotope of argon is commercially
available (either the half-life is too short, or the radioactive emis-
sion is not detectable and measurable by commonly used techniques
and equipment). Radon could be used, but is not as readily avail-
able as others and its decay products, or daughters, are numerous
and also radioactive, and subject to chemical and biological uptake
and exchange in the stream. A suitable radioactive isotope of xenon
20
-------
is available, and could be used as a reaeration tracer, even' though
its half-life is a little short for convenience (about 5 days). For
various reasons, including availability, detectability, half-life,
etc., an isotope of krypton, °^Krf has appeared to be the best avail-
able tracer, and has been selected for application in streams. Its
half-life is long (about 10 years), and this could become a disad-
vantage if the stream reaeration tracer procedure were to become too
widely used. In that unlikely event, further consideration should
be given to the use of the shorter-lived radioisotope of xenon.
Relative Transfer Properties of Krypton and Oxygen
Having selected krypton-85 as the most suitable tracer for stream
reaeration, the next and most important task is to establish, if
Possible, a firm relationship between the transfer properties of
the tracer and oxygen. It is necessary that the tracer faithfully
Deflect oxygen transfer under a wide variety of conditions, espe-
cially of turbulent mixing, temperature, etc.
shown earlier, reaeration is a direct function of turbulence in
of surface water replacement, the greater the turbulence the
Caster the reaeration process. But there is available no procedure
°y which turbulence, or the rate of surface replacement, can be
accurately and independently evaluated. Hence, for example, it is
^ot really possible to reproduce truly identical conditions of tur-
"Ulent mixing from one experiment to the next, even in the labora-
tory. On the other hand, for the tracer procedure to be successful,
*t will be necessary to relate the transfer of krypton-85 to oxygen
transfer under the same conditions of turbulence. The solution to
this experimental problem has been the trick of simultaneity, by
^hich the problem of measuring turbulence is evaded, rather than
Directly solved.
'igure 1 shows the laboratory test system used to establish the rela-
tive transfer properties of krypton and oxygen. In brief, in any
si*igle experiment the transfer of both gases is observed simulta-
^eously in the single turbulent system. As a result, it can be known
that for that experiment the transfer of both gases did occur under
t*"uly identical conditions of turbulent mixing, even though the
degree of turbulence is not measured and remains unknown.
turbulence problem is thus avoided.
I consisted of an open cylindrical recirculating water
factor, with external appurtenant equipment as shown in Figure 1.
^e reactor and most of the external tubing were immersed in a con-
stant temperature bath. Two reactors were used, one of 10-inch and
°le of 12-inch diameter, each 12 inches deep.
Deferring to Figure 1, the test water flowed out of the1 bottom cen-
t**al- reactor outlet, through the pump, and then portions were
Diverted through a dissolved oxygen (DO) galvanic probe chamber, a
21
-------
FIGURE I
REACTOR I
SCHEMATIC
to
M
GEIGER
TO SCALER
• li /D-0.
QXSAMPLE
t fTl BOTTLE
I
D.O. PROBE
DISPERSION
rPLATE
TO MICROAMMETER
8 RECORDER
WATER SURFACE
•t-
t
-------
water-jacketed flow-through Geiger tube, and a sample bottle (for
measurement of DO by the Winkler method). The recombined flow
returned to the reactor under a dispersion plate located at the
bottom of the reactor vessel, and entered the reactor through a set
of peripheral holes in the dispersion plate.
The general test procedure consisted of preparing initial test con-
ditions such that the dissolved oxygen content of the test water
was quite low, whereas the concentration of dissolved tracer gas
was high. The test then proceeded at a fixed temperature and turbu-
lence condition, and the simultaneous increase of dissolved oxygen
concentration and decrease of tracer gas concentration were observed
and recorded until the oxygen concentration approached its limiting
(saturation) value. Since the water surface was open to the atmos-
phere, oxygen concentration in the test water approached, for any
"test, the limit associated with atmospheric oxygen concentrations;
the tracer gas water concentration decreased toward zero, as no
experimentally significant quantity of tracer gas was present in
the atmosphere.
Under these test conditions, oxygen is being absorbed from the
atmosphere, whereas the krypton is being desorbed, and these are
the directions of transfer that will occur under field conditions.
Also, the experimental system lends itself readily to testing under
various conditions of temperature, turbulent mixing and depth.
Figure 2 shows the kind of results obtained from a single experiment.
Both gas transfer reactions are simple first order, and a Kg value
is readily obtained for each gas. Figure 3 shows a typical set of
results from an experiment with radon, one of the other gases tested.
From each such test, a single value of the ratio
(—)
* V '
Kox
vas obtained. A series of 26 such experiments was conducted, under
Different conditions of turbulence (different depths and/or recir-
culation rates), and the results are shown in Figure U, for the
tracer gas krypton-85.
It is evident from Figure k that the ratio of Kg values for krypton-
85 and oxygen is constant for the entire range of test conditions.
From these and other tests the value of the constant is
K,
(_H) = o.83 + O.OU
Kox
Ors the slope of the straight line fitted through the data. A wide
of mixing conditions was tested (K from 0.06 to 0.52 per
as well as temperatures from 13° €o 32°C.
23
-------
c
o
•H
-P
O
e
o
to
flj
o
o
en
CO
time
FIGURE 2
OPEN REACTOR EXPERIMENT
24
-------
160
140
120
FIGURE 3
TYPICAL RADON TEST
OPEN REACTOR
20
-LU Ib 20
TIME IN HOURS
25
-------
K>
O>
0.5
0.4
03
0.2
O.I
K
~R
kr_
ox
= 0.81
O.I
0.2
A or I3°C
0.3 04
Kox/hr
0.5 0.6
0.7
FIGURE 4.—Relative transfer rates of Kr85 and Oxygen.
-------
In order to more firmly establish the krypton: oxygen transfer
ratio, and for purposes of further investigating the general nature
°f gas transfer, additional tests with krypton-85 and with other
gases were performed in the reactor of Figure 1 and in an entirely
different closed reactor in which gas transfer was measured mano-
J&etrically. The gases tested in both reactors included: hydrogen,
helium, nitrogen, oxygen, carbon dioxide, krypton and radon. Figure
5 shows the results of all tests. In each case, the slope of the
straight line is the ratio
From the foregoing series of tests performed in FWPCA laboratories,
& number of conclusions could be drawn directly:
(l) The relative gas transfer capability of krypton-85 and
oxygen, measured as the ratio of reaction rate coeffi-
cients, is 0.83 + 0.0^, the transfer of krypton-85 being
the slower process.
(2) The krypton: oxygen transfer ratio of 0.83 is not signifi-
cantly affected by temperature over the range 10 °C to
32 °C.
(3) The krypton : oxygen transfer ratio of 0,83 is not affected
by the degree of turbulent mixing over the wide range
studied .
The krypton: oxygen transfer ratio is not affected by the
direction in which the gases transfer (into or out of the
water).
(5) The krypton : oxygen transfer ratio is not affected by the
presence of a broken water surface.
(6) From limited tests with LAS and ABS, the krypton : oxygen
transfer ratio is not affected by the presence of such
pollutants.
observations and conclusions have indicated clearly that
*rypton-85 is a practical field tracer for oxygen and for stream
^aeration. Thus, a field-observed value of K. is directly trans-
•1-a-table into a firm value of K undeSr the prevailing test condi-
tions of stream flow, temperature, hydraulic properties, etc. It
^•s also clear that the observed value of K, in any turbulent water
8ystem is an accurate and independent measuFe of turbulent mixing
^ terms of the rate of surface water replacement.
27
-------
3
O
X
•s
m
<
-------
The tests with other gases led. to further conclusions regarding the
general nature of the gas transfer process, and thus further demon-
strate the usefulness of krypton-85 as a tracer. Figure 6 shows
the fundamental relationships involved in gas transfer. Pick's Law
and the Basic Reaeration Equation both apply, as outlined earlier.
The Stokes-Einstein model for the coefficient of molecular diffusion,
I>mj yields quite good numerical results for the transfer of dis-
solved gases, in terms of observed and predicted values of the dif-
fusivity.
In particular, the last relationship shown in Figure 6 is of practi-
cal importance. It can be derived by combining the other models
shown above, and was verified experimentally for all of the gases
Bested. This molecular size rule states simply that for any two
Different gases, A and B, the ratio of observable values of K? is
equal to the ratio of diffusivities of the two gases and is equal
to the inverse ratio of the molecular diameters. Thus, the larger
the gas molecule the less easily it diffuses or transfers from the
Dissolved to the gaseous phase. Using this relationship, for example,
°fle can predict accurate]^ the diffusivity of a gas, D , by compar-
*ng either its known molecular diameter or its observea transfer
behavior to that of another gas whose diffusivity is known.
The details and all of the results of the experiments referred to
^re have been published by the FWPCA and are available (l). Having
firmly established the validity of using krypton-85 as a field tracer
stream reaeration, the next paper will outline the mathematical
s for field use of the tracer and field procedures.
Bibliography
Tsivoglou, E. C. Tracer Measurement of Stream Reaerationj
Fed. Water Pollution Control Admin., June, 196?. 86 pp. U.S.
Gov't. Printing Office, June, 1969.
-------
Fick's First Law
and
dD
dt
Basic Reaeration Equation
and
RT
5nT)rN
o
(Stokes - Einstein)
w
o
FIGURE 6
GAS TRANSFER, DIFFUSIVITY AND
ST2E
-------
Field Tracer Procedures and Mathematical Basis
J. R. Wallace
Fundamental Relationships
The "basic phenomena with which we are concerned are diffusion and dis-
persion. The role played by these physical processes in stream self-
purification has "been outlined by the previous speakers. My purpose
will now be to illustrate how these phenomena can be studied in the
field by tracer techniques.
In order to understand the tracer method, it is essential that the
equivalence of two processes be made clear. These processes are (l)
adsorption of oxygen from the atmosphere into a stream (reaeration)
&nd (2) desorption of a tracer gas from a stream into the atmosphere.
In either case the driving force is the concentration deficit, D. In
the reaeration process the deficit is the difference between the con-
centration of oxygen in the water at the point of saturation, Cg, and
the oxygen concentration that actually exists, C. Thus,
D = (C - C)
ox N s ox
Likewise, the driving force for a tracer gas (in our studies we use
toypton-85) dissolved in the stream is the difference between the con-
centration of the tracer in the stream and the concentration in the
atmosphere . Since the concentration of our tracer gas in the atmosphere
^sj for all practical purposes, equal to zero, the deficit is simply
the concentration in the stream, C, ; that is
Dkr = Ckr
As long as the concentration of oxygen in the stream is less than the
saturation value, there will be a net movement of oxygen into the
stream from the atmosphere, which will tend to reduce the deficit. In
a similar manner the net movement of the tracer gas will tend to de-
Cz>ease the tracer concentration in the stream and thereby reduce the
Diving force. Both of these phenomena can be represented by the
Seneral mathematical expression
31
-------
where K is a proportionality constant which depends on the specific
gas under consideration and upon the intensity of turbulent mixing in
the stream.
If there were no factors other than turbulent mixing affecting the
quantity of dissolved oxygen (DO) in a stream, integration of (l)
would provide a means for determining the proportionality constant
for oxygen, K , through the following relation
OX
D = Doe'Koxt (2)
where D is the initial dissolved oxygen deficit (at t = 0); and D is
the deficit at any later time t. In fact there are many other factors
which affect the DO, and therein lies the need for the tracer method.
It has been shown (1) that the ratio of the proportionality constant
for oxygen, K , to that for krypton, Kkr, is constant as long as both
gases are subjected to the same conditions of turbulent mixing, i.e. ,
•tr
(~£) = constant (3)
IV
OX
(A theoretical explanation for equation (3) will be presented in a
subsequent lecture.) This relationship between the proportionality
constants, together with the fact that the tracer is chemically inert
and is not subject to extraction or degradation by aquatic biota,
makes it possible to use equation (2) to compute Kfcr and, through equa-
tion (3)>to determine the value of K .
OJ£
The tracer method is not quite as simple as it may appear at this point
in our discussion, and it is necessary to consider the field procedures
in greater detail. Consider two points A and B which lie on a stream,
let A be the upstream point, and let a quantity of dissolved krypton-85
be introduced at a point upstream from point A. If this tracer dose
were introduced uniformly across the stream cross section, and if
there were no vertical or horizontal velocity gradients in the stream
causing dispersion and if there were no tributaries causing dilution,
then the numerical value of Kj^, for the reach AB could be obtained
from equation (2):
(10-
where C. and CB are the dissolved krypton-85 concentrations at A and B
and t is the travel time of flow between A and B. However, we do have
dispersion and we do have dilution and they must be taken into account
if this method is to be accurate.
32
-------
Direct measurement of dispersion and dilution is not required; a cor-
rection to equation (h) is made possible by using an additional tracer.
The second tracer is tritium in the form of tritiated water. Tritiated
water is released in the stream simultaneously with the krypton-85.
The tritiated water provides an accurate measure of dispersion and di-
lution. The concentration of tritium decreases between sampling sta-
tions because of dispersion and dilution, but, being in the form of
tritiated water molecules, tritium is not adsorbed on the stream bed
or otherwise lost in any significant amount. Because the tracers are
released simultaneously, the dissolved krypton-85 undergoes exactly
the same dispersion and dilution as the tritiated water.
Under these test conditions, the observed concentrations of tritium
provide an accurate correction for the effects of dispersion and dilu-
tion, and hence the decimal fraction of tracer gas remaining at point
B is just
Ckr
r,
'A
tr A
B "Kkrt
= e
(c, /C, ) A, B are the concentration ratios of krypton-85 and
tritium iS tne samples taken at the time of peak concentration at A
B, and t is the time of flow between the two locations.
we use only the krypton and tritium tracers we have no way of know-
when the tracers are present at the sampling stations, A and B.
Therefore, a third tracer is used to solve this problem. The third
tracer is a fluorescent dye, and it performs two functions: it indi-
cates when to sample for the invisible radioactive tracers, and it
Provides an accurate measure of the time of flow between sampling sta-
''ions. (if it were not for the fact that the dye is absorbed on the
stream bed it could be used to correct for the effects of dispersion
ari(i dilution and the tritium tracer would not be required.)
^6 three tracers are mixed together and are thus injected into the
stream simultaneously. Samples are taken from the stream as the dye
passes A and B, and the concentration of the krypton and tritium
determined in the laboratory by simultaneously counting the activi-
in a liquid scintillation counter. Thus, equation (5) is the basis
the field procedures. We measure the krypton-to-tritium ratio at
at B, we get the time of travel, t, from fluorometer recordings
o the dye concentrations at the two stations and plot the results on
Seflii-log paper (see Figure l). Equation (5) plots as a straight line
°Q semi-log paper when the concentration ratio is plotted on the log
®c&le and time is plotted on the linear scale. The slope of the line
:s equal to K. . Knowing the value of K^ , vre can obtain the value of
(or K2 as it is usually called) from the known value of the ratio of
to KQx
33
-------
w
1.
0.
0.6
O.ll
ej
§ 0,08
0.1*
o.oe
o.oi
L.75-
'•w
m (n
,015
Dump n[ Stations
Dump X !V Stations
„* 12, U
Dump XIV (
FIGURE 1
FLINT RIV8R
KRYPTON TRANSFER COEFFICIENTS
Note: All values are K2/hour
(K2>ox " 6.63'
.5 cfa)
1.85
38
10
11
-------
The procedure we use for determination of the reaeration coefficient
is based on a number of assumptions, and I would like to point these
°ut so that we can all be aware of them. The first assumption is that
the nongaseous dispersion tracer (tritium) undergoes only dispersion
8^ dilution, and is not adsorbed on the stream bed or lost in any sig-
ni? leant amount. The second assumption is that the tracer gas under-
goes dispersion to the same degree as the nongaseous dispersion tracer
ffla, in addition, is lost to the atmosphere; it is not otherwise lost
adsorption or other processes in any significant amount. Third,
tracer gas and the oxygen undergo gas transfer to the same relative
nt, and the ratio of their respective K2 values is not significantly
eted by temperature, turbidity, or the presence of pollutants.
•"ourth, the tracers are released as a truly simultaneous dose, and the
concentrations must be measured in the same downstream sample.
£igld Procedures
1 would now like to make some remarks about the field procedures we
use. Most of our studies have been conducted in the Atlanta area, but
Wlp also have studied two other rivers, one in Maryland and one in Vir-
ginia. The studies have been made, almost entirely, at low flows in
fie rivers in order to determine the reaeration coefficients for cri-
flow conditions. The sketch in Figure 2 shows one of the streams
we worked in. The sampling stations are labeled 1, 2, 3, etc.
the stream. The distances between sampling stations on this
^ were in the range of one to two miles. In all of our field work
e have always made at least two measurements for each section of river
n order to get a check on the accuracy and the repeatability of our
Measurements .
"typical field procedure includes making the dose at a point upstream
fourths sampling stations, setting up the fluorometers at the sampling
Rations, measuring the stream discharge at each sampling station, and
Electing samples from the stream to bring back to the laboratory for
us now consider these steps in greater detail. A typical flow for
Flint River (the river shown in Figure 2) was of the order of 10
cubic feet Per second (cfs). For this stream and others of simi-
size we used a dose consisting of one liter of dye, one curie of
iium, and 0.5 curies of krypton. Our doses were prepared for us by
commercial firm dealing in radioactive tracers, and the quantities
0 radioactivity specified by us were normally 1 curie of tritium and
•5 curie krypton-85, but we observed quite a lot of variation in the
quantities that we actually received. In all cases the dose was assayed
the Georgia Tech laboratory before the tracer was released.
dosing procedure we use is very simple. The dose was delivered to
8 in a one liter bottle. The bottle is placed in the dosing rig shown
G Figure 3. The dosing rig is fabricated from steel channel sections.
35
-------
w
KEY
•^DIRECTION OF FLOW
^-REPRESENTS EVERY
FIFTH CROSS SECTION
FIGURE 2
FLINT RIVER STUDY LOCALE
VICINITY OF ATLANTA
-------
TRACER RELEASE
DEVICE
(MANUAL)
BASE
STRIKER
TRACER BOTTLE
FIGURE 3
37
-------
The bottle containing the dose is placed between the channels and taped
in position. The dose is placed in the stream with the bottom of the
rig resting on the bottom of the stream. When the rig is in place, the
rod which serves as a handle for the rig is struck with a hammer. This
shatters the bottle and provides an instantaneous release of the tracer.
In the smaller streams the dye cloud is dispersed rapidly across the
stream channel and within a few yards completely fills the channel sec-
tion.
Fluorometers, instruments which provide a continuous record of the dye
concentration in the stream, are placed on the banks of the stream at
the sampling stations and put into operation before the tracer material
is released. We use three of these instruments, so we were able to
set up three sampling stations prior to making the dose. A sketch of
the fluorometer is shown in Figure U. Electrical power to run the
fluorometer and the pump is provided by a portable generator. The
first thing that is done when we arrive at a sampling station is to
take a background sample. This provides a measure of the radioactivity
and fluorescence that is naturally present at that point in the stream.
When the leading edge of the dye cloud reaches the sampling station
samples are collected by continually drawing off part of the water^that
is moving through the fluorometer. We continue taking samples until
the dye concentration has peaked and returned to a value equal to about
half of the peak concentration. The samples are bottled and shipped
back to the lab at Georgia Tech. The bottle caps are designed to pre-
vent the loss of gas and the bottles are marked and the time of col-
lection is noted in a field book. After the sampling procedure at a
station is terminated, we select three or four samples which were col-
lected near the concentration peak and send these samples, along with
background samples, into the lab for immediate analysis.
Discussion
Question; Could the procedure that you use be used in a lake or
estuary? (
-------
\ \ ONN\^ I
U£'' ] } ,J*
FIELD SAMPLING
ARRANGEMENT
GENERATOR
CONTINUOUS FLOW
RECORDING
FLUOROMETER
SAMPLE
BOTTLE
FIGURE
39
-------
Question; Will you show later, more in detail, how you collect the
samples? (JEW) Yes, I think you'll see this in the film that we s
later on; it has a good shot of just how we collect samples.
Queution; Have you done any analyses of the dye concentration curves?
(JEW)We don't normally take the complete dye curv2. This requires,
as you might imagine, a considerable amount of time in waiting for the
entire curve to pass, particularly after the flow has progressed a
number of miles. The curve, of course, gets quite elongated and so
in order to avoid this large commitment of time and personnel to
measure the complete dye curve, we have just taken the peak and down,
as I said, to about half the peak which seemed to be the most expedient
for our particular purpose.
Question; What is a typical velocity in the streams you work in?
The velocity is in the order of 1 to 2\ feet per second.
Question; What were the lowest velocities in the streams? (JEW)
the lowest were in pools. We took the velocity measurements at a num-
ber of intervals along the stream between sampling points and, under
these circumstances, we scarcely ever got below 0.9 feet per second i*1
our measurements. Of course, the measurements on these small streams
were made by wading. We avoided the deep pools that we couldn't wade
in and these were very slow, but they represented a small portion of
the total stream, that is, the proportion that would correspond to a
very low velocity was a small part of the total stream length.
Question; Where in the channel section did you take your samples?
(JEW) Predominantly we would take center line samples. We have taken
some for a check at intermediate points across the cross-section and
we haven't found that these give us any measurable difference in our
results when compared to center line measurements.
You have to be careful not to measure at the center line at one point
and over at the edge at the next. Before we locate the intake to the
fluorometer we go out and determine where in the cross-section we have
our maximum velocities, so we try to get the intake where the peak
will be coming through rather than over on the edge where the peak
might be somewhat delayed. But, we have checked this and we can't
find that we get any difference.
Question; Is tritium absorbed and does pollution affect your studies?
(JEW) The question regarding the tritium—we would only be concerned
with it if it were selectively absorbed, i.e., if something happens
to it that doesn't happen to the water. We have no evidence that thi*
occurs. The tritium is in bhe form of triated water and as far as
we can determine it behaves just like water. Now for the second poW
you raised concerning the affect of pollutants of one type or another-
We have run extensive series of tests with various types of pollutants
to see if they affect the ratio, i.e., the proportionality, between
-------
kry?ton coefficients. They do not. Nothing that we have
Val able to find will change this ratio. Certainly the individual
eff Of K2 are affected, and we'll talk more about this later. The
ect of pollutants is on the actual value of K, but not on the ratio.
Would you again explain the use of the tritium tracer? (JEW)
.^ne ratio of krypton to tritium at station B, and divide it by
of krypton to tritium at station A- -the tritium is merely
ng the amount of dilution or dispersion that takes place in
S •am* ^o> ^ "*~s J'us^ an adjustment for any dilutions. If a
is diluted by 50$ then the tritium will be 50$ lower in concen-
k*1 t°n and the same effect will be present on the other tracer — the
Ply ^' ^ Dividing through by the concentration of tritium we sim-
a^ for any dilution or dispersion.
Do you use a different procedure on large streams? (JEW)
ternoon I think we have one lecture scheduled for discussion of
eaeration studies that we've been conducting on the Chattahoochee
* -U. >! -*-s the largest stream that we have studied and at that time
"teas S y°U that a different procedure is used for some of these
urements, but basically our procedure is the same, whether we are
about a small stream, 10 cfs, or a large stream, 2,000 cfs.
-------
Field Hydraulic Studies
J. R. Wallace
D. E. Hicks
working in the field of stream sanitation have for a long number
years tried to develop mathematical models which would predict the
•Ue of K^ for a given set of hydraulic and physical characteristics
the stream. These efforts date "back 60 years or so. Many questions
regarding the available equations, and some of these questions
as follows: First of all how should the hydraulic properties be
ured? If you're going to measure the velocity of the stream or
"e depth of the stream or any cross sectional area characteristic, how
along the stream do you have to measure these quantities,
how well do you have to measure them? There are also questions
Carding the range of error associated with the equations. There are
rts° questions regarding the effects of the non-uniformity of a channel.
a channel is very non-uniform then I think we can anticipate that
of the existing equations for predicting K^ will work less well
they would if we had a uniform section of channels to work with.
-------
appropriate station number. Standard U.S. Geological Survey stream
gauging techniques, with slight modifications, were employed by the
field crew. At each station the stream cross section was divided into
a number of vertical sections, none of which contained more than 10$
of the total flow. An average of 13 vertical sections were taken at
each cross section. The width of the cross section was measured with
a tagline or steel tape. A depth and velocity were measured for each
vertical section by the use of a top-setting wading rod and Price cur-
rent meter. The Price current meter consists of six conical cups about
a vertical axis. Electric contacts driven by the cups close a circuit
through a battery and the rod to cause a click for each revolution in
headphones worn by the operator. By using a stop watch, the operator
is able to record the number of revolutions per time. The meter is
calibrated so that the number of revolutions per time corresponds to
a velocity. All velocities were measured at 0.6 of the depth in order
to obtain a mean velocity in the vertical section. Two men were uti-
lized in measuring distance and making the discharge measurements,
although at times one man could work aLnost as fast as two.
Having obtained these measurements, the other hydraulic values can be
calculated. In Figure 1 the cross-section has been divided into verti-
cal sections. For the section ABCD the cross sectional area A is equal
to the width AB times the depth EF. The discharge Q for this section
is then the velocity measured at 0.6 of the depth, times the cross-sec-
tion area. With the total cross-section divided into n vertical sec-
tions the total discharge is just the summation of the discharges throUg11
the vertical sections. The summation from i = 1 to n of VJ^.
The Flint River rises in southwest part of Atlanta and flows southward.
A reach extending from the Flint River Sewage Treatment Plant, located
immediately south of the Atlanta Airport, to a point 9.9 miles down-
stream was selected for study. The upper two miles is characterized
by alternating riffles and pools. In this section are two mill ponds
followed by dams approximately 12 feet in height. The remainder of
the reach is characterized by a highly variable cross section with
quite a bit of debris in the river. In addition, there are two sec-
tions, one about a mile in length and the other about I-? miles in
length, which flow in multiple channels so that no "typical cross-sec-
tion" can be used to describe these reaches. One reach about 0.3 of
a mile long is a marsh where no valid velocity or cross-section measure'
ments can be made. The average depths range from about 0.7 of a ft. in
the upstream sections to 1.6 ft. in the lower reaches.
In Figure 2 a plot of flow versus distance illustrate the points at
which tributary flows enter the Flint. The Flint River Treatment Plan*
contributes about h cfs, an unnamed stream about 8 cfs, Mud Creek about
2 cfs, and Jesters Creek about 5 cfs. This creates a maximum flow of
slightly less than 30 cfs in the lower reach. Figure 3 shows the loca-
tions of the two dams and the irregular slopes in the upper reach, and
the small slope in the lower section.
-------
METER LOCATIONS
AABCD ' (AB)(EF)
~ VABCDAABCD
Sotal =
(1)
(2)
(3)
FIGURE I
DISCHARGE MEASUREMENTS
45
-------
32
26
DISCHARGE fN CFS
O -f* 00 N O» O *
FIGURE 2
AVERAGE DISCHARGE
MEASURED IN FLINT RIVER
JUNE 12- JULY 31. 1968
a.
ttt-
>
tc.
H
Z
— 3
u.
z
<
_i
Q.
Z
Ul
E
<
UJ
tc
v
^
®
5)
1
~ui
^
o
o
3
— 3E
(
O VO 2.O 3O AO
r>
i —
®
J
CREEK —
JESTERS
®
?
50 60 7O BO 90 100 UO
-------
sec
FIGURE 3
CHANNEL PROFILE
FLINT RIVER
JUNE 12-JULY 31,1968
760
30 40 50 60 70
DISTANCE IN 500 FT. STATIONS
-------
The South River originates in southwest Atlanta and flows in a south-
easterly direction. The portion included in the study extends from
the South River Sewage Treatment Plant to & point 18.3 miles downstream.
The channel is relatively uniform. A typical section in the uppar third
of the reach is 30-^0 ft. wide and one to two feet deep. The depth to
width ratio is fairly constant throughout the reach. The channel is
relatively straight with high, practically vertical banks. There are
a few pools followed by short rapids, "but the predominant characteris-
tic of the channel is its uniformity. The most unusual feature of the
South is Panola Shoals where the water flows in thin sheets over a
granite formation with an elevation drop of about 8 feet. This drop
is preceded by a pool with widths of approximately 100 feet and depths
of six to seven feet. Velocities in the South River ranged from about
0.8 to 1.6 ft./sec., with depths averaging from 1,2 to 2.1 feet.
Figure k shows the discharge of the South. The contributors to flow
in the South River are the South River Treatment Plant, 20 cfs, Intrench-
ment Creek, 25 cfs, Sugar Creek, 15 cfs, Shoal Creek, 12 cfs, Snapfinger
Treatment Plant, 3 cfs, and Snapfinger Creek, 12 cfs. The maximum flow
is just slightly less than 130 cfs in the lower reach. Figure 5 shows
the stream profile. Note the rapid sections throughout the length of
the stream, the location of Panola Shoals, and the pool above the Shoals*
In the fall of 1969 we conducted studies jointly with the Maryland De-
partment of Water Resources on the Patuxent River. This stream is
characterized by its uniformity. During the low flow study period deptfc
ranged from k to 6 inches in riffle sections to about 2 feet in the
deeper pools. Velocities were slow for most part and very uniform over
the reach studied.
Adjustment of Hydraulic Properties
Since the field, and tracer studies were conducted during different
flow conditions, a method had to be devised to adjust the measured
physical characteristics to the actual physical characteristics during
the tracer studies. We had measured several miles of hydraulic char-
acteristics at 500 feet intervals, and in order to relate hydraulic
property to reaeration values we had to have an estimate of the hydrau-
lic properties as they existed at the time of the tracer studies. The
method we used is quite simple and straight forward. Figure 6 shows
typical cross sectional conditions, with Aj and Pn, respectively, the
area and the wetted perimeter at the time we did the hydraulic studies*
Then, on the basis of the Manning equation, equation (l), we adjusted
these values to take account of the changes in depth, area, wetted
perimeter, and hydraulic radius, as they existed at the time of the
tracer study:
(!)
-------
fGOr
140
120
100
~ 80
Ul
1
^ f 0
o
40
20
0
/
r
j
u
5
ij
j
i
i
i
-r1"
T fc
/
Ul
Ul
oc
u
i-
z
Ul
s:
o
i
j
>^^H
r
r
l)
0 20
0
p
/
Ul
Ui
OC
o
OC
3
1
/
Ul
u
a
u
X
mm m*
®
1
r
1
/
t
C\ (H)
(21 J.
f
J
I i
5 u
' e
t
r
e
j
j
^
>
inoc.n irvc.Mirnc.INI
SNAPFINGER
f
Q!
40 60 80 100 120
s
«
/
/
_r— '
)?
M...M,.
T
FIGURE 4
AVERAGE DISCHARGE
MEASURED IN SOUTH RIVER
AUG. 5 - SEPT J3, 1968
140
ISO 180 200 ?2(
DISTANCE IN 500 FT. STATIONS
-------
FIGURE 5
CHANNEL PROFILE
SOUTH RIVER
AUG 5-SEPT. I3J968
655
SO 100
VH 5GOFT.
200
220
-------
1/2
A2 = Al
SAY
FIGURE G—METHOD OF ADJUSTING FLOW
(1)
(2)
(3)
5 1
-------
where Q, is the discharge (cfs), R is the hydraulic radius (A/P), n is
the roughness factor and S is the slope of the energy grade line. The
subscript 1 represents conditions as originally measured and subscript
2 represents conditions during the tracer release.
We are also saying that the perimeter is equal to the perimeter that
we originally measured, plus 2 times AY. The implication of these
assumptions is that we are disregarding the section of the diagram
that is shown cross-hatched. Having decided that we are going to use
the Manning equation, then if we assume that the n value, which is a
measure of the stream roughness, is the same for both flows, and if we
assume that the slope of the stream is the same for both flow condi-
tions, then the quantity
C- n
2/3
will be constant throughout and,the Manning equation becomes Q = CAR >
that is, the area times the hydraulic radius to the 2/3rds is equal to
the discharge divided by this constant. At the time of the tracer
study, we measure Q, so we know what Q« is, we know what C is because
we have solved for it from our previous measurements of Q, A, and R.^
We know A2 and R2 in terms of the change in depth, that is
A = A^ + BAY
and PO = PI + ZAY
A + BAY /
thus Qg = C(A1 + BAY)(p1 + £AY) 2/3 (2)
1
The only unknown in equation (2) is AY. We solve for AY and then use
AY to compute the value of the hydraulic parameters that existed at
the time of the tracers study. In this way, we have an adjusted value
of the hydraulic parameters to be used for correlation with the measure*1
reaeration rates.
Discussion
Question; What was the magnitude of the variation in flow conditions
between the time of the hydraulic studies and the tracer studies?
(JRW) The variation between the conditions at the time we did the
hydraulic study and at the time of the tracers study were not great.
By not great, I mean they were in the order of 10$ of the discharge
at a given point. That's a typical figure. For example, discharge at
a station may have varied from 60 to 66 or 50 to 55 cfs between the
times of different parts of the study.
-------
Question; Did you experience variations of flow during the study?
(JEW] We did the studies during the summer and early fall, when the
streams were at their seasonal low, and if we had any sort of rainfall
event we did not make any additional measurements until the stream had
receded to its base flow level. We always did this in order to elimi-
a large variation during the hydraulic study. The response time
each stream, i.e., the time required for the stream to rise and
is short enough so that it did not present any problem if it
one day. We normally did not have to wait more than one addi-
tional day for the stream to go back down to its normal flow.
SH^gtion; Your adjustment procedures could lead to errors if the
Assumption you made about the vertical banks is not valid. Please
comment on this. (JEW) You are right. This could be very mislead-
II1S. We made the adjustment in this way, of course, with the knowledge
°f what conditions in this particular stream are, and they do follow
the assumption pretty closely. I think I have another slide here that
shows the typical section and you can see the vertical banks. There
some exceptions, of course, and there are always going to be places
e the stream spreads out. We have checked our adjustment procedure
find that the adjustments were always in the range of the accuracy
our measurement, probably about 10$. So we feel like it is better
simply measuring the hydraulic parameters one time and then a
later coming back and assuming that they still exist. It is
only way I know to adjust a large length of river when we are
interested in a large number, 100 to 200, of intermediate stations.
Why not estimate the slopes of the banks at various sections
use this slope in your adjustment procedures? (JEW) I think this
give us added accuracy. We didn't do it primarily because we
that we could reproduce conditions within our accuracy in measur-
it again. All of us have walked these rivers from one end to
so we have a pretty good feel for the physical situation, but
any case you would have to have such knowledge before you apply any
adjustment technique, and you might have to make some modification
it to meet most of the situations you would find elsewhere.
Was there much variation in discharge as you move downstream?
Yes, quite a considerable variation. You probably noticed on
plot of discharge versus distance that the South River Treatment
puts in an amount of discharge that is probably twice as great
the discharge upstream from the plant and when you go on downstream
pick up three or four other sewage treatment plants . We did take
variation into account when we did our studies.
53
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Laboratory Procedures
R. J. Velten
General Discussion
Before discussing the general techniques used in the laboratory pro-
cedures, let me briefly describe what we are measuring.
Tritium is the heaviest isotope of hydrogen and has a mass of 3 atomic
mass units. It decays by beta emission with a half-life of 12.26 years
to helium-3. Its maximum beta energy is 18.6 kilo electron volts (kev).
Tritium can exist in any physical or chemical state in which hydrogen
can manifest itself.
Krypton-85, an inert gas, decays both by beta and gamma emission to
rubidium. The beta emissions occur 99-6$ of "the time with a maximum
beta energy of 6jO kev. The O.k% abundant gamma emissions are charac-
terized by the 512 kev photopeak.
Because of its extremely low energy, tritium cannot be measured by the
usual laboratory counting instruments. Gas counting of the tritium
gas as well as liquid scintillation counting as tritiated water are
the only plausible methods of measurements. Tritium, when used in the
determination of reaeration capacity, is in the chemical form of water
(HTO or ToO) and hence liquid scintillation counting offers the best
choice from the standpoint of ease of sample preparation combined with
detector efficiency and background.
Krypton-85j on the other hand, can be measured by both beta and gamma
counting. However, because of the low gamma abundance, the sensitivity
of gamma counting is poor to such an extent that the concentrations of
krypton that are usually encountered in the tracer reaeration procedure
cannot be measured. Beta counting is the only choice. The dissolved
krypton could be purged from the solution and counted, using a gas
counter. The high counter background plus the uncertainty that all the
krypton has been purged from solution makes this technique less reli-
able and less sensitive.
Liquid scintillation counting thus becomes the only choice and is espe-
cially suited for measuring both radionuclides simultaneously. This
counting technique becomes practical for simultaneous measurements of
two radionuclides whenever the beta energies differ by a factor of five
or more.
55
-------
Sample Preparation
Some care must be exercised in the preparation of the samples. Since
Kr-85 is an inert gas dissolved in the water,, reasonable efforts should
be taken to prevent the loss of the gas from solution while preparing
the sample for counting. In order to minimize the loss of gas, a trans-
fer rig, as shown in Figure 1, is used. It is thought that by applying
gentle pressure to the whole sample and collecting the aliquot from the
bottom of the bottle is a better technique in aliquoting than the usual
suction-type pipetting technique. The aliquot is then transferred to
the scintillation vial and the scintillation solution gently added until
the vial is completely filled. The bottle is tightly capped and the
liquid phases mixed by swirling, not shaking. However, past experience
has shown that the hydraulic pressure created when closing an overfilled
vial has occasionally broken out the bottom of the vial. This may be
especially important if vials with polyseal caps are used.
The sample is then placed in the counter. If the counter is equipped
with a refrigerated system, counting at k°C is recommended to retard
or eliminate any loss of the gas from solution. This is about the
lowest temperature where the scintillation mixture will not freeze.
If the counting instrument is not equipped with some cooling system,
then the instrument should be located in a controlled temperature room.
This is to prevent any expansion in the scintillation mixture because
of increases in room temperatures. These increases will expand the
solutions and samples may be lost be breakage. This will necessitate
cleaning the entire interior of the instrument. In preparing the sample^
the scintillation solution should not be exposed to fluorescent lighting'
This light, as well as sunlight, excites the solution and several hours
are required for this excitation to decay before counting can be initi-
ated. Incandescent lighting is satisfactory although this should be
minimized.
Instrument Set-up
The setting up of the liquid scintillation counters varies with manu-
facturers. Thus, I will describe the instrument with which I am more
familiar and have used for most of our reaeration studies. This instru--
raent is the Packard Model 3320. The analyzer section of this instrument
has three channels, each with its own high voltage supply (gain) and
discriminators (lower and upper). To set up one channel for one radio-
nuclide, a discussion on the use of the discriminators and gain control
is warranted. Let us assume that a sample has been placed in the detec-
tor and the gain is set at some arbitrary low setting. Let us set the
lower discriminator at setting 000 and the upper at 050, a difference
of 50, and then count the sample and record the count rate. Now, let
us increase both the lower and upper discriminator by 50; that is, 050-
100 and then repeat and record the count. Continue this increment until
no counts are observed. Plot the observed count rate versus the energy
56
-------
PRESSURE PIPETTE
(NOT TO SCALE)
STOPPER
ml. PIPETTE
DISPOSABLE
cc SYRINGE
DISPOSABLE
22 g HYPODERMIC
NEEDLE
FIGURE 1
5 7
-------
"band and a curve similar to Curve A, Figure 2, will be described. In
this case, the count rate ceases in the energy band 250-300. If the
gain is then increased, and the counting repeated, Curve A vill take
the shape of Curve B. If we further increase the gain, Curve C will
be described, and finally if the gain is further increased, the upper
edge of Curve C will be beyond the range of the upper discriminator.
It can then be seen that, by adjusting the gain control, the dynamic
range of the discriminators can be used. This is exactly what we do
with each radionuclide, tritium and krypton-85.
First we set the channel which is to monitor the krypton activity.
Place a krypton sample in the detector and set the lower discriminator
to monitor the energy band at setting 1000-00. This will then monitor
any pulse greater than the voltage of the lower discriminators. Increase
the gain until significant counts due to the krypton are observed. Now,
set the lower discriminator to 000 and the upper discriminator to 1000.
What was actually done was to stretch the beta spectrum, like Curve C,
Figure 2, over the full range of the discriminator.
Now, the channel which is to monitor the tritium activity is set. Place
the tritium sample into the detector and the process which was described
above repeated. In this case, because of the low energy of the tritium
beta emission, there may not be enough gain available to stretch the
spectrum to a discriminator setting of 1000-00. If this is the case,
decrease the lower discriminator until counts due to tritium are observed*
Now set the upper discriminator at this setting and the lower discrimi-
nator is returned to 000. This now stretches the tritium beta spectrum
over the widest range attainable by the instrument. Keeping the tritium
sample in the detector, increase the lower discriminator of the krypton
channel until all counts due to tritium are discriminated against. This
then is the final setting for the krypton channel. Now replace the
krypton sample in the detector and lower the upper discriminator of the
tritium channel until the counts in the tritium channel are about 5$ of
the counts in the krypton channel. This is about as far as one can
resolve the two radionuclides without drastically reducing the detection
efficiency of the tritium. This is then the setting of the tritium
channel.
If the tritium channel were subdivided into energy bands of 50 units
(that is, 0-50, 50-100, 100-150, etc.), and the count rate plotted
against energy band, a plot which is described in Figure 3 vill be ob-
served, although it would be the sum of the two components. Figure 3
shows the resolved effects of tritium and krypton. If we did likewise
with the krypton channel, a curve as shown in Figure k would be shown.
The third channel can be used to monitor the external standard. The
external standard is a solid radioactive "pill" which is transported
next to the sample and which irradiates the samples causing an increased
count rate. This count rate is recorded in the third channel. If the
physical and chemical properties of each sample are identical, the count
rate caused by this "pill" will be statistically the same. This techni
-------
I I I 1 I I I
TYPICAL RESPONSE CURVE
100 20O 300 400 500 60O TOO 800 900 1000
Discriminator Setting FIGURE 2
-------
1 [
CD
O
o:
o
O
a>
_o
Q)
o:
i \ \ \ \
T Y PI CA L RES P O N SE CURVE
TRITIUM
KRYPTON -85 ^^
I r
1
100 200 300 400 500 600 700 800 900 1000
Discriminator Settings
FIGURE 3
-------
T T——r r—i r
TYPICAL RESPONSE CURVE
CD
O
o:
c
Z3
O
o
CD
CD
o:
TRITIUM
KRYPTON '85
o
100 200
300 400 500 600 700 800 900 1000
Discriminator Settings
F I G U RE 4
-------
insinuates that, when the external standard count rate of samples is
identical, then the samples are directly comparable. It is a measure
as to whether the detection efficiency of tritium and krypton is vary-
ing because of different chemical and physical properties of the samples.
To set this channel, the krypton sample is placed in the detector, and
the lower discriminator set at 1000-00. The external standard is blown
into place and the sample counted. The gain is increased until a count
rate is observed in the third channel. The external standard is removed
and the upper discriminator is set at 1000 and the lower discriminator
is decreased until the count rate due to the krypton sample begins to
appear. Then the lower discriminator is set slightly above the setting
so that no counts due to krypton are recorded.
Calibration
The detection efficiency for tritium is easily measured, since tritiated
water standards are readily available. Transfer to a counting vial an
aliquot of a tritiated water standard equal in volume to that which is
going to be used in the reaeration determinations. Fill to capacity
with scintillation solution, swirl to mix, and count. The detection
efficiency is calculated by the dividing of the observed count rate in
the tritium channel by the disintegration per minute of tritium in the
aliquot taken from the standard.
Calibrating the channel used to measure the krypton is more difficult
insofar as a standard krypton source is not available. However, the
gamma emissions, although only Q.k% abundant, are sufficiently energetic
so as to measure if enough krypton is present. The photon energy is
51*f kev which is fortunately the same as strontium-85 and which is
readily available as a standardized source^ To calibrate the krypton
channel, a very active krypton source (10° disintegrations per minute)
is counted in the liquid scintillation counter under the same counting
protocol for the reaeration study. The beta count rate is determined.
This same sample is then counted by gamma scintillation counting tech-
niques and the gamma count rate determined. The gamma counter is cali-
brated using strontium-85 and after correcting for the gamma abundance
of krypton-85, the beta disintegration rate is calculated. The beta
scintillation efficiency is calculated by dividing the observed beta
count rate by this calculated beta disintegration rate.
Figure 5 presents the gamma spectral shapes of krypton-85 and strontium-
85.
If gamma scintillation counting is not available, the use of chlorine-3^;
a pure beta emitter whose maximum energy (71^ kev) is very close to the
maximum beta energy of krypton-85 (670 kev), is recommended. In this
technique, however, it is assumed that the beta spectral shapes of the
two radionuclides are identical or nearly identical.
62
-------
103
Q>
*.
o
(t
o
o
Q>
Ct
I03
STRONTIUM-85
115,050 dpm
Photon Abundance -
Photon Efficiency -
100%
8.50%
-/ Background
I
I
10'
KRYPTON - 85
Photon Abundance-A 0.41%
/ Background
I
0.2 0.4 0.6
Photon Energy (MEV)
0.2 0.4 0.6
Photon Energy (MEV)
FIGURE 5
I03
I02
IO
63
-------
Miscellaneous
Although not related to the topic of laboratory procedures, I wish to
present some data which our laboratory determined concerning the han-
dling of samples from the field to the laboratory. These data were
obtained during a study on the James River model at Vicksburg, Missis-
sippi. We wished to see if air transportation could be used to ship
samples back to the laboratory. It was conjecture that air travel,
because of possible pressure gradients between high altitude and ground,
would cause a significant loss in the dissolved krypton. Forty sample
bottles containing krypton-85 were prepared. Half of these were taped
with plastic electrician's tape. All were gamma counted. Ten samples,
five taped and five untaped, were shipped by air to Vicksburg. Another
ten samples, five taped and five untaped, were transported by car to
Vicksburg, while the remainder stayed in the laboratory under reasonable
temperature control. When the study was completed, those that were
shipped by air were returned by air and those shipped by car were also
returned by car. All forty samples were recounted. The time interval
between counts was 12 days. Table 1 gives the results of this experi-
ment and our conclusions. Wot stated, however, is the conclusion that
it appears feasible to ship samples by air provided they are sealed
with tape.
In reaeration studies, dye is used as an indicator as to when to begin
sampling. Most often used is Rhodamine WT, since it is less absorbed
in the stream environment rather than other dyes and thus can be used
as a secondary measure of dispersion. However, this dye, when present
in sufficient concentrations, does quench or shift the beta spectra of
both the tritium and krypton-85. Thus, calibration is required by any
of these shifts. However, it has been observed in this laboratory
that uranine at these same concentrations is completely decolorized by
the scintillation solution and no spectra shifts occur. If dye is used
solely for the purpose of an indicator for sampling, uranine may be
more advantageous to use.
One last remark concerning reaeration studies is worthy of mention.
Most studies have been made using a 2 ml aliquot for counting. There
is no reason, other than extreme turbidity, why k ml cannot be used.^
This, however, is the upper limit because of solubility in the scintil-
lation solution. The use of k ml aliquots would do one of two things:
1. Give greater coverage to a stream, or
2. Reduce the radioactivity concentration in the dose solution.
-------
TABLE 1
TRANSPORTATION STUDY USING KRTPTON-85
cpm gamma radiation
Controls
Air
Car
Tapei
Pre
3581
3603
3589
3597
3556
01 3575
3561
3590
3538
3490
Percent reten-
tion after
12 days
One standard
deviation
a
"Post
3398
3316
3325
3350
3397
3371
3325
3427
3258
3376
94
2
Untaped Taj
Pre Post Pre
3560
3546
3515
3577
3490
3491
3529
3502
3489
3154 3716
2481 3814
2055 3738
3252 3743
3236 3679
2284
3150
3306
3139
82
14
jed
Post
3474
3507
3368
3478
3560
93
2
Untaped
Pre Post
3676 3442
3643 3328
3790 3351
3741 2867
3739 3142
87
6
Taped
Pre Post
3715 3446
3755 3385
3679 3455
3673 3318
3750 3307
91
2
Untaped
Pre Post
3643 3208
3672 1554
3758 3337
3734 3441
3709 3303
80
22
CONCLUSIONS: 1. Based on a statistical evaluation, taped samples were more consistent and had
lower overall losses than the untaped samples.
2. Within the taped samples, there was some indication that the mode of travel con-
tributed to loss of the sample but not to a large degree.
-------
Reaeration Capacity of the Flint
South and Patuxent Rivers
E. C. Tsivoglou
next several presentations will focus on the results obtained
application of the reaeration tracer technique in a number
streams. This first discussion outlines results for three small
, the Flint, South and Patuxent.- Subsequently, results
°btained in a larger stream, the Chattahoochee, will be presented,
then results from a physical model of a large tidal stream, and,
field results observed in a small tidal stream in Oregon.
outlined earlier, the principal purpose of these field studies
Reaeration capacity has been to observe reaeration rates in
that include a wide range of hydraulic features, so as to
study of the basic relationships between reaeration and
hydraulic properties. This should then permit analysis of
accuracy and dependability of currently available predictive
for reaeration, and, possibly, some improvement of these
•?°
-------
FORT MEAD
BALTIMORE
WASHINGTON
PARKWAY /
FIGURE 1
PATUXENT RIVER STUDY LOCALE
MILES
-------
the prevailing stream flows of eight or 10 cfs at the head of
study section, depths of flow through the study reach ranged
a few inches to two or three feet in some pools. Tributary
Branches increased the flow to about 2h cfs at the lower end of
study section, and the time of flow for the entire reach studied
about 30 hours.
•-he Patuxent River studies were conducted jointly with the Maryland
Apartment of Water Resources.
figure 2 shows typical study results for the first four miles below
^he Laurel, Md., waste treatment plant (about lU hours time of flow).
•'•he results have been plotted on semilog paper, so that the slopes
the lines directly represent the reaeration rate coefficients.
for two separate tracer releases are shown, representing
at the head of the study section of 10 cfs and 1? cfs, respec-
tively.
pring to Figure 2, several observations are noteworthy. First,
observed reaeration rate coefficients are quite consistent,
^om one reach to the next, indicating an absence of unusual or
efliarkably different hydraulic features. The relative slopes for
^y one section are also highly consistent for both tracer dumps,
S-nd indicate that, even though the flow for Dump D was nearly double
hat for Dump B, the observed reaeration rate coefficients were only
higher. The range of K^ values was quite small (0.09 to
per hour) for both dumps. In fact, for this coastal plains
m, no important error would be made by using a single average
of K for the whole reach, Stations 1 to U. The single repre-
ive values of K^ would be 0.12 per hour at about 10 cfs and
• per hour at 1? cFs, at 25 °C.
Th
qe reproducibility of results was excellent in these studies.
3 is a map of the South River tracer study section. The
River originates in southwest Atlanta, Ga. The study reach
^ about 18 miles long, beginning at the South River Sewage Treat-
Jjlrt Plant in Atlanta. With a small number of notable exceptions,
K channel is relatively uniform, with typical depths of one to
feet and typical widths of 30 to Uo feet. The bottom is usu-
sandy.
South River is presently heavily polluted. It receives par-
treated and some untreated sewage and industrial waste from
waste treatment plants in the 18-mile study section. These
Lde the South River STP, the Intrenchment Creek STP, the Shoal
^ - STP and the Snapfinger Creek STP. All of these plants are
ei>loaded. Typical flows in the South River range from about
69
-------
>4
O
Kr /H Concentration Ratio
OO O OO O O t-
• • « 99 •••
OH N» W *• O\ 03 C
CO 0 O 0 O 0 ^0 ^ C
TTi
Kr
k^v
^ >v
N
6.
s^
NC^
^^s
Du
^^X^Oy*
S^t^
^^W-,
tip D (~1
KEY
Q Mean Ratio
I Range of Individua
Sample Ratios
(J) Sampling Station
xXjJ
0
Dump
>^
"X
A/
Q
©
Dump
B (-10 <
^%
^
Dump
B Static
fs)
N
^
D Statit
®J
ns
©
FIGURE 2
PATUXENT RIVER
OXYGEN TRANSFER COEFFICIENTS
Note; All values are K2/hour
\
•
t
ns
Ns
10
12
14
16
18
20
1VHV.6. Ot "PI-OW—
-------
FIGURE 3
SOUTH RIVER STUDV LOCALE
VICINITY OF ATLANTA
-------
50 cfs at the upper end of the study section to perhaps 200 cfs at
the lower end. Foam is often observable in the stream in the summer-
time, especially below the Snapfinger Creek STP and in the pool just
below Panola Shoals.
A number of tracer releases were made in the South River, and the
next three figures illustrate the results obtained. Figure k shows
the results of two such releases at the head end of the study sec-
tion. As indicated by the times of flow for the two dumps, stream
flow was not greatly different in the two studies. The observed ^
values ranged from 0.13 to 0.28 per hour in the different reaches.
For any one reach, the reproducibility of results from one dump to
the next was very good. The reach BD exhibited some difference from
the others, having a significantly higher value of K£ in both dumps,
and does contain a short shallower rapids section.
Figure 5 shows the results of five separate tracer dumps, covering
the middle seven to eight miles of the 18-mile study section, from
above Shoal Creek through the large pool just above Panola Shoals.
As may be seen, the reproducibility of results from one dump to the
next was generally very good, especially in the reaches FG and HJ.
A wide range of Kp values was observed, from 0.05 to 0.7^ per hour
for krypton transfer. Results for the section GH were more variable,
the K9 values ranging from 0.39 to 0.7^ per hour for krypton. Section
GH contains a violent rapids section 200 to 300 feet long, with much
white water, and is just below the entry of the effluent from the
Shoal Creek STP. The effect of the rapids section is quite evident
in terms of the high gas transfer coefficients. Results for the
reach JK, which includes the large pool above Panola Shoals, are
also somewhat more variable (Kg ranging from 0.05 to 0.11 per hour
for krypton) for reasons outlined below.
The Panola Shoals section was studied more intensively because of
its unusual hydraulic nature, and Figure 6 shows the results of those
studies. All of the K^ values shown represent krypton transfer, but
can be converted to K^s for oxygen transfer by dividing them by the
basic conversion factor of 0.83. At first glance, these results
appear to be more variable, both for the pool and for the shoals them-
selves. Note, however, that the observed results for the entire
reach are highly consistent and reproducible, ranging only from 0.17
to 0.19 per hour for the four tracer dumps. Further analysis of these
results has resulted in a better understanding of the reasons for the
apparent variability of results in the pool and over the shoals, and
has indicated a possible source of difficulty in field operations.
Flow through the long deep pool just above Panola Shoals is decided-
ly not homogeneous or uniform. Thus, flow from above may at times
remain near the pool surface, rather than mixing throughout the
whole depth of the pool. Under other circumstances, the reverse may
well happen. Thus, the location of the sampling point (the depth of
sampling) just above the shoals could have been less representative
72
-------
1.0
0.9
0.8
0.7
0.6
0.5
0.1*
0.3
0.2
0.1
Vc
®
Dump VI'
^ »\
o
Dump X S
• Dump X
Dump
;ations
Stations
3 k 5
Tljne of Flow - Hours
SOUTH RIVER
KRYPTON TRANSFER COEFFICIENTS
Note; All values are Kg/hour
FIGURK 4
O ^
73
-------
SOUTH FIVER
KRYPTON TRANSFER COOTICIEHTS
O.OU
7 8
Tin* of Flow - Hours
-------
0
3
3
3 0.2
S °-io
ft
SOUTH RIVER
KRYPTON TRANSFER
COEFFICIENTS
Note: AH values are K2/hour
fK.» 0.0 )
anola
hoals
0.08
0.06
0.04
0.02
L 2 3
Time of Flow- Hours
FIGURE 6
75
-------
than necessary in one study or another - although the results
obtained would be accurate for that sampling de|>th, they might not
adequately reflect the mixing action of the whole pool volume. In
Sitfonf the time of flow over the shoals *^el™ V"™^
about 13 minutes between the two sampling stations, and this intro
duces the possibility of error in terms of the observed time of flow
over such Sort periods. Three of the four dumps shown in Figure 6
wire made at the Station immediately above the pool, and under such
Circumstances it is not impossible that the sampling point «d^
above the shoals was not always in the best location ac^s j£JiS
of the pool: time of flow is determined by the time lapse ^tween
peak dye concentrations at successive sampling points and the pool
dust above the shoals is very wide; if the upper sampling P°^* ™*e
not located to catch the exact peak dye concentration, but somewhat
to one side, an error of two or three minutes in the observed time
of Sow could well results. Normally, the time of flow between samp
ling stations is two or three hours, and such an e^°r wouldbeen-
tirely negligible. But for short times, such as the 10-15 minutes
over PanoL Shoals, an error of 2 or 3 minutes would result in a
substantial error in the calculated value of Kg. This may well have
happened in" the Panola Shoals reach because of2the .co^lnjd c^cum-
stlances of dosing not far upstream, nonuniform mixing in the pool an
* " 6
above the shoals was crucial for best results.
For the pool above Panola Shoals the average observed K of 0.0^ per
hour for krypton (0.05 per hour for oxygen) is regarded as close.
-°
our or .
Similarly, e average Kg of 2.5 per hour for kryp ^-^°^
shoals (K =3.0 per hour) is taken to be satisfactory. Thus,
8a-ls in a period of about 13 minutes, about hO per cent o*
a Wo tracer gas was ^t tothe
terms of reaeration, this means that about 5 0 per cent of th e DO
elevation changes in bringing about stream reaeration.
Flint River
Figure 7 is a general map of the Flint River study section. The
Flfn^ also rises in southwest Atlanta and flows generally southward.
The study section was aboul; 10 miles long^™^f 2r^?
River Sewage Treatment
The stream was heavily
76
-------
N
KEY
^DIRECTION OF FLOW
REPRESENTS EVERY
FIFTH CROSS SECTION
FIGURE 7
FLINT RIVER STUDY LOCALE
VICINITY OF ATLANTA
-------
ranged from 5 cfs just "below the STP to 30 cfs or so at the lower
end of the study reach, and depths of flow ranged from one or two
inches to two feet or more in pools.
The study section on the Flint contains a number of unusual hydrau-
lic features, and there is no "typical" section. The stream is made
up of alternating riffles and pools. At the upper end there is a
violent rapids reach perhaps 50 yards in length and containing
several small hydraulic jumps. Below, there are two old mill ponds,
each followed in turn "by a waterfall 12 feet or so high. Farther
downstream, the Flint passes through a marsh in multiple small chan-
nels. The following figures and charts illustrate the effects of
some of these features on the reaeration capacity.
Figure 8 is a semilog plot of the results observed in two separate
tracer releases just "below the Flint River STP. Dump No. Ill was
at a flow of 10 cfs, while Dump XIV was at a flow of only 5.5 cfs,
the lowest encountered. Referring to Figure 8, it is clear that
the slopes of the lines shown, and hence the K^ values, were not
remarkably affected by the difference in stream flow, even though
the time of flow was substantially different. Reach 01P contained
a violent rapids section, R1R3, with small hydraulic jumps, followed
by a long, shallow pool, R31P; the next reach, 1P1, was a waterfall
about lU feet high, with shallow flow over smooth rocks - the time
of flow from Station IP to 1 was 5 or 6 minutes; the reach 1 to 2P
consisted of alternating riffles and small pools until the stream
entered a larger long pool above Station 2P (with depths up to 3
feet and muddy bottom ); the reach 2P2 was a second waterfall, about
12 feet high, with a short deep pool immediately under the fall -
time of flow from Station 2P to Station 2 was of the order of 25
minutes or so, largely in the pool under the falls.
The pattern of gas transfer and reaeration is remarkably consistent}
and the results highly reproducible, as shown in Figure 8. They shc^
clearly the effect of features such as rapids, waterfalls and pools
in determining gas transfer and reaeration, with K? values for kryP*
ton as high as 12 per hour at the waterfalls and as low as 0.015 Pet
hour in the pools. For Dump XIV, the results also demonstrate that
in streams of this type, having distinct hydraulic features such &s
those shown, most of the real work of gas transfer takes place in
relatively short reaches and times: the rapids section R1R3 is w
most of the work of gas transfer takes place in the long reach OlPj
and very little such work is accomplished in the pool between sta-
tions R3 and IP. In contrast, the time of flow through the rapids
was about 7 minutes, and through the pool almost 3 hours.
Considered another way, in Dump XIV, a total of hk per cent of the ,
tracer gas was lost during the h.J hours time of flow between Stati°Jl
0 and IP; of this total lost, about 56 per cent took place in the !•'
hours between Stations 0 and Rl, about 38 per cent took place in
7 minutes between Rl and R3, and only about 6 per cent took place
78
-------
FIGURE S
FLINT RIVER
KRYPTON TRANSFER COEFFICIEKTS
Note: All values are Kj/hour
0.011
5 6
Time of Flew- Hours
11
-------
the 3 hours time of flow through the pool below Station R3. Thus,
9^- per cent of the work of reaeration took place above the pool, or
in about 38 per cent of the time.
At both waterfalls, about 55 per cent of the tracer gas present was
lost over the falls, and about 65 per cent of the oxygen deficit
above the falls was overcome through the falls. These results were
confirmed by independent DO analyses for each study. The reported
K2 values differ sharply because of the different times of flow -
because of the deep pool located under the second falls.
In Dump III, at 10 cfs, 92 per cent of the tracer gas was lost in
the 6.5 hours time of flow between stations 0 and 2; in Dump XIV,
at 5.5 cfs, the loss was 97 per cent in the 9.3 hours required to
traverse the same distance. In both cases, any oxygen deficit per
se at Station 0 was completely overcome, and had there been no pol-
lution load also present, a DO deficit of zero would have been found
at Station 2.
Figures 9 and 10 tabulate a few of the foregoing results, for con-
venience. Clearly, in a. natural stream there is no single value of
Kg that really prevails over long distances, except in the sense of
an average result, as so clearly shown for the reach 01P in Dump XIV-
Thus, although gas transfer is a first-order process under condtions
of uniformly steady mixing, in a natural straam many such first-
order processes occur within a single reach, due to the lack of
hydraulic uniformity, and observed "Kg" represents an average
result rather than a single reaction. In many ways, then, the actual
observed per cent gas loss seems a more significant representation of
gas transfer and reaeration than a calculated value of K2«
80
-------
FIGURE 9
FLINT RIVER
(Summer, 1969)
Reach
Dump
Percent
Gas Loss
(K2)Kr/hr
01
01P
R1R3
1P1
I
III
XIV
III
XIV
XIV
III
XIV
(49.8)
65.9
77.7
31.8
43.5
20.5
50.1
60.5
(0.224)
0.366
0.312
0.141
0.121
1.75
8.9
12.4
8 1
-------
FIGURE 10
FLINT RIVER
(Summer, 1969)
waterfall
Reach
Dump
Percent
Gas Loss
(K2)Kr/hr
12
12P
2P2
I
II
III
XIV
II
III
XIV
II
III
XIV
(75.7)
75.0
77.1
85.1
49.5
50.3
58.9
50.4
53.9
65.8
82
(0.352)
0.401
0.402
0.434
0.220
0.215
0.219
2.01
1.85
2.38
-------
OXTGEN BALANCE OF THE SOUTH RIVER
A. G. Herndon
the last three years the Federal Water Quality Administration,
cooperation with the Georgia Water Quality Control Board, has con-
studies on the South River to determine pollution loads and
ssimiiation characteristics. These studies, classical in nature,
measurements of dissolved oxygen, BOD, ammonia, nitrates, and
parameters. One study consisted of daily sampling throughout
entire reach of the river over a period of three weeks. The re-
Cation coefficients developed by Dr. Tsivoglou, along with data from
^he previous studies, were used to develop a more complete evaluation
of the self purification characteristics of the South River.
r*16 South River is very polluted, even though all wastes discharged
£° it receive from 85 to 90$ BOD removal. Pertinent data on the sewage
ll>eatment plants located in the study area are as follows:
Flow, cfa BOD (Ultimate) Ibs/day
22 U,300
Creek 21 6,600
Creek k 1,300
Creek '5 1,500
the study in 1967, all of the plants discharged effluents with
|8h BOD1 s, due to industrial wastes and excess loadings. Since the
lov in the upper end of the South River is only 13 cfs and it receives
pounds of BODg over a distance of about 15 miles, this river
a heavy pollution load.
from waste loadings within the river and discharges from plants
used to plot the stream loadings as shown in Figure 1. This
shows the ultimate BOD in pounds per day plotted against the
of travel at low flow conditions. The location of the four
. Qe treatment plants (STP) and the water quality sampling stations
^e shown on the chart. Station Number 6 is at Panola Shoals, which
at 0.8 day travel time, or about 15 miles downstream, from the
treatment plant. The solid line of the chart shows the actual
BOD loadings, which began at 4,800 pounds per day at the dis-
point of the first treatment plant.
nS-term BOD tests on river water samples showed that the deoxygena-
rate (k-j_) was 0.15 (base 10). When this rate was applied to the
v,""*^ loadings in the stream, the data shown on Figure 1 as a broken
vlQe were calculated. This shows that about 72$ of the applied BOD
vuld remain at the lower end of the study reach. However, as shown
/ the solid line, only about 32$ of the BOD actually remains at the
Ver end of the study reach.
83
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Figure I
SOUTH RIVER WASTE ASSIMILATION
z-
*
O
X
9 -
8 -
5 '
k 6 -
O
OQ <•
LU
_
-1 ,
— j 3-
K>
O
X
1-
(
) .
STP
/
C
a-
v
STP
S^
\
3
i
+.
O—
\[
6
STP
V
•w ^
•— —
_r-
n
-6
STP
i
.
\
\
— , m__
—
—
O ACTUAL BOD
* CALCULATED BOD
USING k,OF 0.15
6
- -1
k_— -
-
<
7
•
--*•
--*
, — •
-— •
— •*
•
--*
__^ -••
-
D .2 .4 .6 .8 1.0
TIME , days
84
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the a"bove information and the reaeration coefficients (k2) that
Vere measured "by Dr. Tsivoglou, additional k, and kp rates were calcu-
lated, as shown in Table 1. The river was divided into relatively
ehort reaches, which were determined by the sampling stations, num-
bered 1 through 6. No calculations were made on the reach between
6 and 7 because reaeration data were not available from Dr.
's study.
measured deoxygenation coefficients (k,), or BOD reduction .rates,
calculated as the slopes of the solid lines plotted in Figure 1.
The reaeration coefficients (kg) from Dr. Tsivoglou's data were con-
verted to 17°C and per-day basis. Since his study reaches covered
Somewhat different distances, some of his data were averaged to obtain
« values. For example, he measured kp in three reaches between
e"tations 5 and 6. The temperature conversion made all data consistent
the field studies. It should be noted that the measured k^ values
Vafied widely, indicating a very broad range of deoxygenation or BOD
Eduction rates in the South River. These conditions are somewhat
&Pparent upon observation of the stream where some sections have wide,
sandy bottoms and other sections have rocky, turbulent areas.
Streeter-Phelps equation was used to calculate k2 by utilizing
measured k from Figure 1 and dissolved oxygen data from field
surveys. A comparison of the measured and calculated kp indicate
r^ir agreement at some sections, but poor agreement at the section
between stations number 3 and 5. The kp values, obtained by direct
Measurement, were then used to calculate corresponding k values. A
Comparison of the measured and calculated k. values shows that there
s considerable discrepancy in individual reaches; however, almost
the values are much higher than normally observed in larger streams.
high deoxygenation rates (k.) indicate that this shallow, turbu-
stream is exhibiting a phenomenon referred to by some workers as
cal extraction, or perhaps some other terminology. The meas-
r*61! k rates were very high in three sections, where the values were
•62, I.J2, 1.09. If these Is., rates were true deoxygenation rates,
ben an equivalent amount of oxygen to satisfy the BOD demand would
J- ^squired to maintain the dissolved oxygen level in the stream.
Ms would then require very high reaeration rates, as was calculated
^ the sections between stations 3 and 4 and stations 5 and 6. It
Ppears that in some sections of this river the BOD is being removed
requiring an equivalent oxygen demand; or else, additional
is being supplied, other than that of normal reaeration. The
appearance of the stream would indicate that the rocky areas
biological growths would have a higher BOD extraction rate than
areas which have sandy, shallow bottoms.
•^logi
A
* detailed study of the section between stations 5 and 6 may
», some new insight on the assimilation characteristics. In
*8Ure l, this section is shown to have a steep slope of BOD reduc-
however, a closer examination of shorter reaches may reveal
85
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TABLE 1
South River
Deoxygenatlon and Reaeratlon Coefficients
(17°C, Base 10, per day)
Station Measured Calculated
No. k (chart) k2 (Tsivoglou) k^* k2**
.12 1.80 .15 1.64
.62 1.94 .83 1.23
3 1,72 1,62 .45 4.85
4
.14 1.05 .64 ,17
1.09 1.77 .66 2.37
6
*Using k by Tsivoglou
**Using k from chart (Figure 1)
86
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steeper slopes in the rocky, turbulent areas. Dr. Tsivoglou's
er studies showed reaeration rates of 5.6, 2.2, and 0.6 per day in
three subsections of this reach. Correspondingly high and lov BOD
Deduction rates probably occur in these same subsections; however,
were available only on the average reduction as shown in Figure 1
stations 5 and 6.
above data are presented, not to show that all of the answers are
but to show that there is a wide variability in the factors
Affecting assimilation when measured by different methods. Also, the
^ta point out the need for additional studies in various areas. Al-
wiough the original field studies on water quality indicated no signi-
ficant nitrogenous oxygen demand in the study area, there was a major
^emand downstream of the study area. Additional work is needed to
Determine the effects of algae on dissolved oxygen production, since
was done on this in previous studies. The biological growths
the rocks in some areas probably contribute significantly to the
reduction and this should be explored in short reaches of the
^ conclusion, it is pointed out that the direct measurement of re-
lation by the tracer technique is much preferred over the indirect
Iculation arrived at by measuring other factors in the stream. This
particularly true since the phenomenon of biological extraction can
place, which would make the deoxygenation rate or BOD removal
invalid. In this particular study, the rate coefficients which
"be used for prediction of waste assimilation in the South River
be those determined by tracer measurement on reaeration and the
J"0xygenation rates subsequently calculated from those measurements.
,^e tracer technique for measuring reaeration is a significant contri-
tion to the sanitary engineering field and provides a tool for more
CcUrate determination of the assimilative capacity of streams.
87
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Reaeration Studies of the Chattahoochee River
J. R. Wallace
The question that originally concerned us on our studies of the
Chattahoochee River was whether or not we could take the techniques
that we had developed for small streams and apply them to a much
•^ger stream. Through our experience with this river we can now
Affirmatively answer the question. Yes, we can use our methods on a
larger river with some modifications. However, the modifications are
large ones. To give a little information for comparative purposes,
give you typical flows for the rivers we studied. Flows in the
River were typically 10 to 20 cubic feet per second; on the
River the flows were between 50 and 100 cfs, and on the Chatta-
we are working with flows around 1000 to 2000 cfs.
dose procedure is quite similar in all cases. The amount of radio-
material is, by necessity, increased as we go to the larger
Our license calls for a maximum dose of 5 curies of tritium
2-5 curies of krypton on the Chattahoochee. These tracers are com-
with approximately 9 liters of dye and placed in a 9 liter con-
This can be compared to the 1 liter container we were using
^ the smaller rivers. We showed earlier that the 1 liter bottle is
Placed between a couple of angle irons, and we simply hit it with a
£O mafce -the release to the stream. We don't do this with the
aose> we nave a steel basket into which the larger bottle is
We place the basket with the dose into the river and, when
6veryone is clear of the dose point, we break the bottle with dynamite
£a£s which we have strapped to the bottle. The dosing rig (the basket)
& made so that we don't get any splash. This procedure gives us very
v °Se to an instantaneous dose. During the early part of the Chatta-
study we were placing the dose container in the river from a
The dose was suspended from a steel cable stretched across the
in addition, the dose was bouyed up by a float to which it was
by a length of rope. This was the method we used during the
few doses on the Chattahoochee. Since this time we have decided
it is not necessary to have an individual or a couple of individuals
*ft the boat trying to handle this rather heavy weight. For this reason
have gone to a clothesline type of rig where we put a pulley on both
of the river and attach the dose to the line and pull it out to
desired location in the center of the river and then lower it below
surface. Then by means of a firing line attached to the rope we
off the blasting caps and the dose is released to the river.
"the sampling station the only change from the operation on the
rivers was in the manner of positioning the pump. On the
hattahoochee the sampling stations were at bridges, and the submers-
pump was attached to a float, which in turn was held in place by
89
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a rope attached to the bridge. The electrical line which supplies
power to the pump is connected to the rope.
As you can see, we do have a different method of release for the
Chattahoochee doses; we also do some things differently as safety
precautions. For example, we are never in the water with the dose as
we were in the smaller streams. We always have our radiological safety
officer present when we are handling this quantity of radioactive
material. The series of doses that we have made has been marked by
only one incident that caused us to cancel a dose. At the beginning
of one dosing operation we opened the barrel in which the container
was shipped, and we saw that the level of the dye had gone down in the
container. At that time we were using a boiling flask with a long necfc
on it, and we saw the level of the dye was not completely filling the
neck. We immediately took precautions to prevent any exposure. Dur-
ing shipping a crack had developed in this bottle, so we discharged
the contents into the river, and did not try to conduct a study with
this dose. As you know, a boiling flask bottle has quite thin walls.
Since that time we have been using a much heavier bottle. We send the
bottles along with the dye to the firm from which we buy the radio-
active tracers, they put the dye in the bottles and then they insert
the tracers. They then send them back to us in a mixture all ready
to be put into the stream.
The other downstream procedures are similar to what we have in
smaller rivers. There is, of course, more distance between sampling
stations. The sampling stations were on the order of 2 miles apart
on the Flint and South River. We need to use several times this dis-
tance on the Chattahoochee in order to get accurate results. Our
results are not as accurate if we have only 1 percent gas loss as they
are if we have a larger percentage gas loss. For this reason we are
using several miles between sampling stations.
The hydraulic studies on the Chattahoochee were similar to the hydrau-
lic studies on the Flint and the South. We are making cross section
measurements every 500 feet, except this time the measurement of dis-
charge, stream area, etc., have to be made from a boat. Here again
we use standard USGS procedures for making flow measurement from
We are finding the hydraulic properties in the Chattahoochee River to
be less variable than they were in the Flint and South, and I might
add that the studies are done at a flow rate which is controlled by
Georgia Power Company at a point upstream from Atlanta where they have
a small hydroelectric facility. All of our Chattahoochee studies have
been done on the weekend, and during the weekends the power company
has maintained a constant discharge through their generators of 1000
cfs. Studies on the Chattahoochee are not complete, for various
reasons; one of which being that Georgia Power Company had some work
to do on their hydroelectric plant at the time we were going to finish
up our series of studies last winter. The studies were delayed and
the wet season caught us before we completed the series of studies.
We will finish the studies on the Chattahoochee during this summer.
Values for the doses that we have made on the Chattahoochee indicate
90
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KP'S in the range of .01 to .0^, values which are considerably lower
tnan those reported on the Flint and South. These would be in terms
°f K per hour. We will in one of the sessions tomorrow compare K Ts
that we have measured with those given by some of the prediction efua-
tions and will have a little more to say about it then. Are there any
Questions about our study on the Chattahoochee?
Discussion
Are you going to conduct studies at higher flows, or do you
intend to use only low flow, around 1000 cfs, in the Chattahoochee?
(JEW) We intend to work with that figure. We, at this point, are not
Soing to try to run these tests at specific high or low rates; what
^ are trying to do is stay generally with low values. As was indi-
cated earlier we are trying to get values of K~ that will be of value
ttot only to our research but that will be of value to some of the
Agencies that want these values and these are some of the flows that
"they are most interested in.
Question: (inaudible) (JW) If I understood you, you asked for the
Average flow velocity. We are talking about 2 ft. per sec. in the
Chattahoochee with average depths at a cross section of 3 to h ft.
locally cross sections would be deeper than that but these are average
^ePths. So we are talking about a channel maybe 200 ft. wide, 3 ft.
^eep, and a velocity of 1--| to 2 ft. per sec.
Question; What does it cost for a Chattahoochee dose? (JEW) The
er material cost is about $850, field personnel about $250, and
e another $200-250 for lab analysis and computation. This does
include the cost of my time nor that of Dr. Tsivoglou nor does it
Include any equipment costs.
Do you assay your dose before releasing it? (JRW) Yes, we
it when we get it, and take another sample before it is released.
the smaller runs we were specifying 1.0 and 0.5 curies of the
Respective tracers and we were typically getting around 0.7 curies,
total.
Sjjgstion; What are the limitations of your license to release radio-
Active tracers? (JEW) Our license allows us to release a specific
J*°se in a specific river. If we want to make a dose at some other loca-
tion we have to get an amendment to the license.
^ obtaining the license we have to specify what uses are made of the
rs down the stream} but I might add that by the time the material
gone just a few hundred yards the radiation levels are down to a
that are less than the lifetime exposure level and so it is not
a problem.
How much distance do you cover with a release? (JEW) In
order of 8 or 9 miles, something like that.
91
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Model Study of Reaeration Capacity
of the James River Estuary (Virginia)
M. W. Lamraering
frvbreduction
In order to develop a mathematical model to predict the effects of
vaste discharges to an estuary, information must be obtained on the
fixing and dispersion characteristics of the estuary and, in the case
of oxygen-demanding wastes, the reaeration capacity. Avenues of in-
vestigation open to the actual measurement of dispersion character-
istics include the use of organic dye and radioactive tracers in the
fistuary itself and/or a hydraulic model of the estuary. Until recently,
reaeration capacity, expressed as a reaeration rate coefficient(s),
^s computed by mass balancing techniques for oxygen and empirical
correlations (l). A relatively new method involves the use of a
gaseous radioactive tracer, krypton-85, for the direct measurement
°f oxygen transfer across the air-water interface (2).
advantages of a hydraulic model study are economies in time^ mate-
rial, and personnel. Due to compressed scales (model to prototype),
Dispersion and reaeration measurements can be conducted over the en-
tire estuarine system for a period corresponding to a month during an
Actual time of about one day. In most cases, it would not be practi-
cable, or even possible, to carry out the same intensive study on the
Prototype. The disadvantages of a hydraulic model study are inherent
i& the design and construction of the model for uses other than the
Determination of mass transfer coefficients. Mass transfer similitude
^°es not exist, thereby presenting the problem of determining the
Proper scaling relation between mass transfer coefficients (diffusion
*nd reaeration rate coefficients) for the model and those for the
Prototype .
following sections of this paper describe the radio-tracer reaera-
study conducted in the hydraulic model of the James River estuary.
This study was conducted to obtain the reaeration data required by the
Atlantic Region, Water Quality Office, for their mathematical
of the estuary. The hydraulic model is located at the U.S. Army
ers Waterways Experiment Station, Vicksburg, Mississippi. Corps
°f Engineers personnel operated the model during the study.
$gsgription of Hydraulic Model
^e hydraulic model of the James River estuary covers a surface area
°f about one-half to three quarters of an acre (estimated from dimen-
8ions of the shelter housing the model) . The bed of the model is
93
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concrete with copper "roughing" strips strategically located to yield
proper salinity distribution and velocity profiles. Scaling factors
(model to prototype) are as follows:
Horizontal : 1:1000
Vertical : 1:100
Velocity : 1:10
Time : 1:100
Discharge : 1:10°
Tidal cycles (semidiurnal tides) are sinusoidal with a time period of
7-1/2 minutes per cycle. The volume of water in the model during its
operation is on the order of approximately 3x10^ liters.
As shown in the schematic plan of the model (figure l), the limits
extend from Richmond, Virginia, to the Atlantic Ocean. In addition
to the James River, fresh water inflows to the system include the
Appomattox, the Nansemond, and the Chickahominy Rivers. During the
reaeration study, the simulated flow in the James River was maintained
at 3200 cfs. Simulated flows in the tributary streams were:
Appomattox River - 152 cfs
Nansemond River - 89 cfs
Chickahominy River - 56 cfs
Simulated waste discharges from the cities of Richmond and Hopewell
were not included in the reaeration study.
Reaeration Study Procedures
To obtain reaeration data for the model reach of interest, City of
Richmond to Dancing Point (Figure l), the alternative methods for
injecting tracers into the model were an instantaneous release and a
continuous discharge. Both methods would have yielded the temporal
distributions required for calculating diffusion and reaeration rate
coefficients. The method of instantaneous release was selected on tbe
basis of the relative ease with which it could be performed and the
limitation of the model study to a maximum duration of 120 model tidal
cycles (60 model days) or 15 actual hours. A continuous dosing method
requires that the discharge continue until steady state conditions of
constant concentrations (at a given tidal stage) are observed at each
location of interest. There was doubt that such a condition would be
met within the 'imposed time limit. To extend the study beyond 120
tidal cycles was not considered practicable in terms of the additional
data that would have been obtained versus the added costs and person-
nel requirements.
In contrast to a true instantaneous release, dose solution was inject-
ed into the model at a uniform rate over one tidal cycle (centered
about low water slack). This same procedure was used by O'Connell
and Walter (3) for their dye dispersion studies in the hydraulic model
-------
JAMES RIVER MAP
• SALINITY.DYE. AND VELOCITY STATIONS
6 TRACER RELEASE POINT
ATLANTIC OCEAN
-------
of San Francisco Bay. To ensure complete coverage of the reach of
interest and temporal distributions characterized by well-defined
peaks, tracer releases were made at two locations: Richmond and
Station 25 (Figure l). The dose at Station 25 initiated the study
and the tidal counter whereas the Richmond release was made during
tidal cycle 18. The time lag was introduced as an attempt to mini-
mize the overlapping or merging of the separate tracer masses at
stations downstream from Hopewell.
Table I
Dose Solutions
Release Point Fluorescein Dye Tritium Krypton-85
(grams) (millicuric^) (millicuries)
Richmond, Va. - 6 k
Station 25 k k
Total Volume of Dose Solution - 2.2 liters
Volume Released into Model - 1.2 liters
The amounts of tracers in the two dose solutions are presented in
Table I. As indicated, the conservative tracer in the dose solution
released at Station 25 was fluorescein dye whereas tritium was used
in the dose solution released at Richmond. The use of different con-
servative tracers was to facilitate data analysis at stations for which
temporal distributions from the separate releases were measured. Dose
solutions were prepared in the field in the afternoon preceding the
study. The preparation involved the addition of tritium (as tritiated
water) or fluorescein dye and krypton-85; in form of clathrate con-
tained in a capsule (the capsule and the clathrate dissolve after a
few minutes in water, releasing krypton-85 into solution), to approxi-
mately one liter of distilled water in a two-liter glass reagent
bottle. After the water volume was carefully adjusted such that there
was no significant air bubble after sealing the bottle with a rubber
stopper, the dose solution was mixed by a magnetic stirrer for several
minutes. Discharge into the model at the rate of about 1.2 liters per
model tidal cycle corresponded to a prototype discharge of about 0.5
The frequency of sample collection at each station was based on the
relative location of the station in respect to the two dose release
points and the expected shape of the temporal distribution(s) - a
broad or sharply defined peak. In the case of the dose solution con-
taining fluorescein dye, the arrival and passage of tracer mass past
a given location was followed by on-site fluorometric measurements of
dye concentrations. The net seaward movement of the tracer mass con-
taining tritium and krypton-85 was estimated from a prior dye tracer
96
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study conducted by the Corps of Engineers at the same fresh-water
inflow condition. However, this movement was also detected in a qual-
itative manner in the model by a counting assembly consisting of an
end -window Geiger-Muller tube and sealer. When the tube was posi-
tioned just above the water surface (figure 2), the gamma-ray emis-
8ions from krypton-85 were detected. The maximum frequency of collec-
tion, every cycle (low water slack, determined by visually observing
the lack of movement of floating particulates) for 10 to 20 tidal
cycles following dose release, occurred at stations in the immediate
vicinity of the release locations. Once the sampling of a station
^s initiated, sampling was generally continued until the termination
°f the study irrespective of the likelihood for measuring significant
tracer concentrations. To cover all the stations of interest (Stations
36 > 3^, 33-19, 17, 15, and 53) over the study period of 120 tidal
cycles, a sampling crew of eight was employed.
mentioned above, water samples were collected from the model at
water slack. The collection procedure involved gently dipping a
< ml glass vial into the water at a position corresponding to the
location of the main river channel (marked on the model at each sta-
tion). Considering the size of the sampling vial (7/8" dia., 3-5/16""
•*-ength) in terms of model scaling factors and the prototype volume
Represented by each sample (about 6600 gallons) great care had to be
QXcercised to prevent significant surface disturbance other than that
Caused by tidal action. The vials were fitted with "poly-seal" tops
to prevent the presence of an air bubble in the collected sample.
^Qalyses of the dye, tritium, and krypton-85 concentrations in the
^ter samples were performed in the laboratory of the Radiological
Activlties Section (Cincinnati, Ohio). The specific details of deter-
ging the tritium and krypton-85 concentrations by liquid scintilla-
^ion counting have been discussed in the paper by Mr. R. J. Velten.
"luorescein dye concentrations were determined fluorometrically with
* G. K. Turner Associates' Model 111 Fluorometer (lower limit of
4etectability of 0.5
temperature in the model was monitored continuously at Station
and intermittently at other locations. Unlike salinity, velocity,
tidal elevation, no controls were exerted over water temperature.
simulated James River inflow was substantially cooler than the
of the model water. Also, as the outdoor and indoor air tempera
increased during the day, the water temperatures in the model
Creased.
. of Data Analysis
°llowing an instantaneous or nearly instantaneous release into a
T^aulic model or estuary, a conservative tracer (tritium or dye)
*s Dispersed by turbulent mixing whereas gaseous krypton-85, a non-
°Hservative tracer, undergoes the same physical dispersion as well
97
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•O
00
JAMES
RIVER
MODEL
S C AL E
ooo
COUNTING
ASSEMBLY
F
-------
as loss to the atmosphere by diffusion across the air-water interface.
The back and forth motion of the tracer mass caused by tidal action
yields temporal distributions (concentrations as a function of tidal
cycle) at each station which show build-up to maximum values followed
by die-off as the tracer mass passes through the area. In this re-
ject, the advantage of releasing the dose solution over a tidal
cycle is that the temporal distributions can be integrated to yield
steady state concentrations (3). Despite the fact that the estima-
tion of steady state concentrations was not an objective of the reaera-
tion study, it was considered desirable to obtain the necessary data
in the event a future need should arise.
^he ratio of the krypton-85 concentration to the conservative tracer
concentration as a function of time exhibits a decreasing trend at a
Siven sampling station. This is due to the loss of krypton-85 to the
atmosphere as the tracer mass passes through the area. Thus, the rate
constant for krypton-85 loss can be calculated from the temporal distri-
butions for the station by the following relationship:
-(ICj(t)
ln «V°cA =
-------
Results
Examples of typical temporal distributions for krypton-85 and tritium
or dye at several locations in the model are shown in Figures 3, 5, 7;
9, and 11. At each location., except Station 53 in the Curies Neck,
the distributions exhibited a buildup in concentration to a maximum
value and a die-away edge skewed to the right. (The radioactivity
data plotted in terms of activity units, cpm, actually refer to acti-
vity per 2 ml of sample volume. For fluorescein dye, 1 ppb was arbi-
trarily set equal to 1 cpm per 2 ml.) This pattern was not observed
at Station 53 because sampling was not started in time to measure the
leading edges of the tracer distributions. The krypton-85 distribu-
tion for Station 23 (Figure 9) is of particular interest since it
shows the cumulative effect of the mixing of the leading edge of the
dispersed tracer mass released at Richmond with the trailing edge of
that released at Station 25. As shown, both releases contributed to
the instantaneous krypton-85 concentrations after tidal cycle 35.
An interesting observation was the time lag between the peak concen-
trations of krypton-85 and tritium at locations substantially down-
stream from the tracer release point (Richmond). For example, at
Station 29 the peak krypton-85 concentration was observed at tidal
cycle 31 in comparison to tidal cycle 37 for tritium. At locations
close to the tracer release point, Stations 32 and 3^, the peak con-
centrations were coincident in time. The time lag was observed
because the temporal distributions were for a fixed point in space.
If spatial distributions had been determined, such a time lag between
peak concentrations would not have occurred. Although beyond the
scope of this paper, it can be shown that the dispersion coefficient
can be calculated from the magnitude of the measured time lag.
For all main channel locations (except Stations 30, 31, and 32) and
Station 53 in the Curies Neck, the semi-logarithmic plot of concentra-
tion ratio (krypton-85 to conservative tracer) versus tidal cycle was
well fitted by a straight line (Figures k, 8, 10, and 12). In the
case of locations such as Station 23 where the data from both doses
were used to obtain independent measurements of the rate constant for
krypton-85 loss, the plotted values of CKV./CTT o were calculated from
krypton-85 data corrected for the tracer release at Station 25. This
involved a point-by-point subtraction of the extrapolated portion of
the distribution attributable to the Station 25 dose (Figure 9). The
plots of concentration ratio versus time for Stations 30, 31, and 32
could not be fit with a single straight line, but required two lines
with substantially different slopes. As indicated in Figure 6, the
line of greater slope was designated "Mode 1" and the other "Mode 2".
Although this author is unable to provide a positive explanation for
this finding, it is assumed that "Mode 2" reflected the slow bleeding
of tracers from the Curies Neck and the Appomattox River into the main
channel after the bulk of the tracer mass had passed downstream.
100
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10=
I04
FIGURE 3
JAMES RIVER ESTUARY MODEL
32OO CFS
STATION 34
ICT
Q.
O
10
2
10
o TRITIUM
xKRYPTON -85
1
20
40
60
Tl DAL
80
CYCLE
100
120
1 01
-------
5.0
1.0
x
ro
8
FIGURE 4
STATION 34
* 2.824 day'
O.I
20
30 40
i
50
TIDAL
_L
60 70
CYCLES
80
90
102
-------
I03
T
T
FIGURE 5
JAMES RIVER ESTUARY MODEL
320O CFS
STATION 32
6
O.
O
I03
o TRITIUM
KRYPTON - 85
I02
10
I
I
20
40
60
TIDAL
80
CYCLE
100
120
1 03
-------
5.0
FIGURE 6
STATION 32
KKr (Mode I) - 5.447 days'*
KKr(Mode2) * 2.26O days'*
20
50 60 70
TIDAL CYCLE
1 04
-------
T
T
T
FIGURE 7
JAMES RIVER ESTUARY MODEL
32OO CFS
STATION 29
x TRITIUM
o KRYPTON - 85
5
o
k
«»
^
I0a
I02
10
1
1
20
40 60 80
TIDAL CYCLE
IOO
120
1 05
-------
STA TION 29
50 6O
TIDAL CYCLE
1 06
-------
FIGURE 9
JAMES RIVER ESTUARY MODEL
3200 CFS
STATION 23
o
v*
X
Is
0
V
10
o TRITIUM
* KRYPTON -85
« DYE
1
20
40 60 80
TIDAL CYCLE
100 120
1 07
-------
10
UJ
2 i.o
2
I
IO
o
<
a:
01
I I I I I i \ I
I T
FIGURE 10
STATION 23
_ KKr* 4J52 days'1
\ I I I I I I I I L_J I L
20
40 60 80
TIDAL CYCLE
100
120
1 08
-------
I04
FIGURE II
JAMES RIVER ESTUARY MODEL
3200 CFS
STATION 53
,I05
x TRITIUM
o KRYPTON - 85
10*
10
1
1
20
40
60
TIDAL
80
CYCLE
100
120
I 09
-------
5.0
FIGURE 12
STATION 53
1.0
I
ro
in
oo
o
I-
cr
KKr* 2.481 days
-i
O.I
30
40
50 60 70 80
TIDAL CYCLE
90
1 1 0
-------
calculated rate constants for krypton-85 loss, K- , and reaera-
, kp, are summarized in Table II. The close agreement "between
independent measurements at Stations 27 through 23 was indicative
of the relative accuracy of the study procedures, the high degree of
oducibility of the multi-tracer technique under controlled condi-
s and the stability of the model. Support for the assumption
"Mode 2" loss of krypton-85 at Stations 31 and 32 was represen-
ve of the sloshing action between the Curies and the main channel
indicated by the similarity in magnitude of the "Mode 2" rate
onstants with the rate constant for Station 53 (l.l and 2.3 model
~ versus 2.5 model days"1).
^ration rate constants for the prototype were calculated by apply-
a reduction factor of l/100th to the model values. This scaling
was used because it represented the model to prototype ratio
time. That this was a valid approach was indicated by the appar-
success with which the reaeration rate constants were used in the
model of the prototype for oxygen-demanding wastes.
however, the dissolved oxygen profiles predicted by the
model were not influenced as greatly by variations in
6 reaeration rate constant as by small variations in the dispersion
Efficient. An additional piece of data which supports the scaling
cactor of l/100th is O'Connor's (5) estimate of the reaeration rate
>°flstant f°r the lower estuary in the vicinity of Hopewell. For a
River flow of 3150 cfs, O'Connor used an empirical equation to
iate a rate constant of 0.071 days"1 (at 25°c). This is in al-
vexact agreement with the average value of 0.069 days'1 calcu-
ted from the results for Stations 29 and 30.
J^ niethod involving the use of gaseous krypton-85 for the direct
of reaeration capacity was successfully employed in the
model of the James River estuary. Two separate releases
, at Richmond, and at Station 25 in the lower estuary, pro-
independent measurements of the reaeration rate constant at
stations in the lower estuary. The agreement obtained indl-
^e<3- that the method is accurate as well as reproducible.
4fi of a somewhat circumstantial nature indicated that the
t^opriate scaling factor for the conversion of model rate constants
c^ Appropriate prototype values is the scale factor for time. In the
6V8e of the James River model, this scaling factor was l/100th. How-
Ij. ** the question of the appropriate scaling factor remains to be an
t^ of interest and one certainly worthy of additional research. If
H^^n be shown that the reaeration data from a distorted hydraulic
t0 ®1 can be accurately scaled up to the prototype, a most significant
- 1 win have been provided to the engineer faced with the problem
the impact of waste discharges into an estuary.
Ill
-------
Table II
Rate Constants for Krypton-85 Loss and Reaeration
Station
36
34
33
53 (Curies Neck)
32
31
30
29
28
27
26
25
24
23
K-- (nodel days" )
Mode 1 Mode 2
8.0
2.8
3-3
2.5
5.4 2.3
5.7 1.1
6.0 3.9
5.4
5-3
4.9 (2.9)
4.3 (3.7)
2.6 (2.9)
3.9 (3.4)
1.6 (1.4)
kp (model days" )
Mode 1
9.6
3.4
4.0
3.0
6.5
6.9
7-2
6.5
6.4
5-9 (3.5)
5.2 (4.5)
3.1 (3-5)
4.7 (4.1)
1-9 (1-7)
ModjL^
2.8
1.3
4.T
-"
,.
Values in parentheses were computed from temporal distributions produce*
the tracer release at Station 25.
1 1 2
-------
Ac knowledgme n t
generous cooperation and assistance of the Corps of Engineers
responsible for the operation of the hydraulic model during
tracer study is gratefully acknowledged.
E. C. Tsivoglou, Georgia Institute of Technology, provided invalu-
assistance in the planning and conduct of the field study.
personnel who worked long and hard hours in the collection of
included Miss Audrey Donahue, Mr. J. P. Longtin, Mr. B. L.
Mr. W. W. Finley, Mr. K. Ballentine, Mr. L. VanDenBerg, and Mr.
Mierenfeld. The quality of their work is reflected in the compre-
nature and accuracy of the results obtained.
113
-------
References
1, Eckenfelder, W. W., and O'Connor, D. J., Biological Waste Treats
ment, Pergaraon Press (196^).
2. Tsivoglou, E. C., [Tracer Measurement of Stream Reaeration, for
the Federal Water Pollution Control Administration, U. S. Dept.
of the Interior (June 1967).
3. O'Connell, R. L., and Walter, C. M., Hydraulic Model Tests of
Waste Dispersion: San Francisco Bay> R. A. Taft Sanitary Engi-
neering Center, Cincinnati, Ohio (August 1962).
4. Tsivoglou, E. C., Cohen, J. B., Shearer, S. D., and Godsil, P. Jo
"Tracer Measurement of Stream Reaeration II. Field Studies."
Journal Water Pollution Control Federation, 40, 2, Part 1, pp.285'
305 (February 1968).
5. O'Connor, D. J., The BOD Assimilation Capacity of the Lover James
River, Virginia, Report to State Water Control Board, Commonweal*11
of Virginia
-------
Field Studies in Yaquina River Estuary
Of Surface Gas Transfer Rates
^- J. Baumgartner, M. H. Feldman, L. C. Bentsen, and T. L. Cooper
production
He purposes of this study are (l) to measure a range of values for
}|*sfinea j_n equation 1 below) in a natural estuary, using krypton-85;'
j;*v to determine if variations in K-> can be related to energy distribu-
*°n associated with wind stress, velocity gradients in the channel and
ensity gradients in the channelj and (3) to improve procedures for
of K^ in bays and estuaries. The purpose of this paper is
provide preliminary information on accomplishments relating to field
surements .
net surface transfer rate mechanism assumed for loss of dissolved
^"ypton-85 to the atmosphere is
= instantaneous concentration of dissolved
krypton-85 in water;
= krypton reaction rate constant, variously
entitled reaction velocity, and reaction
rate coefficient.
8 urement of KL for krypton is pertinent to the subject of atmospheric
i^Sen transport into unsaturated liquid systems, using the ratio developed
Tsivoglou (1967), viz:
- ^(^KRYPTON (2)
(I5P)
, ^ OXYGEN has historically been suspected of being related to turbulence
C *he liquid phase, either by that name, or something akin to it, as
< e£tical mixing." Streeter and Phelps (1925) mentioned the relationship
B, 'frictional resistance to flow," implying a dependence on energy dis-
«J&tion. Osborne Reynolds, apparently, was the first to describe a
, for the turbulence-energy dissipation function (Hinze, 1959).
c°nnor and Dobbins (1956) established a relationship for (K2)oxyGEN
115
-------
related directly to the rate of energy dissipation per unit mass of
fluid, viz:
(K2) « USg, (3)
OX
where
U = mean stream velocity,
S = slope of energy gradient,
g = gravitational acceleration.
Gameson (1958) mentioned that reaeration at weirs was directly related
to the distance of "free fall." A review by Thackston and Speece (~~
summarizes additional work on aeration at weirs. Rather accurate n
are available to compute the energy loss at such channel transitions.
Dobbins (196*0 pointed out that vertical distributions of energy supply
and dissipation are greater near the stream bottom and less at the sur-
face, and, including other considerations of the surface transfer of
oxygen, developed a relationship expressing the rate determining coeffi*
cient as a function of the energy transfer at the surface and the inter"
facial area. The surface area was recognized as sensitive to wind, but
probably related to a Froude number, and for "most natural streams" not
increased more than eight percent over the projected surface area. He
did not intend to include wind energy contributions. Downing and TrueS-
dale (1955) used a small tank to show that wind speeds increasing from
3 to 1*4- meters/sec (5 cm above surface) increased the mass transfer
coefficient, f, where f = [KpV/A] (V = Volume of liquid participating
in exchange, A = Effective surface area) by a factor of *MD. Waves,
superimposed independently, caused increased transfer at low wind speed^
but hindered transfer at high speeds. Waves, separately, increased
transfer by a factor of nearly 20, depending on wave height and frequerW
Measurements in the Thames estuary indicated an increase in f from 0.5
cm/hr to approximately 30 cm/hr for a range of surface effects due, pre*
sumably, to both wind and wave conditions. Kanwisher (1963) conducted ^
similar tank studies and found that [KgV/A] varied over a range of -~air
30 in approximate proportion to the square of the wind speed.
Guinasso, et al. (1968) used data by Broecker (196*0 on the radon-222
distribution near the sea surface to calculate a transfer coefficient
5 times greater than Kanwisher's value for a comparable wind speed. W^
also measured xenon-133 distributions resulting from an explosive reiea
of two cureis of Xe-133 below the surface. A transfer coefficient cal-
culated from xenon data was about 7 times greater than expected using
Kanwisher's lab data for comparable wind speeds.
Many of these authors, and others, have recognized the importance of v° j,
uniform, vertical density distribution in restricting general applicati
of previous values of (Kp)0x for estuaries, and in use of formulae for
116
-------
°mputing (K^)QX from stream depth and mean velocity; however, no new
Quantitative approaches have been offered for this situation. In addi-
lon, we consider surface wind and wave effects to be of sufficient im-
portance in bays and estuaries to cast considerable doubt on the use of
ctlese formulae for Kg calculations.
method appeared to offer a method directly applicable to
studies to develop new relationships for K~ as a function of
~
aergy input at the surface via wind, and "hydraulic" energy terms.
Qcluding vertical velocity and density gradients.
Of! Ya,ered a ran£e of natural conditions necessary for collection of data
* completely general application, yet it was small enough to fit our
Sistic constraints. Figures 1 and 2 (Callaway, et al, 1970) show a
liBH El Vl6¥ °f the estuary from the ocean to the approximate upper
W of tldal influence. The gas transfer studies conducted to date
re been in the reach from mile l4 to mile 16. Figures 3, 4 and 5 show
6 eta11 of thiB reach» Station numbers are approximately one-half
lntervals startlnS "with mile l4. There are no major changes in
flow direction or channel width between Station 1-4. The depth (at
tide) decreased from 12 to 9 feet near Station 2.
h
g Sure 6 shows a typical set of tidal conditions during a test. The
>g 8e range is about 9 feet and the current ranges from nearly +2 to
j^s&ots. On April 7, the current at Station 2 would be expected to
^ e been somewhat reduced and delayed in time compared to the predicted
Wai The teSt Was Planned for maximum negative current and minimum
ZM+L at BurPee' At other times of the year the stage and current
^ ^es are phased differently so the effects of velocity and depth may
%rparable for the same channel configurations. We anticipate being
v t
in tne estuary. Tests under a variety of density distribution
my provide data useful for relating gas transfer rates to
hydrodynamics. Table 1 is an example of the density distribution
collected for each run.
^
^lhftVfcly' current meters are set in place up-current from the injection
\J ' a vertical profile of salinity and temperature is made, surface
^ ent drogues are released, and approximately 400 millicuries (me)
4 of krypton-85 and tritium water mixed with rhodamine WT and local
117
-------
Mill Creek
Nautical mile
Legend
o Conductivity Meter Location
—*Wind Recorder Location
T Tide Gauge Location
O Stream Gauge Location
River Mil?*
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Station
OSU Dock
Sawyer's Dock
Fowler's Dock
Criteser's Dock
Burpee
Charlie's Dock
(Fritz)
Elk City
(NauticaVlx
o, 1.5
•u 3.5
^7.0
^9.5
M4.0
VI 6.0
VI9.5
* River Mile 0.00 is the
end of the south jetty.
FIGURE 1. FWPCA Stations, Estuary Diffusion Project, Yaquina Estuary
(From Call away et al., 1970)
1 1 8
-------
•rr-i Horizontal Scale
10 feet
0 20 feet
Vertical Scale
I Fritz:
(Charlie)
B
20 0 5
Width (Feet x
FIGURE 2. Cross Sections of Estuary at Conductivity Monitoring Sites, Yaquina Bay, Oregon
(From Callaway et al., 1970)
-------
LENGTH-FT.
2O«O
2105
I960
I960
2000
two
1900
I94O
FIG. 3
REAERATION PROJECT SEGMENT
YAQUINA RIVER -MILE 15-19
Linn cro>» nvw 4.3 mM ucitnom of GMT«IO
*! *V
-------
Sta. i Sta. 3 / Sta. 4
8 -
B C D E F G H I J K
FIGURE 4. Yaquina River Estuary Reaeration Project Segment. Depth at Various Sections.
-------
350
320
01
260
0)
10
to
41
U
at
t
in
230
200
170
Mean Tide
Sta. 1
Sta. 2 Sta. 3
* , *
E
H
0 K
SectAons.
-------
01
-------
TABLE 1
DENSITY DISTRIBUTION NEAR STATION 2, SEPT. 2, 1969
Start
Depth, m
0
1
2
3
4
Finish
0
1
2
3
4
5
S, / 00
6.1
6.3
7.1
7-7
10.1
7.5
7.7
7.8
8.8
9-7
9.8
T, °C
21.2
21.2
21.2
21.4
22.0
21.3
21.3
21.4
21.5
21.5
22.0
p*, kg/m3
1002.64
1002.79
1003.40
1003.80
1005.46
1003.67
1003.82
1003.87
1004.60
1005.28
1005.23
From "Tables for Sea Water Density," U.S. Navy Hydrographic 0£fic&
Publication #615, Washington, D.C., 1952.
124
-------
are discharged into the center of the stream. Distribution of
tracers across the stream was used on some runs before the present pro-
cedure was adopted. Water is pumped from just below the surface (6"-
12") and the discharge end of the injection hose is oriented horizon-
tally the same distance below the surface. It is felt this will
Minimize density differences between the tracer solution and the
Ambient water, and prevent the tracer from spreading too thinly on
the surface or sinking to unknown depths. The boat is driven down-
Current slowly past the dye to the desired sampling location. The
b°at is then directed up-current and held in position against the
Current by alternately engaging and disengaging the clutch at low
throttle. A continuous stream is pumped aboard from 6" -12" below
the surface, through a fluorometer, and a small stream is split from
the discharge line to provide samples for subsequent analyses. The
se stream is inserted in a pre-numbered 25 ml liquid scintillation
and slowly withdrawn when dye is detected in the fluorometer,
being taken to assure 3 volumes or more have been flushed through
vial and no gas bubbles are trapped as the polycone screw cap is
securely attached. Samples are taken until the dye peak has passed,
''hen the boat is moved to the next station. In several early trials,
?• second pass was made through the dye field with the sampler two feet
v the surface. Generally, no dye was detected and the practice
been discontinued to minimize artificial disturbance of the tracer
d. Samples are returned to the lab, transferred to replicate
Counting vials containing scintillation fluid and each counted twice
J& a Packard 3375 (Mention of proprietary names in this report is for
^entification only. No endorsement is implied.). Individual vial
°unts are tabulated, corrected for background, and tritium counts
for krypton "spill-over".
logs of the corrected (krypton count/tritium count) ratio are
Olaputed and tabulated by a digital computer.
8ures 7, 8, 9, and 10 show the results of five trials conducted
^nce June 1969. Not all ratios obtained were plotted since many
°Unts were judged not sufficiently above background.
b
®8Ults for runs on June 17 and September 2 are plotted on the same
aph (Fig. 7) to show what may have been the result of a significantly
Beater flooding current on June 17. Data for the run on September 9,
°& but the wind was higher (wind speed at 22 ft 15 k with frequent
to 35 k)' On a11 runs there may k^6 been other similarities or
erences we did not measure.
125
-------
HI
O>
September 2, 1969
K3 =
50 60
Time, Minutes
1 . Xaqvnua WA^er Estuary kas, Transfer- Data for Reaeration Project
0.18/hr
4.3/day
June 17, 1969
K2 = 0.73/hr
= 18/day
-------
3.5
3.4
3.3
3.2
3.1
3.0
2.9
2.8
§> 2.7
3
2<6
2.5
2.4
2.3
2.2
2.1
2.0
1.9 ,
8
Kz = 0.72/hr
= 17.3/day
«=C
to
Uncertainty exists regarding the "spill over" correction
used for these data. Experience indicates that the Kr/H
ratios are influenced by this correction but the slope of
the line is not materially changed.
TO 40 50
Time, Minutes
60
70
80
FIG 8. Yaquina River Estuary Gas Transfer Data for Reaeration Project
September 9, 1969
1 27
-------
2.4
2.2
2.0
1.8
1.6
1.4
1.2
1.0
.8
.6
.4
.2
0
(K2),,D " 0.41/hr
'KR
e
9.8/day
e
o
60 fe"
TO 20 30 40 50
Time, Minutes
FIS.
9. Yaqulna River Estuary Gas Transfer Data for Reaeratlon Project
September 17, 1969
1 21
-------
1.7 r
1.6
1.5
1.4
.6
.5
.4
(K2)
Kr
e
0.71/hr
17/day
NOTE: Wind speed at 22 ft varied from 3 to
35 knots and averaged 15 knots during
the test.
To 35 40
Time, Minutes
50
60
70,
80
FIG. 10. Yaquina River Estuary Gas Transfer Data for Reaeratlon Project
May 26, 1970
1 29
-------
Equipment
Equipment, as our procedure, has "been modified and supplemented as we
progressed. Our work boat is equipped as shown schematically in
Figure 11. A submersible pump is used to maintain positive pressure
on all fittings above the water line. The only modification we plan
is to add a second system for simultaneous sampling at a second depth.
Our wind measurement system will consist of two Climet cup anemometers
and direction vanes sampling at 8 and 2.6 feet above the water surface.
Data are traced on two two-channel Esterline Angus recorders. As
shown in Figure 12, the height is maintained constant by a floating
dock. The dock is also to be used to indicate stage on a Leupold and
Stevens recorder. Bottom channel currents are measured by Geodyne
digital film recording, Savonius-type current meters. They are mounted
on rigid tripod structures so that the speed sensors are respectively
1 and 6 feet off the bottom (Figure 13). A Marine Advisors ducted
impeller current meter is buoy-mounted to record analog traces (Rustrak;
of both speed and direction 1 foot below the surface. An Industrial
Instruments induction salinometer (Model RS-5) is used to indicate
temperature and salinity. Data are recorded manually by a crew member-
Discussion
In general, the krypton distribution in a body of water cannot model
exactly the oxygen distribution in the same body of water; and, in
general, the oxygen distribution cannot be used to model either gas
transfer at the air-water interface or the vertical distribution of
properties, due to insufficient knowledge of the biochemical inter-
action terms. Krypton, however, has been shown to be a linearly pro-
portional analog for estimating oxygen transfer across the air-water
interface. In order to estimate the influence of hydrodynamic pro-
perties on the vertical distribution of dissolved oxygen, simultaneous
distributions of other properties, such as velocity, tritium water,
salt, and in some cases either temperature, density or rhodamine dye
must be provided. Historically, (K^)px has been used to predict oxyge"
concentrations, assumed to be vertically uniform to a depth, H, in an
attempt to incorporate both the interfacial transfer and vertical
transport mechanisms. Dobbins (1964) pointed out that .there is little
justification to inclusion of H in prediction formulas since H can be
determined separately, thus removing its apparent influence on f, the
gas transfer coefficient. H frequently has been interpreted as the
total depth of the stream, although it should be obvious that since
it is defined by [V/A] , in many ponds, estuaries, bays, fjords,
oceans and possibly some rivers, it is related to a depth defined in
terms of either boundaries or parameters indicating gradual or abrupt
vertical flux inhibition. Variations in H may be greater or lesser
than variations in total depth depending, among other things, on the
presence and dynamic stability of pycnoclines. We reported our resul*
today in terms of [f(A/V)]KR rather than f^ because we have not
130
-------
u
Auxiliary
Power
Not to scale
FIGURE 11. Research Vessel Adapted for Gas Transfer Data and Flourometry
-------
26 ft.
u
K>
Not to scale
8 ft.
Water Surface
FTgating Dock at Burpee
*\
-------
FIGURE 13. Water Current Meter Set Up for Reaeration Project, Yaquina River Estuary
-------
obtained sufficient data nor conducted sufficient analyses to determine
V/A. Both f and (A/V) can vary during the interval between samples;
f because the wind stress might change, for example, and (A/V) because
the tracer may be continuously dispersed vertically. We have plotted
a straight line through the data points as though the product of f
and (A/V) were constant. This of course needn't be the case, in fact,
with good measurement of (A/V) a major value of the method is realized
in determining the variation of f and f (A/V) for succeeding stream
sections. To aid in interpreting our results we can assume that (A/V)
is at most 1 ft and probably decreased gradually to \ to 1/3 ft .
Some discussion is warranted on how our procedure is appropriate to
measurement of f— and (K^)— in vertically non-uniform flows. An
assumption impliea in plotting the data as in Figures 7-10 is that
the tritium tracer is dispersed identically as the krypton tracer
so that the ratio changes reflect only the surface boundary transfer.
An inspection of the general mass transport equation
at ax ay az ax ay
shows that both mean convective and turbulent transport terms include
products of the spatial gradients of the tracers. These generally
cannot be the same in our experiment because of the surface boundary
transfer of one of the tracers. The difference is usually assumed to
be negligible, and, for the field tests reported here where tracer
depth was approximately less than two feet, we have judged this to be
so from the distributions of salinity and temperature. Caution is to
be exercised when the experiment is conducted during or shortly after
rains, which, in the Pacific Northwest, cannot be considered an unusual
event. Aside from energy input and the effects on A, a thin lense of
fresh water may develop on the surface. Accepting this assumption,
it does not matter that the dye is released near the surface and dis-
perses in three directions.
Aquation 1, as written, implies further that the measured concentra-
tion of escaping gas (or in this case, the ratio) is the mean concen-
tration of the volume, V, and furthermore is the concentration at
the water "surface." Judging again from the salinity and temperature
data we consider the latter true enough for practical application in
our trials to date. We expect, however, that during all runs, the
concentrations were slightly greater than the properly averaged con-
centration would have been.
Knowledge of the vertical distribution of tracers is much more impor-
tant, however, to the calculation of V, which is defined as H A. where
A. is the horizontal projection of a short stretch of stream ana He
is a depth effective in vertical transport. In our studies we have
13 k
-------
not measured the vertical tracer distribution nor have we completed
analysis of other data which would allow us to compute an estimated
value for H . In some runs we expect H was increasing at a rate
greater than in others.
It is important to recognize that H for the tracer experiment does
not necessarily equal H for vertical transport of oxygen transferred
at the surface, although it may approach it, and that H for oxygen
^ould not necessarily be constant in time for an estuarlne system.
Under these circumstances it is clear that the best alternative is
to release the tracer near the surface and measure, or compute, the
Vertical distribution of properties. To release the tracers at depth
"Without knowing beforehand what the vertical density distribution is
and what can be forecast for the ensuing tidal cycle is surely to
invite trouble. If the tracer doesn't reach the surface, the surface
transfer rate cannot be measured. To attempt uniform vertical distri-
bution of tracer initially may require considerably more tracer (and
Collars) than is necessary.
the procedure outlines, it takes two man days to set up meters,
-., and two men to conduct the test. It presently costs about
$200 for the combined dose of tracers.
^e intend to continue our experimental studies, adding measurement
Capabilities and increasing tracer doses as budget and other con-
etraints allow.
nt s
^ Tsivoglou's assistance in the early stages of getting this pro
tect started and his continued interest and encouragement are
hatefully appreciated.
physics services and counting facilities are provided by
State University's Radiation Center. V. N. Smith, Chemist,
Center, conducted recent counting procedures. W. A.
and D. R. Hancock have assisted in equipment preparation and
collection.
135
-------
References
1. Broecker, W. S., "An Application of Natural Radon to Problems in
Ocean Circulation," Symposium on Diffusion in Oceans and Fresh
Water, Lamont Geological Observatory of Columbia University,
Palisades, New York, August 31-September 2, 196^, pp. 116-145.
2. Callaway, R. J., G. R. Ditsworth, and D. L. Cutchin, Salinity,
Runoff and Wind Measurements, Yaquina Estuary, Oregon, Working
Paper 70, Pacific Northwest Water Laboratory, Federal Water
Quality Administration, Corvallis, Oregon, March, 1970, p. 42.
3. Dobbins, W. E., "BOD and Oxygen Relationships in Streams," Journal
Sanitary Engineering Division^ ASCE, SA3, pp. 53 -78, June 196TI
4. Downing, A. L., and G. A. Truesdale, "Some Factors Affecting the ^
Rate of Solution of Oxygen in Water," Journal of Applied Chemistry^
pp. 570-581, 1955.
5. Gameson, A. L. H., A comment during informal discussion, p. 31,
Proceedings, Oxygen Relationships in Streams, Public Health Service
Technical Report W 58-2, Cincinnati, Ohio, March 1968, p.
6. Guinasso, N. L., Jr., D. R. Schink, and R. L. Charnell, "The
Effects of Vertical Mixing and Surface Outgassing on the Rn-222
Concentration Profile in the Surface Waters of the Sea," Paper
presented at American Society of Limnology and Oceanography
Meeting, Logan, Utah, June 26, 1968.'
7. Einze, J. 0., Turbulence, McGraw Hill, New York City, New York,
p. 586,1959.
8. Kanwisher, John, "On the Exchange of Gases between the Atmosphere
and the Sea," Deep Sea Research, 10, pp. 195-207, 1963.
9. Krenkel, P. A., and G. T. Or lob, "Turbulent Diffusion and the
Reaeration Coefficient," Journal of Sanitary Engineering DivisioO;
ASCE. SA2. pp. 53-83, March 1962. '
10. O'Connor, D. J., and W. E. Dobbins, "Mechanism of Reaeration in
Natural Streams," Journal of Sanitary^ Engineering Division, ASgEj
Paper 1115* December 1956.
11. Streeter, H. W., and E. B. Phelps, A Study of the Pollution and.
Natural Purification of the Ohio River. III. Factors Concerned^
in the Phenomena of Oxidation and Reaeration/ Public Health Bui"
letin No. 146, USPHS, Washington, D.C. , 1925.
136
-------
12. Thackston, E. L. and R. E. Speece, "Review of Supplemental
Reaeration of Flowing Streams/1 Journal Water Pollution Control
Federation, 38, pp.l6l4-l622, "
13. Tsivoglou, E. C., Tracer Measurement of Stream Reaeration,
A Report to FWPCA, USDI, Washington, B.C., June 1967.
137
-------
Radiological Safety
Jon P. Longtin
Consideration of the radiation safety aspects of the double tracer
^aeration technique must be separated into two areas of concern:
1. Radiation exposure to the general population in the area of
the reaeration study;
2. Radiation exposure to the personnel performing the study.
order to gain approval from the Atomic Energy Commission (AEC) to
radioactivity to the environment, it is necessary to demon-
that the proposed limits are not likely to cause any indivi-
in the unrestricted environment to receive a dose to the whole
in any period of one calendar year in excess of 0.5 rem. This
most easily be done by using the nature of the dispersion of a
source of radioactivity in a flowing stream to show that MPC(w)
are approached in a time less than that required for the
to reach a potable water intake. The MPC(w) values listed
10CFR20, Appendix B, Table II, column 2, are such that continuous
at these levels to a specific radionuclide will not result
ft a dose to the whole body in excess of 0.5 rem per calendar year.
°* a mixture of several nuclides, the sum of the ratios of the con-
^Utration to the MPC(w)'s must be less than or equal to one in order
0 meet this dose condition.
^ order to gain some perspective about the dispersion of material
as a point source, consider the one dimensional dispersion
for a conservative substance,
o
/ ^ M (x-vt)
C(x,t) = - exp V '
A
i
looking only at the peak concentration (x = vt),
C (t)
C(y ,t) = concentration at x at time t
M = mass of material dosed
A = cross sectional area of stream
D = dispersion coefficient
L
139
-------
t = time from dose
x = distance from dose point
v = stream velocity
According to Gloyna and Ledbetter (l), for flows ranging in size g
between small streams and large rivers, DT equals about 0.02 miles /
day. As an example, the following data, taken during a reaeration
study from a reach on the Great Miami River between Dayton and
Hamilton, Ohio, are used.
Table I
Elapsed Time H-3 ,. Kr-85
Station (hours) {jiCi/mlxlo" _) (u.Ci/mlxlO"ll
..Jirm-ui-i- : — _i_i--,j-i -,-_ m Mil i i -i *'"' tT '
Dose 0 1x10 0.5x10
l 2.4i 5.97 1.25
2 4.58 2.75 0.430
3 8.99 0.597 0.083
4 12.66 0.394 0.062
2
Cross sectional area estimated at 1500 ft
Dose 1 Ci H-3
0.5 Ci Kr-85
Substituting parameters and making proper conversions yields
Cp(t) = 4.357 x 10"5 -i-
/t
for M = 1 curie. This curve is plotted along with the tritium data
in Figure 1. It is seen that this model predicts a very rapid
decrease in concentration in the first few minutes. In fact, solv-
ing for the time required for the tritium MPC(w) level to be reached
(lxlO~^ ^Ci/ml) yields about 7 seconds. Thus, in this example, al-
most from the very start it is to be expected that the tritium acti-
vity levels will be less than MPC(w).
At the end of one hour, the Kr-85,-concentrations (for a half curie
dose) is predicted to be 2.l8xlO"'? p,Ci/ml neglecting losses to the
atmosphere. The difficulty in evaluating the significance of the
concentration is that there is no MPC(w) given for Kr-85 and thus 0°
direct standard exists to make a comparison. However, the primary
point to consider is that the MPC(w) values can be averaged over a
i4o
-------
ONE DIMENSIONAL
DISPERSION
(ONE CURIE POINT SOURCE)
© GREAT MIAMI DATA
— CALCULATED
0
0
0.1
1 I I
-r
5
TIME (HOURS) 10
FIGURE 1
1 41
-------
year. Thus, since the reaeration study spans only a few days out
of the year in any given reach, the annual average concentrations
are much less than those produced during the survey_period. For
example, if the Kr-85 concentration were about 2xlO~p jxCi/ml above
background (about one hour after dosing 0.5 curie) at a potable water
intake two days (two overlapping doses) the annual average would be
about 1x10 (j,Ci/ml. This number can be compared to 1x10"' ^Ci/ml
which is the limit for unidentified mixtures of radionuclides known
to be free of 1-129, Ra-226, and Ra-228.
Due to the fact that Kr-85 is chemically and biologically inert, it
should not be considered to be, in comparison to other radionuclideB;
a relatively hazardous material. Because of this, the lxlO~' p,Ci/ml
unit is very conservative and probably unduly restrictive. However;
it is a number which is approached in studies in small streams using
up to one curie of krypton per dose and can thus be used to show
that the dose in the unrestricted environment will not result in an
exposure to individuals in excess of 0.5 rem per year.
In addition to the above, krypton will be lost to the atmosphere
from the stream. Riffle areas, dams, and other effects can increase
this loss by significant amounts. Large, slow-moving pools will
decrease the loss. However, the rate of loss is not in general suf-
ficiently great to make a significant difference.
The above considerations show that doses on the order of one curie
of krypton-85 and one curie of tritium in moderately sized streams
will not in general cause exposure to the general population to be
in excess of that permitted by the AEG. In most cases, it should
be relatively easy to maintain exposure far below that permitted.
The second area of radiation safety is that of exposure of the per-
sonnel performing the study. Tritium is a soft beta emitter being
characterized by a 0.019 Mev teta (max). Because of the low energy
of the beta emission, there is no external exposure from tritium
since the radiation is completely absorbed by the solution and the
walls of the container. Krypton-85 is primarily a beta emitter
(0.67 Mev beta max) with 0.4 percent of the decay resulting in
emission with an energy of 0.514 Mev. Maximum ranges for the 0.67
Mev beta in various materials, along with the half-value layers fo
the 0.5l4 gamma, are shown in Table II.
The slowing down of the beta particles as they pass through absorb-
ing material results in an additional radiation source known as
Bremsstrahlung which is comparable to soft x-rays. The tritium? ^°e .$
is too weak to produce significant Bremsstrahlung. However, about ..
percent of the Kr-85 beta energy is converted in aqueous solution (
-------
TABLE II
Max range
(inches) Half value layer
0.09 7.8 inches
0.0k
TO 236 feet
0.00? ^.1 millimeters
, the bulk of the external exposure from dose solutions containing
*"itium and krypton-85 will be from the gamma radiation and from the
"emsstrahlung associated with the krypton beta. An estimate of the
from a point source of one curie of krypton-85 can be made from
following expressions taken from the Radiological Health Handbook (3):
Dose (mr/hr) =
ly = 0.156 n E (105
where: N = number of millicuries
S = distance to source (meters)
n = gamma quanta per disintegration
E = gamma energy in Mev .
p,a = air absorption coefficient (cm" )
For N = 1000 mCi, n = 0.004, E = 0.51U, and p,a = 3.87 x 10"5
Dose (mr/hr /curie at 1 meter) = 1.2^-
from liter bottles of dose solution containing one curie
Kr-85 at 18 inches gave dose readings of about 8 mr/hr. This can
compared to a calculated value of 5.9 mr/hr at 18 inches.
can enter the body by inhalation exchange in the lungs and
directly through the skin. Trace levels of tritium have
observed in the urine of individuals performing the dosing opera -
There are two points at which there is potential for direct
to the radioactive tracers and thus internal dose. The first
sampling or assaying of the dose solution. During the removal
sample of solution via syringe, krypton gas and tritiated water
are apt to be released to the atmosphere. If the procedure is
in the open air, there is little build-up in the immediate
and consequently little potential for exposure. If, on the other
the procedure is done in a confined area, it is possible to
temporary increases in background as krypton escapes. Thus,
working in a confined area, a hood, if available, should be used.
-------
In the absence of a hood, fans, open windows, etc., should be employed.
In addition, the area should be monitored with a survey meter and the
occupancy controlled until normal background is reached.
The second direct exposure can occur during dosing in the stream. If
the actual dosing is done manually, that is, breaking the dose container
by hand in the stream, there is a temporary potential exposure to krypton
gas and tritiated water vapor in the air and an immersion in fairly con-
centrated solution in the eddy caused by the water flowing around the
dosing personnel. Wearing rubber waders which do not leak and keeping
exposed areas of the body from contacting the water immediately after
dosing will minimize exposure.
Occupational exposures recommended by the NCRP and required by 10CFR20
for licensees of by-product material limit the accumulated whole body
dose to a maximum of 5 (N-l8) rems where N equals the age of the indi-
vidual in years. In addition, a limit of 3 rems per calendar quarter (13
weeks) is imposed.
The dosing procedure requires only a few minutes of close exposure to
the dosing solution. Thus, it can be expected that the whole body radia-
tion dose per application of a one curie Kr-85 solution will be on the
order of one mr. The highest dose rates occur to the hand when handling
the dose container. Calculating the dose rate for one curie of Kr-85
at the surface of a one liter container (5 cm) results in about 500 mr/
hr. Such handling requires about one minute and results in a dose of
about 8 mr to the hands.
The following procedures are recommended to minimize radiation exposure
to personnel:
1. Use lead shielding wherever and whenever possible. Carry out
dose preparation and assaying behind lead bricks.
2. During storage and transporting, maintain adequate distances
from source material and personnel. If possible, do not con-
centrate all the source material required for a study in one
location unless adequate shielding is available.
3. Vary personnel assignments - involve as many individuals as
possible. Use different groups of individuals for dose pre-
paration and dose release, thus distributing the dose and
minimizing individual exposure.
For minimizing exposure to the general population:
1. Use only the quantities of tracers that are absolutely required*
Excessive quantities are not only costly, but inconsistent
a policy of minimizing the release of radioactivity to man's
environment.
2. Plan the study and release points such that the tracer concen-
trations will be essentially undetectable at points of water
-------
Monitoring of the personnel is required by by-product licensees. Film
"badges are routinely used for this purpose in addition to pocket dosi-
meters and survey meters (which record external exposure in mr/hr).
Because of the potential escape of krypton when preparing or assaying
dose solutions, it is advisable, when working in a confined space, to
have available a direct reading survey meter. It is preferable to use
one with an audible alarm. To date, film badge readings during reaera-
tion studies have not shown exposures above background.
Water use points such as water intakes should be monitored by obtaining
water samples during critical periods of the study.
In summary, while the total quantity of radioactivity involved in the
reaeration measurement technique can be fairly large, the rapid disper-
sion in the stream coupled with the low relative hazards associated with
tritiated water and krypton-85 insure that, with proper planning and
execution, the exposures to the general population and to the personnel
conducting the study can be kept well below those permitted by the AEC.
-------
Bibliography
1. Gloyna, E. F., and Ledbetter, J. 0., Principles of Radiological
Health , Marcel Dekker, Inc., New York (1969).
2. Evans, R. D., "The Atomic Nucleus ," McGraw-Hill Book Company, Inc.
(1955).
3. , Radiological Health Handbook., U.S. Dept. of Health, Educa-
tion, and Welfare, Public Health Service, Consumer Protection
and Environmental Health Service (January 1970).
-------
Effect of Hydraulic Properties on Reaeration
Edward L. Thackston
Introduction
The ultimate objective of the current studies to measure reaeration
rates under many different conditions is to improve our ability
to predict the reaeration coefficient from basic hydraulic data.
The measurement of the reaeration coefficient by the tracer method
is accurate and reliable, but it is also expensive and time-consuming,
and it requires highly-skilled personnel and a major investment
in instrumentation. Most organizations interested in obtaining
reaeration coefficients cannot justify this investment.
However, many times basic hydraulic data (discharge, depth, slope,
velocity, temperature) are available for the reach of stream in
question, or they can be obtained for less expenditure than a tracer
test would require. It is quite possible that acceptably accurate
average values of the hydraulic parameters could be obtained with
significantly fewer measurements than the research program described
earlier has used. One of the valuable conclusions to result from
this research will be an indication of how extensive a stream survey
is necessary in order to obtain values of the hydraulic parameters
which are sufficiently close to the true average values to give
"acceptable" results when used in a mathematical model for prediction
of the reaeration coefficient.
Previous Attempts at_ Reaeration Prediction
There have been many previous attempts to relate the reaeration
coefficient to hydraulic variables, so it could be predicted from
a knowledge of the hydraulic data from a particular stream. The
prediction equations discussed in this section are those which have
been proposed for actual field use. There have been many other
reaeration equations derived to fit the data from a particular set
of laboratory tests, usually by empirical correlation techniques,
but those equations have not found use by engineers in practice.
Black and Phelps - The first attempt to predict oxygen transfer
into polluted water was a method developed by Black and Phelps(2)
in 1910 for prediction of reaeration in the New York harbor. The
Prediction equation assumed that reaeration was accomplished by
niolecular diffusion alone and was based on Stephan's(17) solution
to Fick's second law of diffusion. The equation predicted the average
°xygen concentration in a vertical column of quiescent water at
a given time after being exposed to the atmosphere.
-------
Velz(24) applied this concept to flowing streams in 1938. He assumed
reaerationty molecular diffusion under quiescent conditions for given
periods interspersed by periodic instantaneous complete mixes which
destroyed the vertical oxygen profile and mixed the oxygen which
had been absorbed at the surface downward into the entire depth
of stream. The time between mixes was empirically correlated with
stream depth and velocity. Although not physically realistic, the
method is still used by some workers and may give reasonable results
because of the form of the empirical correlations developed for
the ficticious "time of mix".
Streeter and Phelps - The concept of a "reaeration coefficient",
k2, was first proposed by Streeter and Phelps(18) in 1925 in their
report of studies of the pollution of the Ohio River which produced
the first equation for the oxygen sag curve. They suggested that
k2 = C (1)
in which C and n are "constants", U is the average velocity, and
H is the river stage above extreme low water.
Streeter and Phelps found that, on the Ohio River, k2H2 was proportional
to Un, but values of C ranged from 0.23 to 130.0, and values of
n ranged from 0.57 to 5.40 for the different reaches. They showed
graphically that there was a relationship between C and low water
slope and channel irregularity, a crude measure of roughness.
They also graphically related n to the relationship between velocity
and river stage primarily a measure of channel shape.
The results demonstrated that a simple relationship between k2
and average velocity and depth is unrealistic. Other factors, such
as roughness, channel slope, and channel shape, must also be considered
when U and H are the primary variables. Although Streeter and Phelps
were the first to attempt a prediction of k2, their work demonstrated
a more thorough insight into the factors which influence reaeration
than many of the investigators which followed.
0'Connor and Dobbins - The first rational attempt to predict reaeratio*1
coefficients from basic hydraulic data was by O'Connor and Dobbins0-4)»
using a hypothesis based on an oxygen transfer model developed by
Dobbins(6). Dobbins considered that the controlling factor in oxygen
absorption was the resistance of a liquid film at the surface, through
which oxygen must move by molecular diffusion. The film was assumed
to be constantly renewed by unsaturated elements from the body of
-------
the stream through the mechanism of turbulence, as originally proposed
by Higbie(9). The rate of transfer through an element of the surface
depends on the length of time it has been exposed to the atmosphere.
The function describing the age distribution of surface elements
was taken to be that of Danckwerts(4), which is
re"rt (2)
in which f (t)dt = the relative part of the surface area having ages
between t and t + dt, and r = the rate of surface renewal. By
combining Equation 2 with Fick's law of diffusion,
— = - D A —
8t m A 3y
in which 8m/8t » the rate of mass transfer, D » the molecular diffusion
coefficient, and A = the surface area, Dobbins obtained the relation
) (4)
m
in which HL « the liquid film coefficient, and L « the thickness
°f the surface film. Because the coth term is very close to unity
in the normal streamflow range and 1^ - K2/h, O'Connor and Dobbins
concluded that
rate of surface renewal was considered to be thejcatio of the
v*rtical rms velocity fluctuation at the surface, /-rr, to the mixing
ength at the surface, 1 . Because, according to tne Prandtl mixing
theory, m
f1 (6)
m dy
-------
r may be expressed as
du
dy
In developing the formula for isotropic turbulence, the measurements
of Kalinski(ll) in the Mississippi River were used. These measurements
showed the vertical velocity fluctuation to be about 10% of the
mean velocity and the mixing length to be about 10% of the mean
depth. Thus,
Substitution of Equation 8 in Equation 5 yields
/D U
m
2.30
The results of a laboratory investigation were presented to show
that k2 was proportional to r , and a collection of "measured" and
predicted values of k2 were given which apparently demonstrated
close correlation.
Churchill, Elmore, and Buckingham - Churchill, Elmore, and Buckingham(3?
presented an analysis of 30 measurements of k2 in streams in the
Tennessee Valley. They are believed to be the most reliable group
of field scale reaeration data reported in the literature. These
data were measured on unpolluted streams under conditions of uniform
steady flow, and all the effects of photosynthetic activity were
systematically eliminated. Churchill, et al., used the methods
of statistical correlation analysis to derive as a formula for the
prediction of k2 at 20°C,
k2 = 5.026 U°'969 h"1>673 (10)
They also concluded that the inclusion of several dimensionless
groups of hydraulic variables would not significantly improve the
fit of the equation to the observed data, as long as velocity and
depth were used. However, no other single variables were tried
150
-------
in combination with depth and velocity or instead of one of the
primary variables.
Dobbins - In 1964, Dobbins(7) proposed new equations, based on the
Kolmogoroff similarity principle, for the determination of r and
L in Equation 4, which were
(11)
and
in which u = the kinematic viscosity, a = the surface tension, p
* the density, and <\ and €5 = constants. The factor €5 should
be an absolute constant, while C^ should be determined by the dynamics
of the system. Through a series of laboratory experiments, GS
was determined to be about 14.3.
Dobbins ( 8) later combined these equations, expressed u, a, p,
and D as functions of temperature, and proposed for the prediction
0.12 CAAE
k2 -- —, - ^— (13)
in which Ci»' - 0.9 + F; CA = 1.0 + F.2; A= 9-68 + 0.05^(T - 20); B
81 0.976 + 0.0137(30 - T)?/2; E = 30.0 SU; and F - U/^gh. The term
C. = the fktio between the actual interfacial area and the projected
surface area; F » the Froude number; S = the slope in ft per 1000
ft; u « the velocity in ft per sec; T » the temperature in C;
*nd k£ is given as per day. The constant Ci^ was evaluated using
fche data of O'Connor and Dobbins(l4), Churchill, et al. (3) and Krenkel(12),
the original formulas of O'Connor and Dobbins (14) and the newer
formulas of Dobbins (7) are based on the relation which had been
derived earlier by Dobbins (6) (Equation 4). However, the basic premise
r is equal to the velocity gradient at the surface, as well
the methods chosen to express it, has been questioned (16, 5).
151
-------
The expression for the rate of surface renewal In the isotropic
flow formula, while possibly less rational than the method used
in the now-abandoned non-isotropic flow equation, is apparently
more nearly correct. The measurements in the Mississippi River
reported by Kalinske(ll) showed the velocity fluctuation to be
about one-tenth the mean velocity. This produced the simple
relation shown by Equation 8, which was assumed to hold universally.
However, the data of Kalinske clearly showed that j^u'^/U was
a function of the distance from the bottom. For the six different
measurement series, the depth at which v^T**/U =0.1 varied from
about 0.27 of the total depth to about 0.55 of the total depth.
Most measurements showed values of 0.1 at about 0.4 of the total
depth and values of 0.08 near the surface. The total depth averaged
about 19 ft. If /u'*/U is a function of the distance from a
solid boundary, a value of 0.1 should occur at the surface when
the depth is about six ft to ten ft. This is precisely the range
of depths for which the isotropic flow formula fit the data of
Churchill best. At shallower depths, where the Kalinske data
would predict a value of /u'^/U of 0.12 to 0.20, instead of 0.1,
the predicted values were too low. If Af^/U had been assumed
to be 0.15 for these shallower reaches in accordance with the
data of Kalinske, the agreement would have been much better.
An opposite effect, possibly caused by variations in mixing length
rather than the velocity fluctuation, takes place at very shallow
depths. The isotropic flow formula overestimates values of k2
measured in a laboratory flume by a factor of 10.
The reason cannot be due to dropping the hyperbolic cotangent
(coth) term, because any deviation of coth (rL2/D )*g from unity
must increase k2« Thus, ignoring the coth term would make the
predicted value of k£ too small. This is not in accord with
the actual effect.
The somewhat questionable method of estimating the rate of surface
renewal for this formula probably accounts for its inability
to accurately cover a wide range of depth scales. Another possible
reason may be in the assumption that k2 is proportional to the
square root of the rate of surface renewal. Diachishin(S) demonstrated
that the experimental verification of this assumption in the
laboratory was insufficient because the data also supported the
hypothesis that k2 was proportional to r.
The formulas of Dobbins(7) were the result of an attempt to develop
more rational expressions for the rate of surface renewal and
the thickness of the surface film. The proposed relationships
were based on logical concepts, but attempts to establish numerical
values for the hypothesized constants and proportionality factors
were somewhat less than successful. In particular, the variation
in the "observed" values of C^, the ratio of surface film thickness
152
-------
to minimum eddy size, did not support the proposed relationship and was
criticized by Thackston and Krenkel (19). The failure of this proposed
proportionality to be verified casts serious doubt on the validity
of all the relationships, since they all depend on Cif.
The approach of Churchill (3) differed radically from that of O'Connor
and Dobbins. His equation was based on a correlation analysis of
observed values of k2 and various hydraulic parameters. The resulting
equation naturally fit his particular group of experimental data
better than any other, but it cannot be considered reliable outside
the range of hydraulic variables used in its derivation. There
is also some evidence that, on occasion, it does not give reasonable
answers when the values of the hydraulic variables are within the
original range.
Thackston and Krenkel - Thackston and Krenkel (20, 23) recently proposed
a new approach to reaeration coefficient prediction, based on the
vertical mixing coefficient. The basic premise was that k£ was
proportional to some function of surface turbulence or renewal and in-
versely proportional to some function of depth, representing both the
water volume and the resistance to complete vertical mixing.
The measure of surface turbulence chosen was the vertical mixing
coefficient at the surface. The vertical mixing coefficient was
assumed to be equal to the momentum transfer coefficient, which
can be expressed as
ey - C16)
Equation 16 indicates that the value of e at any relative depth,
y/h, is linearly proportional to e , which, from the work of Al-Saffar(l) ,
153
-------
may be taken as Khu^/6. Thus, it may be assumed that ky at any relative
depth, including the surface, is proportional to hu^, or
kv f " C, T ""* " C0 hu. (17)
^surface 1 6 * 2 *
Thackston and Krenkel (22) have shown that, in uniform two-dimensional
flow, DT can be expressed as
LI
DL = C3 hu* (18)
where DT is the longitudinal mixing coefficient. Equation 18 has the
same form as Equation 17, indicating that, in uniform two-dimensional
flow, ky at the surface is proportional to D . Thus the relationship
shown by Krenkel and Orlob (13) between k_ and D_ in uniform, two-
dimensional flow must also hold for k , and, therefore,
k
. = C JWface (w)
* ti
Substituting Equation 17 into Equation 19 and simplifying,
C_hu.
<20>
Non-linear least squares regression analysis (21) using laboratory data,
the data of Churchill, et al. (3), and the data of O'Connor and Dobbins
(14), showed that, in each case, the best fit exponents to u^ and h
were close to 1 and -1, as predicted. The constants for the three
groups of data were 0.000215, 0.000208, and 0.000171, respectively.
The variable coefficient was assumed to be at least partially attributabl6
to the increase in surface area at high Froude numbers, and a form of
the constant CA was introduced, making the final version of the equation
A
k u*
k_ = 0.000125(1 + F8) 7— (21)
2 n
or, reduced to fundamental hydraulic variables,
k2 = 0.000125 1 +(—n-\/-r- (22)
-------
The formula was tested on the field data of Churchill (3) and O'Connor
and Dobbins (14), along with 3 other prediction formulas, the the results
are shown in Table 1.
TABLE 1 - STANDARD DEVIATION OF PREDICTION
BY DIFFERENT PREDICTION FORMULAS
Formula Standard Deviation (I/day)
Thackston-Krenkel 0.369
Churchill, et al. 0.383
Dobbins 0.425
O'Connor-Dobbins 0.443
The Thackston-Krenkel equation was thus shown to be slightly more
accurate than any of the others based on the limited field data available.
The inclusion of the Churchill equation, which apparently demonstrates
good correlation, in the comparison is really not valid. The Churchill
equation was developed explicitly to fit 30 of the 64 observations used
in the comparison, and thus possesses a significant positive bias.
Computation of the value of F between the Thackston-Krenkel equation
and the Dobbins equation yields a value of 1.33, implying statistical
significance at approximately the 13% level.
Plots of observed and predicted values of k_ are shown in Figures 1
through 4 for the four equations listed in Table 1. An examination of
these figures will disclose the regions in which each equation is accurate
or inaccurate, and the degree to which the points cluster about the 45°
line is an indication of the overall predictive ability of the equation.
The figures also disclose that some data, such as that of Owens, Edwards,
and Gibbs (15), cannot be predicted by any of the equations discussed.
Summary of Hydraulic Variable Effects
The approximate effect of the different hydraulic variables on k_, as
predicted by the various equations, can be deduced from Table 2, which
tabulates the exponent to which each variable is raised in each equation.
In some equations, a particular variable is not raised to a simple
constant power, so a complete comparison is not possible.
155
-------
1000
<
_J
D
2
a:
o
u_
Q
UJ
CO
o
CL
O
or
CL
t
CM
Q
UJ
Q
UJ
CC
CL
100
10
.1
1 1 1 t
1 1 1 1 1 1 1 1 1 1 1 1
00
I I I I I i 11
a This Investigation '
A Churchill
o O'Connor-Dobbins
• Krenkel
x Owens, Edwards, ,
a Gibbs
(MIL II I I I I I
.1
100
I 10
OBSERVED k2
FIG, I, OBSERVED VERSUS PREDICTED VALUES OF K2 FROM PROPOSED FORMULA
1 56
-------
lOOOr
100 r
d
x
rr
x
CNJ
I-
O
S
LU
o:
Q.
i i i i i i i i i i
D This Investigation
Churchill
o O'Connor-Dobbins
• Krenkel
x Owens, Edwards,
f 10 100
OBSERVED k2
FIG, 2, OBSERVED VERSUS PREDICTED VALUES OF K2 FROM CHURCHILL FORMULA
I 57
-------
1000
100
CO
2
CD
CO
O
Q
w 10
Q
LJ
I-
O
Q
Ul
cr
Q.
.1
1II MINI
1 I I I I M i I I I TT
- O
I I I I I I I I I
D This Investigation-
A Churchill
o O'Connor-Dobbins-
• Krenkel
x Owens, Edwards, •
8 Gibbs :
i i i i M i
i i i i
.1
100
I 10
OBSERVED k2
FIG, 3, OBSERVED VERSUS PREDICTED VALUES OF K2 FROM DOBBINS FORMULA
1 58
-------
lOOOc:
CO
D This Investigation
Churchill
O'Connor-Dob bins -
• Krenkel
x Owens, Edwards, -
8 Gibbs
i i i i M 111 i i i i i 1111 i i i i i 1
I 10
OBSERVED k2
FIG, /». OBSERVED VERSUS PREDICTED VALUES OF K2
FROM O'CONNOR-DOBBINS FORMULA
100
1 59
-------
TABLE 2 - POWER TO WHICH EACH HYDRAULIC VARIABLE
IS RAISED IN VARIOUS REAERATION FORMULAS
Formula U h S
— — —e
Thackston-Krenkel -0.1 --0.5 0.5
Churchill, et al. 0.97 -1.67 0
Dobbins -1.0 ~-1.5 -0.37
O'Connor-Dobbins 0.5 -1.5 0
From Table 2 and Equation 22, it can be seen that the Thackston-Krenkel
equation is less sensitive to changes or errors in the hydraulic variables
than any of the other equations. This is an important practical advantage
in addition to its better accuracy.
The average velocity, which is difficult to determine accurately, has very
little influence on the calculated value of k^. Even a large error in
estimating the average velocity would cause only a small error in the
predicted value of k». On the other hand, an error in velocity would
cause a large error in k~ as estimated by the other equations.
The most important practical advantage of the Thackston-Krenkel equation,
however, is the relatively small influence of the depth. It appears
approximately to the one-half power, whereas it appears to approximately
the three-halves power in the other equations. Thus, an error in
estimating the average depth, which is difficult to determine accurately,
will cause a much lower error in the values of k« predicted by the
Thackston-Krenkel equation than by the three other equations. As an
example, consider a case in which a stream with a true depth of five feet
was estimated to have a depth of four feet. This would cause an error
of 10% in the value of k- predicted by the Thackston-Krenkel equation,
27% by the O'Connor-Dobbins equation, and 30% by the Churchill equation.
The cost of the stream surveys is directly proportional to the accuracy
required. Since the Thackston-Krenkel equation is less sensitive than
the others to data error and inaccuracy, its use should allow stream
surveys to be made for a lower cost, since fewer cross sections or depth
meaurements are required and only a general estimate of the velocity is
required.
Its dependence on the slope of the stream rather than the velocity also
should simplify its use. The slope is one of the simplest hydraulic
variables to measure accurately, and can sometimes even be estimated from
USGS maps with acceptable accuracy. The slope also changes very little
with changes in discharge, if measured over a reach of several miles.
Thus, the Thackston-Krenkel equation is more adaptable for use in the
prediction of changes in k2 with changes in discharge. All that is
required is an approximate relationship between average depth and discharge*
160
-------
Limitations and Uncertainties
All of the equations have their limitations. The Thackston-Krenkel
equation has questionable accuracy at low Froude numbers, in streams
with slow velocites and deep depths, because there is no reliable data
in this range to fit the equation to. The Churchill equation is
definitely inaccurate in slow, deep streams, and it and the Dobbins and
O'Connor-Dobbins equations are inaccurate in very shallow, swift streams.
The Thackston-Krenkel equation cannot be used at all in very slow, deep
streams such as estuaries or reservoir backwaters, because the slope
is so flat that it cannot be determined accurately. In these situations,
the O'Connor-Dobbins equation seems to fit the data best, but is is
uncertain whether or not this is good, because the data is of questionable
accuracy.
Very low values of k,, predicted by any of the equations are likely to be
too low, because of the effect of wind. The wind will increase the true
surface area and will cause surface currents, increasing the vertical
diffusion rate. Thus, even perfectly still water can be reaerated by
wind. However, the contribution of wind to the reaeration process is
variable and unreliable, and cannot be depended upon to be present at
all times.
All of the equations apply to relatively clean and unpolluted water, and
all predicted values of k~ should be reduced somewhat if the subject
reach is highly polluted. The amount of reduction required may vary
from 10% to 50%, but, in most cases, will probably be in the range of
20% to 30%.
All the equations apply to fully developed turbulent shear flow with a
regular vertical velocity profile and do not apply to laminar flow. They
also do not apply to conditions so turbulent that waterfalls, riffles, or
"white water" is present, and bubbles are entrained directly in the water.
It is hoped that the current work at Georgia Tech on the measurement of
Reaeration coefficients will supply data which can be used as standards
against which the present prediction equations can be compared and
Defined, if necessary, to improve their accuracy and reliability. The
tracer method is certainly the most accurate method of measurement
Available, and should produce much reliable data to supplement the
limited data presently available.
161
-------
REFERENCES
1. Al-Saffar, Adnan Mustafa, Eddy Diffusion and Mass Transfer in
Open-Channel Flow, thesis presented to the University of Cali-
fornia at Berkeley, in 1964, in partial fulfillment for the degree
of Doctor of Philosophy.
2. Black, William, and Phelps, E. B., Location^pf Sewer Outlets and
Discharge^ of Sewage into New York Harbor , 1910.
3. Churchill, M. A., Buckingham, R.A., and Elmore, H. L., The
Prediction of Stream Reaeration Rates , Tennessee Valley Authority,
Chattanooga, Tennessee, 1962.
4. Danckwerts, P. V., "Significance of Liquid Film Coefficients in
Gas Absorption", Industrial and Engineering Chemistry, Vol. 43,
No. 6, June, 1951.
5. Diachishin, A. N., discussion of "Mechanism of Reaeration in Natural
Streams", by O'Connor and Dobbins. Transactions, ASCE, Vol. 123.
1958, p. 672.
6. Dobbins, William E., "The Nature of Oxygen Transfer Coefficient
in Aeration Systems", Part 2-1 of BiologicalJTreatment of Sewage^
and Industrial Wastes, by McCabe and Eckenfelder, Reinhold, New
York, New York, 1956.
7. Dobbins, William E., "BOD and Oxygen Relationships in Streams",
Journal of the Sanitary Engineering Division, ASCE, Vol. _90J No.
SA3, Proc. Paper 3949, June, 1964, pp. 53-79.
8. Dobbins, William E., closure of "BOD and Oxygen Relationships in
Streams", by William E. Dobbins, Journal of the Sanitary Engi-
neering Division. ASCE. Vol. 91. No. SA5, Proc. Paper 3949,
October, 1965, pp. 49-55.
9. Higbie, R., "The Rate of Absorption of a Pure Gas into a Still
Liquid During Short Periods of Exposure", Transactions. American.
Institute of Chemical Engineering. Vol. 31. 1935, p. 365.
10. Holley, E. R., Jr., Some Data on Diffuslon_and Turbulence in
Relation to Reaeration, Research Report No. 21, University of
Illinois Water Resources Center, July, 1969.
11. Kalinske, A. A., "The Role of Turbulence in River Hydraulics",
Bulletin No. 27, Proceedings, The 2nd Hydraulics Conference,
University of Iowa Studies in Engineering, University of Iowa,
Ames, 1943.
162
-------
12. Krenkel, P. A., Turbulent Diffusion and the Kinetics of Oxygen
Absprption . thesis presented to the University of California, in
1960, in partial fulfillment for the degree of Doctor of Philo-
sophy.
13. Krenkel, P. A., and Orlob, G. T., "Turbulent Diffusion and the
Reaeration Coefficient", Journal of the Sanitary Engineering
Division, ASCE, Vol. 88, No. SA2, Proc. Paper 3073, March, 1962,
pp. 53-84.
14. O'Connor, D. J., and Dobbins, W. E., "Mechanism of Reaeration in
Natural Streams", Transactions, ASCE, Vol. 123, 1958, p. 631.
15. Owens, M., Edwards, R. W., and Gibbs, J. W., "Some Reaeration
Studies in Streams", International Journal of Air and Water
Pollution. Vol. 8. p. 469, 1964.
16. Pearson, E. A., discussion of "The Measurement and Calculations of
Stream Reaeration Ratio", by D. J. O'Connor, Oxygen Relationships
in Streams, Technical Report No. W-58-2, Taft Sanitary Engineering
Center, 1958.
17. Stefan, M. J., "Uber die Diffusion der Kohlensoure durch Wasser
und Alkohol", Sitzungsberichte der Akad. der Wissenschafter, Class
II, Vienna, 1878, p. 371; Uber die Diffusion der Flussigkeiten,
Vol. 79. 1879, p. 161.
18. Streeter, H. W,, and Phelps, Earle B., A Study on the Pollution
and Natural Purification of the Ohio River, III , Public Health
Bulletin, No. 146, Washington, 1925.
19. Thackston, E. L., and Krenkel, P. A., discussion of "BOD and Oxygen
Relationships in Streams", by William E. Dobbins, Journal of the
Sanitary Engineering Division, ASCE. Vol. 91, No. SA1, Proc. Paper
3949, February, 1965, pp. 84-88.
20. Thackston, E. L., and Krenkel, P. A., Longitudinal Mixing and
jteaeration in Natural Streams, Technical Report No. 7 in Sanitary
and Water Resources Engineering, Vanderbilt University, Nashville,
1966.
2l. Thackston, E. L., Hays, J. R., and Krenkel, P. A., "Least Squares
Estimation of Mixing Coefficients", Journal of the Sanitary
Engineering Division. ASCE, Vol. 93, No. SA3, Proc. Paper 5288,
June, 1967, pp. 47-58.
22. Thackston, E. L., and Krenkel, P. A., "Longitudinal Mixing in
Natural Streams", Journal of the Sanitary Engineering Division.
ASCE. Vol. 93, No. SA5, Proc. Paper 5521, October, 1967, pp. 67-91.
163
-------
23. Thackston, E. L., and Krenkel, P. A., "Reaeration Prediction in
Natural Streams", Journal of the Sanitary Engineering Division,
ASCE, Vol. 95, No. SA1, Proc. Paper 6407, February, 1969,
pp. 65-94.
24. Velz, C. J., "Deoxygenation and Reoxygenation", Transaction, ASCE
104, 1939, pp. 560-578.
-------
Pollutant Effects on Reaeration
L. A. Neal
Introduction
Certain pollutants can alter the reaeration capacity of a stream.
This paper describes some of the results of laboratory studies dealing
with the effect of pollutants on reaeration. The purpose of the research
has been to test the sensitivity of physical gas transfer to pollution.
Basic Considerations
Aeration of water is a gas-liquid mass transfer process that takes
place as the result of the combined effects of molecular diffusion
of oxygen and physical mixing of the water.
The basic mathematical expression describing aeration of clean water
is
dD
in which D is the dissolved oxygen concentration deficit below the
saturationHimit, in mg/lt at time t, and KZ is the gas transfer rate
coefficient for oxygen in clean water (I/ time) . Equation (1) may also
be written as
d(Ce - C )
dt s
in which C is the dissolved oxygen saturation limit for clean water,
and C is the dissolved oxygen concentration at time t, both in mg/1.
A derivation of equation (1), from basic considerations of the kinetics
of gases, has been presented earlier (1).
Equation (2) is a formulation of oxygen transfer in a clean water system.
Other complicating factors must be accounted for if one is to consider
a polluted water. A general expression may be written as
d(3C - C )
- C. ) + r (3)
, a .
at *• s t
in which 6 is the ratio of dissolved oxygen saturation for the polluted
Water to that for clean water, « is the ratio of the gas transfer rate
165
-------
coefficient for the polluted water to that for clean water, r is the
rate of dissolved oxygen utilization, with other terms as previously
defined.
The beta (B) factor accounts for any difference between the actual
and "book value" dissolved oxygen saturation limit. Standard Methods
(2) shows the depression of oxygen solubility due to chloride ion concen-
tration. Generally, however, the 3 factor is not readily predicted
and must be determined experimentally.
The alpha (a) factor accounts for the fact that various pollutants
can alter the ability of gas molecules to enter and escape water.
This alteration causes the value of K_ to vary under the same conditions
of turbulence depending upon whether clean water or polluted water
is being aerated. It has been pointed out (3) that the ex factor is
not only related to the pollutant constituents and concentrations but
also the turbulent mixing regime within the fluid. This means that
a determinations must either be conducted in the full-scale system
or in a system that duplicates the turbulent mixing within the real
system.
With appropriate modification, the foregoing expressions also describe
the transfer of other gases. Specifically, consider a dissolved tracer
gas, krypton-85, which has been added to the water. The amount of
kyrpton-85 present in the atmosphere above the water can be taken to
be zero, for practical purposes. Hence, the driving force for gas
transfer will be just the partial pressure of the dissolved krypton-
85 in the water. Thus, in the case of desorption of the tracer gas
we can write
(4)
where C is the concentration of the dissolved tracer gas remaining^
in the water at time, t, C is the concentration at t » 0, and K is*
the gas transfer rate coefficient for the tracer gas in clean water.
Equation (4) can be modified to describe the desorption of the tracer
gas in polluted water so that
C - Coe-aKt (5)
where alpha (a) is the gas transfer rate coefficient for the polluted
water to that for clean water.
It has been shown (4), both experimentally and theoretically, that
for the same conditions of turbulence
166
-------
0.83 + 0.04 (6)
and this is the basis for using krypton-85 as a tracer gas for oxygen
in aeration studies. The numerical constant, 0.83, in equation (6)
is independent of the degree of turbulent mixing, independent of the
directions in which the two gases (krypton-85 and oxygen) happen to
be moving and independent of temperature within the range 10 to 30°C.
Additionally, the ratio has been verified (5) in a biologically active
wastewater.
Since the pollutant effect on krypton-85 transfer can be equated to
the pollutant effect on oxygen transfer, the tracer gas is well suited
to the measurement of alpha factors in an experimental system.
Measurement of Alpha Factors.
In order to measure the effect of pollutants on the gas transfer rate
coefficient, an open top mechanically mixed reactor was constructed
as shown in Figure 1. The reactor was immersed in a constant temperature
(20°C) bath. The reactor was a four liter reaction kettle, and was
operated with a water volume of 3600 ml.
One pollutant effect test consisted of two reactor runs. The first
run was conducted on clean water and a krypton-85 transfer rate determined,
The second run was conducted on the polluted sample under conditions
identical to those of the clean water run. For each pollutant effect
test, the alpha factor was computed from
(7)
water
where K - , was the observed krypton-85 transfer rate coefficient
for thePpolSufed sample and KWater was the observed krypton-85 transfer
rate coefficient for the clean water sample.
Operation of the Pollutant Effects Reactor
In the typical experiment, the reactor system was initially dismantled,
cleaned, rinsed thoroughly with distilled water and reassembled. The
reactor was then filled with 3600 ml of distilled water and allowed
to stir. When thermal equilibrium was achieved, the distilled water
Was dosed with a homogeneous mixture of dissolved krypton-85 gas and
tritiated water molecules with both tracers contained in 'about two ml
°f distilled water. The tritiated water was used to account for disper-
sion, as described elsewhere (1). After allowing the tracer dose a
few minutes to disperse, the first sample was taken directly from the
Reactor with a 2-ml pipette immersed so that it filled by gravity to
16?
-------
variable speed motor
support bracket
stirrer
open top reaction kettle
FIGURE 1
REACTOR ARRANGEMENT
(pollutant studies)
1 68
-------
a point above the fiducial mark. The pipette was then removed from
the reactor and excess sample wasted until the liquid reached the mark.
The 2-ml sample was then transferred to a 25-rnl counting vial that
had been previously filled with 10 to 15 ml of liquid scintillation
fluid. The transfer technique was designed to minimize the loss of
dissolved kyrpton-85 gas. After the transfer was complete, the vial
was then filled with the scintillation fluid, capped, and loaded into
a liquid scintillation counter for measurement of the tritium and krypton-
85 concentrations.
Subsequent samples were taken in the same manner until the run was
complete .
The reactor was then drained, refilled with the polluted sample and
the second run conducted just as the first described above.
Each tracer sample was subsequently counted for 10 minutes at least
two different times and the concentration ratio of krypton-85 to tritium
obtained.
.Calculation of Krypton-85 Transfer Rate Coefficients
For each run, the krypton-85 to tritium concentration ratios were plotted
as a logarithmic function of time. The line of "best fit" was then
obtained by the method of least squares. The slope of this line was
reported as the krypton-85 transfer rate coefficient for the particular
run. The alpha factor was then calculated from equation (7).
A typical test result for the pollutant linear alkylate sulfonate (LAS)
is shown in Figure 2.
pollutant Studies
detergent surface active agent LAS was selected for a series of
Pollutant effect studies in the reactor system previously described.
A total of 12 tests (24 runs) have been conducted with LAS concentrations
UP to 11 mg/1. All 24 runs were conducted at one mixing speed so that
effect of LAS concentration on gas transfer could be studied.
order to determine the relative magnitude of pollutant effects on
reaeration of natural river waters, 10 reactor tests (20 runs)
conducted on highly polluted samples from the South and Chattahoochee
Divers in the vicinity of Atlanta. The tests were conducted at several
Different mixing speeds so that the range of alpha values in the rivers
could be estimated.
%gerimental Results
^though analysis and interpretation of the data obtained is not complete,
the results thus far provide considerable Insight regarding the effect
Of pollutants on the reaeration of water.
169
-------
1.0
0.8
0.6
\\
0.2
-P
a
K
I 0.08
0.06
O.OU
0.02
0.01
20
28.1 mins
5
S
Diluted sar
\
FIGURE 2
TYPICAL REACT OR EXPERIMENT
Note:
le)
) = kVf, rec
action
16'8
I5TT
.8 mins (c
0.60
ean sample)
UO 60 80
Elapsed Time - Minutes
100 120
1 70
-------
It is obvious from the summarized LAS data in Table 1 that the alpha
factor decreases as LAS concentration increases. Figure 3 is a graph
of the 12 LAS tests and appears to follow a smooth relationship as
shown.
A few tests (not reported) have been conducted on water containing
10 mg/1 LAS with a different mixing speed for each test. The results
of these tests indicate that an increase in mixing speed tends to decrease
the alpha factor for the same LAS concentration.
Table 2 is a summary of the test results obtained for 10 alpha determina-
tions on South and Chattahoochee River water samples. The station
identifications used in Table 2 correspond to those used in Tsivoglou's
field investigations of reaeration capacity.
In February of 1970, samples were collected from four stations on the
South River for the purpose of determining the LAS concentration at
each point. The sampling stations corresponded to those used in Tisvoglou's
field investigations and the results of the LAS determinations are
in Table 3.
Discussion and Summary
It is clear from test results that the reaeration rate in a stream
can be significantly reduced by the surface active agent, LAS.
The reaeration rates in the highly polluted reaches of the South and
Chattahoochee Rivers are lower than they would be in the absence of
Pollution.
For a particular stream section, it would seem that the measured reaera-
tion rate would vary from one study to another if the pollutant effect
(alpha) was not the same for each study. Apparently, at least one
°f the tracer studies conducted in the South River was influenced by
8Uch a variation in the alpha factor. Figure 4 is a comparison of
two different tracer studies on the same stretch of the South River.
Measured flows and travel times were identical, for practical purposes,
both studies. From Figure 4 it is obvious that a discrepancy
between the observed reaeration rates for the two studies.
difference in reaeration capacity was greater in the upper reaches
than in the lower reaches. The observed reaeration rate for the last
*&ach (E to F) is essentially the same for both studies. It is important
to note that the City of Atlanta South River Sewage Treatment Plant
Discharges directly to the South River just above Station A (see Figure
*)• Apparently, some pollutant released from the South River Plant
Curing Study X) caused the reaeration capacity to be lower for Study
X than for Study VI. The pollutant effect variation diminished in
the lower reaches (see Figure 4), due to dilution and possible degradation
Of the pollutant in the stream.
LAS data in Figure 3 are considered as typical and indicate that
171
-------
Table 1. Summary of Alpha Tests on Linear Alkylate Sulfonate In
Distilled Water
K .
lesc
8
8
9
9
10
10
11
11
12
12
13
13
14
14
15
15
16
16
17
17
18
18
19
19
K.un
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
A
B
LAO uonc .
(mg/1)
0.0
3.0
0.0
3.8
0.0
4.8
0.0
6.0
0.0
11.0
0.0
0.96
0.0
2.0
0.0
5.2
0.0
7.0
0.0
9.2
0.0
9.5
0.0
8.3
JS.
(1/hr) @20°C
water
1.791
1.946
1.805
1.904
1.900
2.065
2.125
2.034
2.127
1.903
2.016
2.04
water + LAS
1.431
1.437
1.373
1.289
1.240
1.908
1.832
1.584
1.561
1.426
1.408
1.40. ...
K .
water
0.80
0.74
0.76
0.68
0.65
0.92
0.86
0.78
0.73
0.75
0.70
0.69
172
-------
1.00
0.95
0.65
FIGURE 3
EFFECT OF LINEAR
ALKYLATE SULFONATE
(LAS) ON THE REAERATION
OF WATER AT A CONSTANT
MIXING SPEED
2468
LAS CONCENTRATION, mg/1
1 73
-------
Table 2. Summary of Alpha Tests on Chattahoochee
and South River Water Samples
K
river
River
South
Chatt .
Chatt.
Chatt .
Chatt.
Chatt .
South
South
Chatt.
Chatt.
Table 3.
Station
G
0
0
0
0
0
between
A & D
J
above 0
0
(1/hr)
"clean"
water
0.937
2.29
2.47
0.52
1.92
0.49
0.83
1.04
0.83
2.04
(X
@20°C
river
water
0.796
1.48
1.48
0.40
1.17
0.43
0.68
0.74
0.69
1.63
K .
clean
0.85
0.65
0.60
0.77
0.61
0.88
0.82
0.71
0.83
0.80
Summary of Linear Alkylate Sulfonate
Data, South River
Station
G
below H
J
L
LAS Cone.
(mg/1)
2.6
2.7
2.0
1.8
-------
SOUTH RIVER
KBYPTON TRANSFER COEFFICIENTS
Hotes All values lire Kg/hour
0.1
>* 5
Time of Flow • Hours
1 75
-------
the observed reaeration rates in the South River studies of Tsivoglou
were probably lower than the rates that would have been observed for
clean water conditions.
Current research effort involves investigation of the effect that other
pollutants have on reaeration.
176
-------
BIBLIOGRAPHY
1. Tsivoglou, E. C.t "Tracer Measurement of Stream Reaeration",
Federal Water Pollution Control Administration, U.S. Department
of the Interior, Washington, D.C. (June, 1967).
2. Standard Methods for the Examination of Water arid Wastewater,
12th Edition, American Public Health Association, Inc., New York
(1965).
3. Eckenfelder, W. W. Jr., Industrial Water Pollution Control, McGraw-
Hill Inc., New York (1966).
4. Tsivoglou, E. C., O'Connell, R. L., Walter, C. M., Godsil, P.
J., Logsdon, G.S., "Tracer Measurements of Atmospheric Reaeration.
I. Laboratory Studies", Journal Water Pollution Control Federation,
vol 37, no. 10, p 1343 (1965).
5. Gordon, J. A., Etzel, J. E., "Mechanical Surface Aerator Evaluation
Using Radio-Krypton as a Standard Indicator of Mass Transfer",
Unpublished Report of Research Performed at Prudue University,
1968-1970 (July, 1970).
177
-------
Observed vs. Calculated Reaeration
Cagac_it_i_e_s__gf^ Several Streams
J. R. Wallace
We have prepared comparisons between our measured Kg values and
Kp values computed from several of the formulas that are available.
Specifically we have made and will show comparisons with three equa-
tions. One of these we refer to as the O1Conner-Dobbins equation,
which was published in 1956. It is like neither the O'Connor nor
the Dobbins equation that Dr. Thackston presented earlier, but it
is similar to the Churchill equation in that it has a velocity in
the numerator and a depth in the denominator. The velocity is
raised to the 1/2 power and the depth to the 1 and 1/2 power. The
other two equations we will be looking at in terms of their predic-
tions are Churchill's equation, as shown on Table I, and then Dr.
Thackston1s equation which is also shown on Table I.
Now I would like to make just a couple of remarks about how we
determine the values of the parameters in these equations. In the
equations that we are considering we have three different parameters,
two in two of the equations and three in the third. We have velocity,
depth, and slope. The velocity used in these equations was simply
the length of the reach divided by the time of passage as measured
from our dye studies. The depth of flow was the average of the
average depth at each cross section. For example, maybe we had a
reach that was, let's say, 5,000 ft. long; within that we would
have had 10 - 500 ft. stations at which we measured the hydraulic
properties. At each of these 500 ft. stations we determined an
average depth by dividing the cross sectional area by the width of
the stream. The value of the depth which we subsequently used in
the calculation was the average of these average cross sections
depths. We determined slope as the difference in elevation at the
upstream and downstream end of the reach divided by the length.
In our discussions our results should be separated into two cate-
gories depending upon the hydraulic characteristics that were found
in each of the reaches. The first category would be that of a reach
that has a relatively uniform cross section with unbroken surface.
The second category would contain those reaches that are highly
Variable in cross section and are reaches which contain features
that create high gas losses, i.e., reaeration rates, such as rapids,
shoals, and falls. I would like to point out that it is not intui-
tively clear in every case where we make the break in category.
That is, where does a stream become variable or turbulent to the
degree that we take it out of one classification and put it into
another. If you will keep that limitation in mind as we go along
179
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TABLE I
Comparison
of Observed and Predicted Results
Reaeration Rate
River
Flint
Flint
Flint
Flint
South
South
South
South
Patuxent
Patuxent
South
South
South
Flint
Flint
Flint
Chattahoochee
* 25 °C
Churchill
Reach
01
12
24
46
AE
EG
GJ
JM
14
47
GH
GT2
KL
R1R3
1P1
2P2
OC
et al.: !
Observed
0.37
0.52
0.27
0.10
0.22
0.15
0.30
0.17
0.13
0.13
0.64
1.6
2.5
2.0
12.7
2.7
0.031
L = 0.543 V°
O'Connor
0.12
0.18
0.11
0.08
0.18
0.14
0.08
0.09
0.14
0.11
0.12
(0.25)
(0.10)
(0.43)
—
—
0.037
.969
Coefficient, K/hr*
Churchill
0.06
0.13
0.08
0.05
0.18
0.13
0.06
0.07
0.08
0.06
0.12
(0.27)
(0.07)
(0.35)
—
—
0.035
Thackston
0.29
0.24
0.15
0.09
0.13
0.10
0.11
0.10
0.12
0.12
0.17
0.36
0.47
0.64
2.4
0.38
0.022
Hl-673
0'Conner-Dobbins: K = 0.573 V
.0.5
Thackstons
P. 5
1 80
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it might be helpful. First of all I think we can conclude that the
mathematical models that we have examined provide predictions that
are closer to the observed K values in the uniform reaches, and this
is certainly what I think would be expected. The equations, to some
extent, have been based upon assumptions about the uniformity of
the channel and on the assumption of unbroken surfaces. One author,
Churchill, points out that his equation should not be used in any
reach in which there is white water rapids. I am just going to give
a summary of the data here and then we'll look at a graphical com-
parison. If we start up at the first line of Table I we see that
for the Flint River, reach 0 to 1, the observed value of K^ was 0.37,
and the 0'Conner equation predicts 0.12, Churchill 0.06 ana Dr.
Thackston's equation 0.29. Likewise, on the second reach of the
Flint River, which is similar in nature hydraulically, we observed
a value of 0.52, ©'Conner's equation predicted 0.18, Churchill 0.13
and Thackston 0.2U.
The hydraulic characteristics of these reaches are such that they do
contain some fast moving water and the depth is relatively small,
typically on the order of a foot or less. However these sections
do not contain the waterfalls that we talked about before. Those
are included in a later entry. As we go on down the list we see on
the Flint River an observed value of 0.27, O'Conner 0.11, Churchill
0.08 and Thackston 0.15. Again on the Flint, this is down on the
lower reaches where we're getting into slower moving water and some-
what deeper channel, 0.1 observed, 0.08 O'Conner, 0.05 Churchill,
Thackston 0.09. Then we move over to the South River, which is a
little larger stream, where the velocities are somewhat similar to
these on the Flint. We have here 0.22 observed, 0.18, 0.18 and 0.13
Predicted. I will have to ask Dr. Thackston later why his value at
this point seems to be lower where it was higher in the others, but
J&aybe we can get into this at a later time. Moving on down the South,
We have 0.15 observed, 0.1^, 0.13 and 0.10 predicted. 0.30 observed,
0.08, 0.06, and 0.11 predicted, and 0.17 observed, 0.09, 0.07, O.'IO
Predicted, and similarly until we get on down to section GH. At this
Point we start picking up more rapids. The K observed goes up and
the equations at this point are significantly under predicting the
observed K-. On the South River K^ now goes up to 0.1$, which, is quite
high, and at this point I place parenthesis around the Churchill and
O'Conner results because these are in quite turbulent waters, and as
1 have pointed out, Churchill stated that his equations should not
be used under these conditions. The only reason for not also setting
apart Dr. Thackston's predictions for this stretch would be that they
6ive much higher values than the others, and we thought there was
Something fundamentally different in his equation in comparison with
the others. As we go on down the table to the Flint River, we see
values that include reaches with waterfalls and we don't even make a
comparison with the other two equations. We have put in the values,
for what they are worth, into Dr. Thackston's equations, and the equa-
predicts quite high values at this point, but certainly nothing
181
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that would come close to the actual measured values. We certainly
don't criticize his equation, because we are using it in an instance
here for which it was never intended to be used. We have only one
result from the Chattahoochee shown in this table. The value for
the Chattahoochee falls off quite significantly and to two decimal
places then we would have 0.03. This then, is a summary of the re^
suits that we have.
To give a little better comparison between the equations, the pre-
dicted values, and our measured values I have eliminated all sec-
tions that contain any white water, and only the most uniform sec-
tions are included in this next comparison. On Figure I you see
plotted the observed K~ per hour and the predicted K* per hour, with
the various equations indicated by different symbols. The tendency,
as you can see, is for the predictive models to appear low by some-
thing on the order of 30 to 50 percent. These are probably too few
data to draw any conclusions, but I would say that the error tends
to decrease as we get into lower values of Kg. The other conclusion
that I think we can draw from this is that, at least for these data,
no one model appears to be better than the other in its predictive
abilities over the range of data that are here presented. Those are
.the only comments that I had to make on our comparisons, if I can
have the lights back on maybe we can have a few minutes to discuss
these results. Are there any questions or comments from anyone?
Discussion
Question; Much of your data is from streams where the flow is not
uniform; is that correct? (
-------
00
u
0.25 _
O O'Connor
S Churchill
V1 Thackston
0.20
^
•d
-p
o
•H
•o
0)
CVJ
0.15
0.10
0.05
0.0
0.05
0.10
0.15
0.20
0.25
Observed
FIGURE I—OBSERVED vs CALCULATED REAERATION COEFFICIENTS
-------
Relationships Between Hydraulic Properties
and Reaeration
E. C. Tsivoglou
As indicated earlier, the main purpose of this research has been to
evaluate the basic relationships between the reaeration capacity of a
stream and its hydraulic properties, with the practical aim of devel-
oping the capability to predict reaeration on the basis of field mea-
surement of appropriate hydraulic properties. We have seen that the
rate of reaeration is directly proportional to the rate of water sur-
face replacement. So in order to accomplish the above objective, we
need to define the rate of water surface replacement in terms of those
hydraulic properties that cause surface replacement, and then it is
necessary to select or develop ways to measure hydraulic properties with
accuracy in natural streams.
One of the real problems that we have encountered involves the basic
meaning of certain traditional measures of hydraulic properties - the
meaning specifically in terms of water surface replacement. Stated
another way, sometimes the very method of measurement of a hydraulic
property, or the method of computing it, modifies its real meaning in
the physical sense. For example, as indicated earlier, if we consider
a section of a natural stream, the way in which we measure the water
depth affects its real meaning in terms of its relationship to the actual
rate of water surface replacement. The measure, for instance,
_ 4t. Occupied Channel Volume
Depth • %—7 :
r Surface Area
is valid only if there is complete and homogeneous mixing of all of the
water in the channel, especially vertical mixing. To consider an ex-
treme, in a stratified channel or reservoir the whole volume is sepa-
rated into hydrodynamic regions, the depth that is effective in regard
to surface replacement (and reaeration) is much smaller than the above
expression would imply, and reaeration of the lower regior is virtually
nil. In many natural streams of relatively small slope the water depth
that is effective in regard to surface replacement and reaeration is
considerably smaller than the measurable whole depth of flow, due to
poor vertical mixing.
Let us consider some of the hydraulic properties of natural watercourses,
the possible ways of measuring them, and the resulting meanings or im-
plications as regards reaeration capacity.
Velocity - Most of the available models for predicting reaeration capa-
city include the "mean velocity", either directly or indirectly, and at
first glance it seems obvious that the rate of water surface replace-
ment ought to be a function of the velocity. But on closer inspection
185
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two questions present themselves: first, how shall this "mean velocity"
be measured, and secondly, does this method of observation affect the
usefulness of the result as a measure of surface replacement? A third
question, namely, is velocity a basic property that causes surface re-
placement, is perhaps the most important question of all.
There are at least two commonly used methods of obtaining the "mean velo-
city". The first involves direct physical measurement of the velocity
at a number of locations in a stream cross-section by the use of a cur-
rent meter; if enough such measurements are made, a reasonably accurate
measure of the average forward velocity through that cross-section can
be obtained. If, then, this procedure is repeated at a sufficient num-
ber of cross-sections in a specified length of stream channel, the re-
sults can be combined to obtain a reasonably accurate estimate of the
mean forward velocity of flow that prevails throughout the length of the
stream section. This procedure is subject to certain obvious sources
of error relating especially to the statistical adequacy of the number
of observations made in any one cross-section, the statistical adequacy
of the number of cross-sections involved, and the accuracy of the current
meter observations when forward velocities are relatively small. But
in addition, and even more importantly, there would appear to be legit-
imate question as to whether the forward velocity is that velocity that
is most nearly related to the rate of surface replacement.
The other commonly used method of obtaining the "mean velocity" in-
volves measurements of the distance travelled and the time of flow.
The distance travelled can be obtained readily and with quite adequate
accuracy from USGS quadrangle sheets or by field survey; the time of
flow can be measured with great accuracy by the use of dye tracers.
The resulting "mean velocity", the distance divided by the time, is re-
latively precise because of the precision of the measures involved.
Depending upon the degree of homogeneity and completeness of mixing in
the channel, it is not necessarily the same "mean velocity" as that ob-
tained by the first method outlined above, but it clearly reflects the
actual forward velocity that is effective in the channel. Whether or
not such a forward velocity adequately relates to the rate of surface
water replacement is again open to serious question.
To summarize, although a measure of stream velocity can be obtained as
outlined above, and although such a measure may be a "mean" in the usual
sense, there is real question as to its usefulness as a representation
of surface replacement. Perhaps a more meaningful measure for our pur-
poses would be an estimate of the mean vertical velocity component in
the stream channel, as this would seem to be more directly relatable
to the rate of surface replacement. Again, however, the very method of
observation could greatly affect the meaning and the usefulness of the
result.
Depth - So far as the hydraulic properties are concerned, reaeration is
a function only of the rate of surface replacement, and, hence, stream
depth has importance only in terms of a possible relationship to the
186
-------
rate of surface replacement, and only then if mixing is complete and
homogeneous. Although it seems unlikely, therefore, that depth itself
is in any direct way a cause of surface replacement, let us examine the
methods of observation. One has been outlined already, namely, the
result of dividing the occupied channel volume by the whole surface
area, and its meaning has been discussed. The other commonly considered
method of observing the "mean depth" involves measurement of the dimen-
sions of the stream cross-section by field survey, wherein the mean
depth of the cross-section is obtained by dividing the observed cross-
sectional area by the measured stream width. Of course, if an accurate
measure of the "mean depth" of a length of stream channel is to be ob-
tained by this means, a substantial number of cross-sections must be
included for purposes of statistical adequacy. A substantial amount of
field survey work is therefore involved. However, the result is sub-
ject to much the same criticism as was made for the volume/surface area
method - the "mean depth" obtained is a measure of the effective depth
only if there is complete and homogeneous mixing in the stream channel,
and this requirement is not met in a large number of cases.
The available methods of obtaining an accurate measure of the effective
mean depth of flow in a length of natural stream channel are tedious at
best, even if there is complete and homogeneous mixing. In any event,
the real meaning of such measures in terms of the rate of surface water
replacement is not readily apparent, and it appears quite unlikely that
depth itself has any causative relationship to surface replacement.
The velocity and depth of flow are the two hydraulic properties that
appear directly in most of the available hydraulic models for predicting
stream reaeration capacity. Other properties that appear either direct-
ly or by implication include the slope of the channel and channel bot-
tom roughness.
Slope - The physical slope of a natural stream channel, namely the de-
crease in elevation per unit of channel length, is readily observable
by field survey, although the fieldwork may be somewhat tedious and time-
consuming. Surprisingly, although the slope would appear to be an im-
portant hydraulic feature, such measurements are not commonly made or
available. Indeed, intuitively the slope of the stream channel would
appear to be more nearly a determining or a causative property than
most others - it is an independent property except where engineering
works have modified it, and properties such as the velocity and depth
of flow are functions of the slope rather than vice versa. In essence,
the steeper the channel slope, the more violent the tumbling action that
creates water surface replacement, and, hence, it appears that the
channel slope should not only be related to the rate of surface replace-
ment but should, in fact, be a basic cause of surface replacement. As
indicated above, it can be measured with entirely satisfactory accuracy.
Roughness - One other property that would seem to be important in terms
of water surface replacement is the physical channel roughness, in the
sense that a very rough stream bed should create better vertical mixing
18?
-------
than a smooth sandy stream bed. Of course, the bottom roughness cannot
be measured directly or independently, and the available method of ob-
taining an estimate of bottom roughness, namely calculation by means of
the Manning equation, is circuitous and subject to substantial error.
In addition, the character of a stream bed, or its physical roughness,
is not so independent a hydraulic property as might appear at first
glance - in fact, the bottom character results from properties such as
the velocity and the slope of the channel. Hence, although the bottom
roughness may be related in some way to the degree of vertical mixing
and the rate of surface replacement, it would not appear to be a basic
property that independently causes surface replacement.
Certain of our experimental results have caused us to view the hydraulic
properties in a somewhat different way that appears to have more promise
in terms of developing a basic relationship between stream reaeration
capacity and hydraulic properties. This point of view involves consid-
eration of the relationship between surface replacement and energy dis-
sipation.
Reaeration and Energy Dissipation
Consider a length of natural stream channel between two points, 1 and
2. The usual one-dimensional energy equation indicates that the amount
of energy expended between the two points is
v2 v2
where V is the velocity in ft/sec, z is the elevation of the stream bed
above mean sea level in ft, H is_the depth of water in ft, and g is the
gravitational constant in ft/sec .
2 2
V - V
Rearranging terms,
(E1 ~ V * ( 2g
where
(Zl + H1) - (z2 + H2) = Ah (3)
and Ah is the change in water surface elevation between points 1 and 2.
188
-------
2 2
With few exceptions, the difference in velocity head, (V.. - V,, )/2g,
is negligibly small compared to the change in elevation Head, Sh.
Hence, for most reaches of stream
(Er- E2) - Ah (4)
for practical purposes.
The rate of energy expenditure is just the amount of energy expended
per unit time, or
where tf is the time of flow from 1 to 2.
It has also been shown in our earlier work that
(6)
where K^ refers to the gas transfer coefficient for any gas , the con-
stant, a, refers to the molecular properties of the gas and the quality
of the water, n is the number of surfaces of area A replaced per unit
time, and V is the whole volume of water. -The product (nrr) is therefore
just the rate of ..surface replacement in cm per second per cm of vol-
ume, if metric units are employed.
It appears logical to suppose that the rate of water surface replace-
ment will be related to the rate of energy dissipation, probably in
a simple and direct way. We have therefore postulated as follows:
POSTULATE: The rate of water surface replacement is proportional to
the rate of energy dissipation in open channel flow.
Using the expressions given in equations (5) and (6) above, the postulate
may be expressed as follows:
(7)
where b is the necessary proportionality constant.
It now follows from equations (6) and (7) that
189
-------
K = c (8)
where c = ab.
Equation (8) is our basic model relating the reaeration coefficient, K_,
to the stream hydraulic properties. The coefficient K. actually refers
to any gas, including krypton as well as oxygen, the only difference
being the numerical magnitude of the constant, c. The hydraulic pro-
perties Ah and t- can be measured directly and independently, as well as
with quite satisfactory accuracy, for any length of stream channel.
Hence, equation (8) and its underlying postulate given previously can be
tested directly with field observations. A few of our relevant results
will be presented for this purpose. However, before doing so, one
other useful expression will be derived.
It has been noted earlier that for the length of stream between points
1 and 2
C2 = cie~?f
where C, and C« are the concentrations of dissolved gas at points 1 and
2. Replacing K_ by its hydraulic equivalent from equation (8), we ob-
tain Z
do)
where y is just the decimal percent of dissolved gas remaining at point
2. It follows also that
(1 - y) - z - (1 - e~cAh) (11)
where z is now the decimal percent of dissolved gas that has been lost
between points 1 and 2. Equations (10) and (11) refer directly to the
tracer gas, krypton, but may also be used to refer to the decimal
fractions of the DO deficit remaining and satisfied, respectively.
Equation (11) is of very strong interest. It states, simply, that gas
transfer in a turbulent natural stream is dependent only upon the change
in water surface elevation, in the hydraulic sense. In other terms, at
a given water temperature the amount of tracer gas that will be lost to
the atmosphere in a specific length of stream channel, or the amount of
DO deficit that will be satisfied, can be predicted on the basis solely
of the change in water surface elevation. Alternatively, the numerical
190
-------
magnitude of K can be predicted on the basis of the change in water
surface elevation and the time of flow, according to equation (8).
Figure 1 is a graph of our presently available results from the tracer
studies of the Flint, South and Patuxent Rivers, in which the mean value
°f KnX^25°C^ for the 8Peclfic stream reach has been plotted as a function
of the rate of energy dissipation measured as (Ah/t.). The reaches re-
presented include waterfalls and rapids, as well as Panola Shoals and
the relatively gentle mixing in reaches of the Patuxent. The range of
values of KQX> from 0.10 to 2.7 per hour, is quite large. As may be
seen, these currently available results strongly support the straight
line relationship predicted by equation (8), with a numerical value for
the coefficient c of about 0.045 per ft. The single aberrant result
(29, 2.7) is for the reach 2P-2 on the Flint River, which includes
essentially the second waterfall, and this particular observation is
regarded as presently still questionnable to the extent that the ob-
served short time of flow may contain some error. This is being checked.
Figure 2 provides a separate test of the relationship predicted by equa-
tion (11), wherein gas loss was shown to be a function only of the change
in water surface elevation. All of the individual tracer gas loss data
obtained from the five separate dumps in the Patuxent River have been
plotted, with the observed percent loss of tracer gas shown as a func-
tion of the change in water surface elevation between sampling points.
The relationship predicted by equation (11) is clearly demonstrated
by the data, as is the effectiveness of equation (11) for predicting
gas transfer from energy dissipation. If these same results are plotted
in the form required by equation (10) on semilog paper (log percent
remaining vs elevation change), a straight line results, as predicted
and the degree of correlation is very good.
It is emphasized that the foregoing results must be regarded as prelim-
inary at this time. Additional data are still being obtained, and final
computation and correction of all of our observed results is still not
complete. In brief, the research is still in progress, and these cur-
rently available data are presented here primarily to illustrate the
direction that our research has taken and our current approaches. Sev-
eral questions remain and are under investigation, relating largely to
study of the observed spread of data about the predicted relationships.
In particular, we know that the presence of pollutants does affect the
numerical value of K2. We have also observed that in at least one case
different tracer dumps in the same river may produce excellent indivi-
dual fits of the relationship predicted by equation (11) but still lead
to different values of the coefficient c. Current effort in this re-
search therefore involves investigation of the "finer structure" of the
relationships that have been shown, and of the hydraulic properties and
the water quality properties that may bring about such variability.
191
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EAERATION COEFFICIENT, K(PER HOUR)
P — r- rv> ix>
u» O m O 01
o o o o o
WATERFALL
40
0 10 20 30
RATE OF ENERGY DISSIPATION,
FIGURE 1
MEASURED REAERATION RATES
FLINT, SOUTH, AND PATUXENT RIVERS
50
1 92
-------
o
I
00
co
O
5 10 15 20 25
ENERGY DISSIPATION, Ah(FT)
FIGURE 2
GAS TRANSFER FOR PATUXENT RIVER STUDIES
30
1 93
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Summary
Stream reaeration has been shown to be directly related to the rate of
water surface replacement in a natural stream. It has been postulated
here that the rate of surface replacement is directly proportional to
the rate of energy dissipation, which can be expressed as the change in
water surface elevation divided by the time of flow, for most stream
reaches. Both the change in water surface elevation and the time of
flow can be observed with accuracy, and, hence, the reaeration coeffi-
cient can be predicted on the basis of observable fundamental hydraulic
properties. Extending this approach, it has also been shown that the
actual gas transfer that takes place in a reach of stream can be pre-
dicted solely on the basis of the change in water surface elevation.
These relationships have been adequately demonstrated with currently
available research data. Current research involves investigation of the
hydraulic properties and the water quality properties that may bring
about "fine structure" variability of individual observations about the
predicted general relationships.
These considerations have also indicated that, because they are not
fundamental hydraulic properties that cause water surface replacement,
measures such as the mean forward velocity of stream flow and the mean
water depth are not likely to be adequate indicators of stream reaera-
tion capacity.
-------
1
5
Accession Number
« Subject Fn-ld & Group
05F, 05C
SELECTED WATER RESOURCES ABSTRACTS
INPUT TRANSACTION FORM
Organization ' _____ ____ ____ ______ _____
Atlanta, Georgia
Title
PROCEEDINGS OF A SYMPOSIUM ON DIRECT TRACER MEASUREMENT OF THE REAERATION
CAPACITY OF STREAMS AND ESTUARIES
10 j Authorfs)
Ss--J Tsivoglou,^Ernest C,
McClanahan, Mark A., and
Sanders, Walter M., III
16
Project Designation
Project 16050 FOR
21
Note
Citation
Descriptors (Starred First) " ~ ~
*Tracers, *Tritium, *Reaeration, *0n-site Data Collection, *Measurement, Model
Studies, *Estuaries, *Streams, Radioactivity Techniques, *Radioisotopes, *0xygen,
Dissolved Oxygen, Biochemical Oxygen Demand, Water Pollution Effects
Identifiers (Starred First) ~ ~~"——————— :
*Krypton, Flint River, South River, Patuxent River, Chattahoochee River, Yaquina
River Estuary, James River Estuary Model, *Turbulence, *Mixing, *Gas Transfer,
*Hydraulic Properties
Abstract ~ ~~~~~—
A symposium on direct measurement of the reaeration capacity of streams and estuaries
was conducted in July 1970, for the purpose of making immediately available the
results of current research on this subject at the Georgia Institute of Technology.
The symposium was designed to make public for the use of other engineers and scientists
all of the available information on the subject at that time.
The papers presented provide an outline of the fundamentals of gas transfer in
turbulent systems, the theory and application of radiotracers for measuring gas
transfer in natural waters, and the associated field and laboratory procedures. Other
papers provide tracer-observed values of the reaeration capacity of several streams,
and comparisons with computed values obtained from well-known predictive models. A
new theory regarding the relationship between the reaeration capacity and the
hydraulic properties of natural streams is presented, together with early supporting
observed results. The effects of pollutants on the reaeration capacity, and some
observed results, are discussed in another paper. Invited papers provide the initial
results of tracer measurement of the reaeration capacity of a small estuary, as well
as the oxygen balance for an inland stream using the tracer-observed reaeration
capacity (by Georgia Tech) together with DO and BOD data obtained independently
(by EPA). (Tsivoglou-Georgia Tech)
JL« C. Tsivoglou
Institution
tut ion .
Georgia Institute of Technology
(REV. JULY
SEND TO: W*TER RESOURCES SCIENTIFIC IN FORM A TION C EN TER
U.S. DEPARTMENT OF THE INTERIOR
WASHINGTON. O. C. 20240
*U.S. GOVERNMENT PRINTING OFFICE: 1972-484-484'177 1-3
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