Regulatory Guide 1.113
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| Issue date: | 04/30/1977 |
| From: | Office of Nuclear Regulatory Research |
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| -nr RG-1.113, Rev 1 | |
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Revision 1 US. NUCLEAR REGULATORY COMMISSION
April 1977 REGULATORYGUIDE
OFFICE OF STANDARDS DEVELOPMENT
REGULATORY GUIDE 1.113 ESTIMATING AQUATIC DISPERSION OF EFFLUENTS FROM
ACCIDENTAL AND ROUTINE REACTOR RELEASES FOR TH
E. PURPOSE
OF
IMPLEMENTING APPENDIX I
USNRC REGULATORY GUIDES
Regulatory Guides we issued to describe and make available to the public methods acceptable to the NRC saff Of implementing apecific parts of the Commission's regulations, to delineate techniques wad by the staff in evaluating sperific problems or postulated accidents. or to provide guidance to applicants. Regulatory Guides era not substitutes for regulations, end compliance with them is not required.
Methods and solutions different from those ut out in the guides will be accept amle if they provide a basis for the findings requisite to the isuence or continuance of permit or license by the Commowion.
Comments and suggestions for Improvemants i the guides we eonowraged at all times. and guides will be revised, as appropriate. to wcommodate comments OW
to reflect nw information or experience.
This guide wse revised ea a result of lubstantive comments received from the public and eddlitional staff reviw.
Comments should be sett to the Secretery of the Commission. US. Nucleer Regu litory Commission. Washington. D..
20556. Attention: Docketing end Service Branch.
The guides are issued in the following ton broad divisions:
I. Power Reactors
6. Products
2. Research and Tess Reactors
7. Taportnetlon
3. Fuels and Materiels Facilities S. Occupetlonal Health
4. Environmental nd Siting
9. Antitrust Review S. Materials end Plant Protection
10. General Requests for single copies of issued guides lwhich may be reproduced) or for place ment on en automatic distru*btion list for single copies of future guides in specific divisions should be mnde in writing to the US. Nuclear Regulalory Commission.
Washington. D.C.
20555. Attention:
Dector. Division of Document Control.
TABLE OF CONTENTS
A.
INTRODUCTION.
......................................................
1.113-1 B.
DISCUSSION ..................................................................
1.113-1
C. REGULATORY POSITION
................................................. 1.113-2 D.
IMPLEMENTATION ...................................................................
1.113-3 APPENDIX A. LIQUID EFFLUENT TRANSPORT AND WATER USE MODELS ............................
1.113-4
1.
Initial Dilution ............................................................
1.113-4
2.
Nontidal Rivers .............................................................
1.113-4 a.
Model Formulations ......................................................
1.113-4 b.
Model Applications ......................................................
1.113-8
3.
Open Coasts .................................................
- ...............
1.113-11 a.
Great Lakes ............................................................
1.113-11 b.
Oceans ..............................................................
ý...
1.113-16
4.
Estuaries ...................................................................
1.113-17 a.
One-Dimensional Models ..... ;............................................
1.113-17 b.
Multi-Dimensional Models ................................................
1.113-21 c.
Exchange Coefficients .................................................
1.113-22 d.
Applicability of Models ...............................................
1.113-25
5.
Impoundments .....................................
..........................
1.113-26 a.
Simple Analytical Models ................................................
1.113-26 b.
Numerical Models ........................................................
1.113-38
6.
Water Use ...................................................................
1.113-41 a.
Users .........................
.. ...........
..........................
1.113-41 b.
Usage ...............................
....................................
1.113-41 c.
Existing Studies ........................................................
1.113-44
7.
Sediment Uptake and Transport Models ........................................
1.113-44 LIST OF SYMBOLS .......................................................................
1.113-46 CITED REFERENCES ............................................
..........................
1.113-49 ADDITIONAL REFERENCES ................................................................
1.113-53 iii
LIST OF FIGURES
Figure Page
1 Model of an Infinitesimal Stream Tube in a Natural Stream ..................
1.113-6
2 Dimensionless Concentration of Nondecaying Radionuclide Discharge at the Shoreline vs. Dimensionless Downstream Distance ....................
1.113-10
3 Dispersion Values at Surface for Liquid Effluents in a Large Lake ..........
1.113-14
4 Dimensionless Plot of Contaminant Concentration vs. Distance from Source ........................................
..........................
1.113-19
5 Correlation of Dispersion Parameter to Degree of Stratification ............
1.113-24
6 Closed-Loop Cooling Pond ...................................................
1.113-27
7 Flow-Through Cooling Pond, .................................................
1.113-28
8 Completely Mixed Model .................................
...................
1.113-29
9 Steady-State Concentrations in Completely Mixed and Plug-Flow Models .......
1.113-31
10
Plug-Flow Model ............................................................
1.113-32
11 Partially Mixed Model ......................................................
1.113-33
12 Concentration in Partially Mixed Case ......................................
1.113-35
13 Lumped Parameter Stratified Reservoir Model ...............................
1.113-36
14 Buildup of Radioisotopes in Completely Mixed Model (Normalized) ....
.......
1.113-39
15 Dimensionless Time To Reach 99% of Steady-State Concentration in Completely Mixed Case .................................................
1.113-40
16 Typical Schematic Diagram of a River Basin .................................
1.113-42
17 Effect of Flow Averaging Period on Normalized Concentration ................
1.113-43 iv
A.
INTRODUCTION
Section 20.106, "Radioactivity in Effluents to Unrestricted Areas," of the Commission's regulations in 10 CFR Part 20, "Standards for Protection Against Radiation," establishes limits on concentrations of radioactive material in effluents to unrestricted areas.
Paragraph 2 0.1(c)
of 10 CFR Part 20 states that, in addition to complying with the limits set forth in that part, licensees should make every reasonable effort to maintain releases of radioactive materials in effluents to unrestricted areas as far below the limits specified as is reasonably achievable (ALARA).
Section 50.34a, "Design Objectives for Equipment to Control Releases of Radioactive Mate rial in Effluents - Nuclear Power Reactors," of 10 CFR Part 50, "Licensing of Production and Utilization Facilities," sets forth design objectives for equipment to control releases of radioactive effluents from light-water-cooled nuclear power reactors.
Section 50.36a, "Tech nical Specifications on Effluents from Nuclear Reactors," of 10 CFR Part 50 further provides that, in order to keep power reactor effluent releases as low as is reasonably achievable, each operating license will include technical specifications on effluent discharge limits, operating procedures for installation, use, and maintenance of effluent control equipment, and require ments for reporting measured releases of radionuclides to the environment.
Appendix I, "Numerical Guides for Design Objectives and Limiting Conditions for Operation to Meet the Criterion 'As Low As Is Reasonably Achievable' for Radioactive Material in Light Water-Cooled Nuclear Power Reactor Effluents," to 10 CFR Part 50 provides numerical guidance for radioactive effluent design objectives and technical specification requirements for limiting conditions of operation for light-water-cooled nuclear power plants.
To implement Appendix I, the staff has developed a series of guides that present methods acceptable to the staff for calculating preoperational estimates of effluent releases, dis persion of the effluent in the atmosphere and different water bodies, and the associated radi ation doses* to man.
This guide describes basic features of calculational models and suggests methods of determining values of model parameters for the estimation of aquatic dispersion of both routine and accidental releases of liquid effluents.
The methods described herein are general approaches that the NRC staff has adopted for the analysis of routine and accidental releases into various types of surface water bodies.
Models for the ground-water pathway are not covered in this guide.
Those few cases where the ground-water pathway makes a significant contribution to the dose estimates will be analyzed on a case-by-case basis.
Standards for analysis of releases to ground water are currently being developed by the American Nuclear Society and will be published by the American National Standards Institute.
B.
DISCUSSION
Radioactive material in aqueous effluents may be released from nuclear power stations, either routinely or accidentally, into a variety of receiving surface water bodies, including nontidal rivers, lakes, reservoirs, cooling ponds,,estuaries, and open coastal waters.
This material is dispersed by turbulent mixing and by streamflow in rivers, by tidal or nontidal coastal currents in estuaries and coastal waters, and by internal circulation or flow-through in lakes, reservoirs, and cooling ponds.
Parameters influencing the dispersion patterns and con centration reduction near a site include the direction and speed of flow of currents, both natural and plant-induced, in the receiving water; the intensity of turbulent mixing; the size, geometry, and bottom topography of the water body; the location of effluent discharge in relation to the receiving water surface and shoreline; the amount of recirculation of previously dis charged effluent; the characteristics of suspended and bottom sediments; the sediment sorption propertiesi and radioactive decay.
This guide describes calculational models acceptable to the NRC staff for estimating aquatic dispersion of routine or accidental releases of radioactive material from a nuclear power station to a surface water body.
The models discussed include both simplified models having straight forward analytical solutions and more complex models requiring numerical solution.
In general, In this guide, the term "dose," when applied to individuals, is used instead of the more precise term, "dose equivalent," as defined by the International Commission on Radiological Units and Measurements (ICRUM).
1.113-1
the modeling techniques discussed represent adaptations of work currently available in the liter ature.
Because. of increasing environmental concerns during the past decade, considerable effort has been expended in advancing the state of the art of water quality simulation and thermal plume modeling.
The models discussed herein draw heavily from this body of information.
Although specific models are considered, they are intended to represent specific classes of models.
Furthermore, discussions of particular techniques for determining model parameters are intended to provide guidance and to stress the desirability of determining these parameters from physical principles or measurements.
Applicants may, however, use modeling techniques other
- 1 than those considered herein.
In particular, physical hydraulic models that may have been con structed for hydrothermal studies or other purposes may often be used as reliable predictive tools for radionuclide dispersion.
Tracer release studies conducted in situ can provide accurate predictions without need for a model.
The degree of realism inherent in each model described in this guide depends on the ability of that model to account for the physical processes involved and the validity of model coeffi cients and assumed future flow fields.
As a general rule, more complex models are capable of yielding more realistic results.
However, a realistic model requires realistic input data, and little is gained by using highly sophisticated calculational models when the input parameters are ill-defined.
The simplest models are closed-form analytical solutions of the governing transport equations.
Such solutions are possible only for simplified cases. It is seldom pos sible to obtain analytical solutions for time-dependent flow fields or for complex receiving water geometry.
Consequently, any analytical solution should be carefully assessed by the applicant to ascertain the conditions under which the model might be a valid predictive tool.
Simplified models do not necessarily produce conservative results.
If such models are used, it is the applicant's responsibility to demonstrate their degree of conservatism.
The staff's position on such demonstration is presented in Section C of this guide.
In identifying liquid pathways to man, applicants should identify the location of water users, the types of uses, and the usage estimated out to a distance of 50 miles from the site.
Because of high usage rates along many streams and estuaries, the effects of water usage on the spatial and temporal distribution of flows should be estimated.
In addition, water usage up stream of a nuclear plant can alter flows at or downstream of the plant.
This guide presents an acceptable methodology for evaluating water usage and the consequences thereof on streams and estuaries receiving routine or accidental releases of radionuclides from nuclear power plants.
The ability of suspended and bottom sediments to absorb and adsorb radioactive nuclides from solution, thereby concentrating otherwise dilute species of ions, may create a significant pathway to man.
Sorption by sediment is also an important mechanism for reducing the area of influence of plant releases.
Unfortunately, the state of the art in evaluating sediment-related effects is less advanced than in other engineering disciplines.
Consequently, the transport models discussed in this guide do not explicitly include sediment uptake mechanisms.
Until reliable generalized sediment uptake and transport models become available, the NRC staff will rely on existing field studies and the staff's and consultants' experience to determine the level of conservatism or realism of the applicant's estimates.
If the appTicant elects to take credit for removal of certain ions from the surface waters by the process of sediment uptake, verification using site-related field data will be necessary.
C.
REGULATORY POSITION
1.
The transport and water use models described in Appendix A of this guide are acceptable to the NRC staff for use in calculating the potential annual average radiation doses to the public that may result from radioactive material in liquid effluents routinely released to sur face water bodies.
No general models for transport in ground water are included, as such analy ses are considered to be site-specific.
The models in Appendix A are also acceptable to the staff for analyzing the dispersion and dilution of accidental spills of radioactive material in liquids to surface water bodies.
Standards for ground-water analysis, currently being prepared by the American Nuclear Society for publication by the American National Standards Institute, will be evaluated for acceptability by the NRC staff when completed.
2.
Although specific models are cited in Appendix A of this guide, the citations are intended to provide guidance in the selection of model types rather than to specify models.
Applicants may use models other than those described in Appendix A, but should justify fully the analytical techniques, assumptions, and level of conservatism of the model ultimately chosen.
- Lines indicate substantive change from previous issuance.
1.113-2
3.
The choice of a specific model, values of input parameters, and assumed future flow fields is the responsibility of the applicant.
The NRC staff recognizes that the applicant may choose initially to use simplified models employing demonstrably conservative assumptions.
The most conservative assumption would be no dilution of the radwaste discharge and a travel time ofI
zero.
In some cases, this extreme approach may be acceptable for calculation of dose to man.
Should the results of this Initial analysis support a cohclusion of compliance with Apoendix I
of 10 CFR Part 50, no further effort is indicated.
However, if compliance is not demonstrated by the simplified analysis, more refined and more realistic analyses of liquid transport may be undertaken.
The NRC staff will also consider such analyses acceptable provided the applicant establishes the realism of the model, coefficients, parameters, and flow field.
0. IMPLEMENTATION
The purpose of this section is to provide information to license applicants and licensees regarding the NRC staff's plans for implementing this regulatory guide.
This guide reflects current Nuclear Regulatory Commission practice.
Therefore, except in those cases in which the license applicant or licensee proposes an acceptable alternative method, the method described herein for complying with specified portions of the Coamissions regulations is being and will continue to be used in the evaluation of submittals for operating license or construction permit applications until this guide is revised as a result of suggestions from the public or additional staff review.
1.113-3
APPENDIX A
LIQUID EFFLUENT TRANSPORT AND WATER USE MODELS
This appendix describes transport and water use models for calculating the radiation doses to the public that may result from radioactive material In liquid effluents released to surface water bodies.
Symbols used in this description are defined in the "List of Symbols" following the appendix.
1.
INITIAL DILUTION
Initial dilution of liquid radioactive effluents (e.g., dilution upon discharge to the receiving water body) is often accomplished by using relatively high-velocity surface or sub merged jets or multiport diffusers.
Mathematical modeling of such discharges requires solution of the conservation equations applicable to buoyant jets.
These equations are solved routinely as a part of the near-field analysis for thermal discharges.
Initial dilution rates for water borne radionuclides should be obtained directly as an integral part of the thermal analysis.
Applicable near-field models are In comnon usage throughout the industry and are not dis cussed in detail herein.
Jirka et al.
(Ref. 1) and Dunn et al. (Ref.
2) discuss in detail the theory and ranges of applicability of near-field models.
These references should be consulted for guidance in determining the modeling approach to be used for a specific problem.
General remarks on surface and submerged jet discharges are presented below.
For surface discharges, acceptable initial dilution analyses may be obtained from the models of Stolzenbach and Harleman (Ref. 3), Stolzenbach et al.
(Ref. 4), Prych (Ref. 5), Shirazi and Davis (Ref. 6), and Pritchard (Refs.
7 and 8).
Dilution estimates for surface discharges require a careful assessment of the adverse effects of shoreline and bottom interference.
Methods for estimating the magnitude of these boundary effects under given receiving water conditions are discussed in detail in Reference 1.
Estimates of dilution from submerged discharges require careful analysis of the flow con ditions in the immediate vicinity of the discharge.
The two possible flow conditions, stable o1%
unstable, depend on the discharge and receiving water characteristics.
Under stable conditions the discharge, upon reaching the free surface, spreads laterally in the form of a stable density current.
As a result, there is little re-entrainment of previously discharged water.
Such stable discharges can be characterized as "deep-water."
Unstable or "shallow-water" discharges are characterized by counterflow which causes re-entrainment of previously mixed effluent into the discharge jet.
Application of deep-water jet models to shallow-water discharges can result in serious overestimation of initial dilution.
References 1, 9, and 10 discuss in detail the behavior of stable and unstable discharges and stability criteria for various types of submerged discharges.
In practice, the results of a stability analysis will determine whether a "deep water" or "shallow-water" model should be used for a given discharge-receiving water system.
For deep-water (stable) conditions the commonly used submerged Jet models of Koh and Fan (Ref.
11) and Hirst (Ref.
12) and similar models are applicable provided the thickness of the buoyant surface layer is taken Into account.
For shallow-water (unstable) conditions the above models (and other similar deep-water models) are not applicable and their use will result in predicting excessively high dilution.
The models of Lee et al. (Ref. 10) and Jirka and Harleman (Ref. 9), with appropriate stability analyses, are directly applicable to either deep- or shallow-water discharges.
2.
NONTIDAL RIVERS
a.
Model Formulations
(1)
Steady-State Stream Tube Model Application of the models herein is restricted to those portions of the river removed from influences of the discharge.
Initial dilution near the point of discharge is usually con trolled by turbulent mixing induced by momentum effects of the discharge jet. Techniques for the determination of initial dilution were discussed in Section 1 of this appendix.
1.113-4
For nontidal rivers the flow is assumed to be uniform and approximately steady.
Under these conditions, the diffusive transport in the flow direction may be neglected compared with the advective transport (Ref. 13).
It has been shown that far-field transport of dissolved constituents in rivers can be satisfactorily treated by a two-dimensional model in which vertical variations of velocity and concentration are averaged out (Refs. 14, 15, and 16).
Such a model, however, retains transverse variations of river bottom topography and velocity.
Consider a section of a steady natural stream as shown in Figure 1.
The origin of the coordinate system is placed on the near shore.
The x-axis Is taken positive in the downstream direction, the z-axis is directed vertically downward from the water surface, and the y-axis is directed across the stream.
The steady-state mass balance equation for a vertically mixed radio nuclide concentration may be written (Ref. 14) as follows:
ud LC - l (Kd'3C) -
(Xd)C
(1)
ax a
where C
is the radionuclide concentration (activity/volume);
d is the stream depth;
Ky Is the lateral turbulent diffusion coefficient (vertically averaged, two dimensional);
u is the stream velocity; and A
is the decay coefficient and is - (ln 2)/half life.
Since, for a real stream, u and d will be functions of the transverse coordinate y, Equation (1) will generally not have a closed-form analytical solution.
A more tractable form of the equation is obtained through introduction of a i.aw independent variable q, defined by q -
(ud)dy
(2)
Jo The quantity q is the cumulative discharge measured frnu the near .shore.
Hence, as y - B, q
,
where B is the river width and Q is the total river floe.
Substitution of Equation (2) into Equation (1) yields the following transport equation:
2-_ . L-_
-(yu2 IC
i C
."(3)
In the decay term, the velocity umay be.replaced, to a good approximation, by the sectional mean value u.
If this is done, the decay term may be removed through the transformation A x C(xq) - x(x,q)e u
(4)
The result is the following transport equation for the nondecaying concentration x:
S~(s)
The quantity Kvud2 is known as the "diffusion factor."
Yotsukura and Cobb (Ref. 14) have shown that the variable diffusion factor may be replaced by a constant factor Kyud , where Q
1 Kyud fo Kyud 2dq is the discharge-weighted mean value.
Equation (5) may now be written
1.113-5
x - Downstmma y - Aro, Strum z - Verticly Doaumld From Water Surface u(y)- Ve.ocity in x Direction Varying with y S.0
u(y FIGURE 1. MODEL OF AN INFINITESIMAL STREAM TUBE IN A NATURAL STREAM
(Rdamwn frmo Yotukua oad Cobb. Ref. 14.)
I-
(6)
ax aq where D a K--
ud a consta-nt diffusion factor y
Equation (6) is a standard diffusion equation which has a closed-form analytical solution.
Assume a steady vertical line source discharge emitting a constant W Cl/sec is located at x = 0, y = ys. Since there is a one-to-one correspondence between the transverse distance y and the cumulative discharge q, the vertical line source discharge may be located at x a 0,
q m qs"
A closed-form solution to Equation (6) that satisfies the condition that there be no flux of material across the bounding surfaces is given by X a W
+2 nil n2w2Dx e
Q
Cos n4 ZOS
This expression, although of different form, is equivalent to Equation (14) of Reference 14.
If the liquid effluent Is injected as an area source perpendicular to the river flow, the solution may be obtained by integration of Equation (7) over the source dimensions.
If the source is located in the river between distances ysl and y.2 (cumulative discharges qsl and qs2),
the area source solution may be obtained from Equation (7) by integration with respect to qs between the limits qsl < qs Iq s2.
XAreaj)-W
L+
n2w2Dx e" QT
n.1 sin na cos n (qs 2 +qsl
"niq no Q
cos where
7 Q
Note that the more familiar solutions for the concentration, as a function of x and y in a uniform, straight, rectangular channel of constant velocity U, can be obtained immediately from Equations
(7) and (8) through the transformation of the terms within the brackets:
{D/Q2}
{K yUB2}
The more general forms given by Equations (7) and (8), however, are preferable, since they are applicable to irregularly shaped channels.
Yotsukura and Sayre (Ref. 16) have recently gen eralized Equations (5) and (6) so that these can be applied to any nonuniform channel with a minor modification to the diffusion factor.
(2)
Transient Release Model In many cases, routine releases of radioactive effluents are batched and infrequent, rather than continuous.
In such cases, it may be important to calculate concentrations as a function of both time and space.
The concentration in a straight, rectangular channel cor responding to the instantaneous release of a finite quantity of material from a vertical line source at x = 0 and y - ys is:
C "
-
ePxp
-x
-- _t)
+ 2 Jlexp
.cos n Y- cosnirfJ(9)
(4WKxt) 112A
BF
1.113-7
(7)
(8)
where A
is the cross-sectional area;
B
is the channel width;
i is the longitudinal turbulent transport coefficient (vertically averaged, two M
is the amount of activity released (in curies);
t is the time after the release;
'and the other terms are as previously defined.
Note that this solution accounts for turbulent diffusion in the direction. of flow, which may be important for short-duration releases.
The case of a more general time-dependent release may be obtained by integrating Equation (9) with respect to time:
o XWl)
A
- utt - T ]2 C .(4WK)I/A(t
-. ),1/
2. exp f
4Kix it .
T)
At
[+2 i exp n-rK t cos n Yscos nnr*
d-
(10)
where the release rate is Wf(T) curies/sec.
In general, Equation (10) must be solved by numerical quadrature..
Near the source, convergence of the Fourier series terms In Equations (9) and (10) may be extremely slow.
However, in this region, the effects of the far shore are not usually impor tant, and the series solution may be replaced by a single image source at the near shore (see the transient lake solution, Equations (19) and (20), Section 3.a.(2)(b) of this appendix).
In this case, the solutions do not involve infinite series and present no convergence problems.
b.
Model Applications
(1)
Steady-State Stream Tube Model Application of the model requires determination of stream channel geometry, the cross stream distribution of flow, and the diffusion factor at representative river cross-sections downstream of the effluent discharge.
In addition, definition of stream discharge is necessary (see Section 6 of this appendix).
The preferred method of determining the flow cross-sectional distribution is by current-meter measurements using standard stream-gaging techniques.
Because it is not always practical to obtain velocity measurements at every river cross-section at which concentration distributions are desired, transverse velocity distributions may be estimated from observed stream bottom profiles and the application of steady-state flow equations such as Manning's formula to channels of compound cross-section (Refs.
17 and 18).
Evalatio ofthe iffuionfactrKu--d requires a separate determination of the dif Evaluation of the diffusion factor ;;I
fusion coefficient.Ky.
For steady open-channel flow, Ky can be determined from hydrodynamic properties of the channel by using Elder's empirical formula (Ref. 19):
Ky w Bu*d
(11)
where d
is the river depth;
u*
is the shear velocity; and
1.113-8
0
is a dimensionless constant.
(The user is not restricted to this formula.
A number of alternative approaches have been published.)
For straight natural stream channels B has a value of approximately 0.23 (Refs. 14 and
16).
For curved channels, however, secondary flows can lead to Increased lateral mixing and the value of B is larger (Refs. 20-22).
Fischer (Ref. 20), for example, has shown that the lateral mixing coefficient is increased in bending streams, varying Inversely as the square of the radius of curvature.
In general, to obtain realistic transport estimates, values of the lateral mixing coefficient should be determined by onsite tracer studies.
Although transverse variations of Ky have not been adequately confirmed in field tests, longitudinal variation of Ky in a sharp bend has been reported by Sayre and Yeh (Ref. 22).
Equations (7) and (8) may be modified as follows to account for a diffusion factor that varies in the direction of flow:
Ux -,fXD(x)dx a0
If the diffusion factor is known for each river cross-section of concern, the integral can be evaluated by simple numerical integration.
If the variation in D(x) is small over the river stretch under consideration, then Equations (7) and (8) may be used directly, with the quantity D being interpreted as the mean value over the river reach.
It is useful to write Equation (7) in dimensionless form.
I + 2 ef n2W2; cos nlr cos nwi
(12)
n=l where S= q/Q
is the dimensionless cumulative discharge;
i x/ý
is the dimensionless concentration relative to the fully mixed value; and i -
is the dimensionless downstream distance.
The utility of the dimensionless form is illustrated in Figure 2, which shows near and far-shore concentrations resulting from a near-shore point discharge.
For a given downstream location and given flow parameters, the dimensionless concentration for either shoreline may be obtained directly from the two curves.
The near-shore concentration exhibits the expected x"1/2 dependence for two-dimensional mixing until the influence of the far shore if felt.
Both curves in Figure 2 approach unity (complete sectional mixing) for large values of x.
Hence, for a given set of flow parameters, the downstream distance to sectional homogeneity ("mixing distance")
can be estimated directly.
(Note that the mixing distance for a shoreline discharge is four times the mixing distance for a centerline discharge.)
(2)
Transient Release Model The transient release model is formulated in this guide only for the case of a vertical line source in a straight rectangular channel, since Its primary purpose Is to furnish informa tion on the time-dependent behav or of non-continuous releases.
However, the model can be extended to treat other source configurations in stream tube coordinates as employed in Section 2.a.(l) of this appendix.
Application'of the model requires the determination of the longitudinal turbulent dif fusion coefficient Kx, in addition to the parameters necessary for the steady-state model in the previous section.
The longitudinal dispersion coefficient should be obtained by site-specific tracer experiments.
However, crude estimates of Kx may be obtained from the following formula, which is similar to that for the lateral diffusion coefficient (Ref. 19):
1.113-9
10
z 0
z 00
z
_U
o
.
10-
t!
w
/
w F/
io-1 I
,t
10-4
10-3 I0- 2 IV-1 DIMENSIONLESS DOWNSTREAM DISTANCE
. D
FIGURE 2.
DIMENSIONLESS CONCENTRATION OF NONDECAYING
RADIONUCLIDE DISCHARGE AT THE SHORELINE
vs DIMENSIONLESS DOWNSTREAM DISTANCE
1
10
6
Kx = ou*d,
(13)
where d
is the river depth;
u*
is the shear velocity; and
0
is a dimensionless constant.
(Again, the user is not restricted to the use of this formula.
A number of alternative approaches have been published.)
cor straight rectangular stream channels, o has a value of about 5.93.
The value of s, however, increases in curved channels and in general must be determined by field studies (Refs. 20-22).
The two-dimensional coefficient, Kx, is usually much smaller in magnitude than the one-dimensional coefficient, E, as described later.
The usefulness of the transient model, even for simplified rectangular geometry, is that it allows analysis of the dispersion of material released In a realistic fashion.
In the case of short-duration batch releases, spreading in the direction of flow may be an important.
mechanism for effluent dispersion, which is not included in the steady-state continuous release model.
3.
OPEN COASTS
a.
Great Lakes
(1)
Discussion Field studies in the Great Lakes have shown that coastal currents are predominantly parallel to the shore and have typical speeds of 10 to 20 cm/sec (0.2 to 0.4 knots).
These cur rents usually persist in one direction for several days.
Then, in direct response to wind shifts, they quickly reverse and persist in the opposite direction for several days.
The stagnation time at reversal seldom exceeds a few hours (Refs. 23 and 24).
The studies further suggest that each reversal of the coastal current is accompanied by a large-scale mass exchange with offshore waters that effectively removes pollutants from the shore zone.
Possible physical mechanisms responsible for this behavior are discussed by Csanady (Refs. 25 and 26).
Observations near pollutant discharges have shown a well-defined pollutant plume hugging the shoreline for several days, then relatively quick dispersal offshore, followed by redevelopment of the plume in the opposite direction.
Throughout this sequence, the buildup of pollutant concentration in the vicinity of the discharge is small (Refs. 23 and 27).
A stable coastal current of, say, 10 cm/sec that persists for about three days before reversal causes an upcoast or downcoast excursion of an effluent plume which is of the order of 25 Ikn (about 16 miles).
In view of the above findings, it is'possible to construct a quasi-steady-state model valid for distances of about 25 Ikn and time scales on the order of a few days.
For those cases in which lateral mixing and mass exchange occur during flow stagnation periods, extension of the model beyond these limits should provide conservative results.
It should be emphasized, however, that knowledge of Great Lakes coastal circulation patterns is far from complete.
The existing data base is inadequate to conclude that the behavior described above is applicable to the entire Great Lakes system.
A general knowledge of near-shore current climatology is needed.
It is therefore recommended that modeling efforts be accompanied by time series current measurements at the site.
Such measurements should be of sufficient duration to resolve the important time scales of flow variability.
Of particular importance are field studies to define the extent and frequency of near-shore fumigation occurring at a given site.
(2)
Analytical Models (a)
Steady-State Model Analytical models of routine releases of liquid effluents along open coasts are usually based on Gaussian-like solutions to the steady-state diffusion equation.
The form of each solution may differ in detail, depending on the number of dimensions retained, the loca tion of the bounding surfaces, and the discharge configuration.
1.113-11
A simple diffusion model for a steady point-source discharge into a lake having a known steady longshore current, u, may be formulated by neglecting the longitudinal diffusion and time dependence in the dissolved constituent transport equation as follows:
aC
a2C
ax "- y az
77 c~-
(14)
where Cy and ez are the lateral and vertical turbulent diffusion coefficients, respectively.
The remaining symbols are as defined in Section 2.
The decay term may again be removed through the transformation
- XX/U
C(x,y,z) - x(x,y,z)e
(15)
resulting in the following equation for the nondecaying concentration x:
U x 32 a2 ax CY
Czy
(16)
It is assumed that the discharge Is located at the point (O,yszs), i.e., at the origin of the x-axis and a distance ys from the shoreline and zs beneath the water surface.
For a large lake of constant depth d and straight shoreline the solution is x
a f(az,zzs.d)f(oy.y,ys)
(17)
where f(azsz,z
-,d)
M
+ z
-
z-z)
)2o f Syyy)
uexp (ysy)2 + ex J
L JJý
This model may be used for curved shorelines by substituting, for y and yst the corresponding distances normal to the shoreline.
In Equation (17), the condition that there be no flux of material through the bounding surfaces is ensured by placement of an image source of strength W (Ci/sec) at y -
-y and an infinite series of image sources along the z-axis.
Equation (17) is a basic expression that can be modified to yield solutions for a variety of discharge configurations into bounded water bodies.
For the sake of simplicity, the present discussion is limited to point discharges.
However, If W is interpreted as source strength per unit length, or per unit area, line and plane sources, respectively, may be treated by integration of Equation (17) over the source dimensions.
The predictive capabilities of this model are limited because of the spatial variations in the flow field under actual conditions and because there are large uncertainties in the diffusion coefficients Cy and ez (or. equivalently, n. the standard deviations ay and az).
Studies in the Great Lakes and other large lakes suggest that "representative" near-shore values of ey are roughly in the range of 500 to 1000 Cm
2/sec (0.5 to 1.1 ft 2/sec) and that cz is in the range 1 to 30 cm2/sec (0.001 to 0.030 ft 2/sec)
(Refs. 23 and 28).
These values are typical only
1.113-12
of the near-shore zone.
Furthermore, there is evidence to suggest that the C is reasonahly cnn stant for discharge plume widths exceeding about 50m (- 165 ft) (Ref. 23).
Pence Richardson's
"four-thirds power law" should not be used to describe the lateral diffusion coefficient without justification on the basis of site-specific tracer studies.
Figure 3 shows centerline and shoreline values of x/W calculated from Equation
(17) for the case of a point source discharging at the surface 500 m (1640 ft) offshore into a
10 cm/sec (0.3 ft/sec) current.
The horizontal and vertical mixing coefficients are 1000 cm2/sec I
(1.1 ft 2/sec) and 5 cm2/sec (0.005 ft 2/sec), respectively.
The depth is 10 m. The centerline concentrations decrease inversely with distance from the source, x-1, for about the first 10 km
(6 miles), beyond which the concentration decrease is approximately x-1/2.
The dilution factor, DF, is given by DF
W/(xq)
(18)
where qp is the volumetric discharge rate of the effluent.
The dilution factor, for example, at 10 km (6 miles) downcurrent is approximately
7 for a 52 m3/sec (1,830 ft 3/sec) discharge.
This result suggests that, for a nondecaying substance, the downstream concen tration reduction in lake plumes parallel to the shore is rather small.
This is consistent with observations reported for several of the Great Lakes (Ref. 23).
It should be kept in mind that the dilution calculated above is for the far field and does not include possible additional dilu tion arising from initial mixing in the near field.
For a given location, the presence of a plume might be periodic.
Therefore, long term average dilution factors can be estimated from the above model by multiplying the solution by an appropriate flow-field frequency function.
Asdiscussed previously, observations suggest that the directional distribution of Great Lakes coastal currents is approximately bimodal.
In such a case, long-term dilution factors would be about twice those calculated from Equatior (17).
It is emphasized, however, that the presence of reversing currents at a given site should be demonstrated by field observations of flow patterns before credit is taken for concentration reduction attributable to intermittent plume behavior.
(b) Transient Source Model For other than a continuous source, the transient form of the constituent trans port equation must be solved.
In this case, diffusive transport in the direction of flow may be important, especially for short-duration releases, whereas it is unimportant in the case of con tinuous releases.
For an instantaneous release of a finite quantity of material from a vertical line source at x a 0, y - ys9 Into a lake of known steady longshore current u, a simple transient model can be formulated:
c.
exp
+,,
\\
,
x
+ ex~p
,st
/-
(19)
where d
is the depth;
M
is the amount of activity released (in curies);
t is the time after the release;
and the other terms are as previously defined.
The case of a more general time-dependent release may be obtained by integrating Equation (19) with respect to time:
1.113-13
- 1L-CLL* L
RADIONUCLIDE CONCENTRATION
I
,( in seconds per cubic metr)
PER UNIT RELEASE RATE
w C
C
-
C
al I
F
I"
m
"m
2 m
n 0
zr
- m>
r
0lM
Z
0
c t Wf(T)
ri u~ - )2
2 C a Y,
dx (t -
T))) lexp /(y-YS
fo
~
~
ex~
4 K-
)
4x~
)VYt-T
-(y + Y)
exP(4KY(t -
TT
dr
.
- )*(20)
where the release rate is Wf(T) curies/sec.
In general, Equation (20) must be solved using numerical quadrature.
Equations (19) and (20) are also useful for releases into rivers in the region near the source, where the effects of the far shore are unimportant.
(3)
Numerical Models Analytical solutions to the diffusion equation are strictly applicable only to cases of steady uniform flow.
In coastal regions having complex geometry and time-dependent nonuniform flow, analytical models might not be adequate for predicting realistic concentration values.
In such cases multi-dimensional numerical models are more suitable.
The use of such models is becoming increasingly common in water-quality simulation.
Typical acceptable numerical models are the two-dimensional, vertically integrated models developed by Leendertse and co-workers (Refs. 29-34), Codell (Ref. 35), Loziuk et al. (Ref. 36),
and Eraslan (Ref. 37).
These and other numerical models fall into two broad categories, depending on the method in which the advective velocity field is obtained.
The Leendertse, Codell, and Loziuk models, for example, compute the velocity field from the following vertically integrated two-dimensional equations of mass and momentum conservation:
aU
aU
aU*S
g(2
+ V 2 )
S+ U -- + V -8 -f g 1 1 + x -9 Ch2H
.av +3V
+ VA+ fu
--gi+ -j- MAV+
(21)
7Fa y +
Ch*
2H1 at ax ay)+*
,)
where Ch is the Chezy coefficient;
f is the Coriolis parameter;
H
is the depth from water surface to bottom;
(U,V)
are the vertically averaged x and y component velocities;
C
Is the water surface location above an undisturbed level datum; and TX sTy are the x and y component surface stresses.
The resulting velocity field then becomes the advective mechanism in the following vertically averaged conservation equation for the dissolved constituent concentration C:
C +
(HUC)
+
- (HVC)
(HKx 'C +2- (HKy
-C
(5 C
ax a y a"
-1 By+*
-HC(2 where Kx and Ky are the dispersion coefficients in the indicated directions.
1.113-15
The Eraslan model, on the other hand, requires synthesis of the flow field from current
,
measurements.
Use of this technique requires a careful analysis of the flow data to ensure that the resulting velocity field conserves mass.
The velocity field is then applied to the integral form of the conservation equation for the dissolved constituent in question (donor cell method)
(Ref. 37).
b.
Oceans Modeling techniques for estimating radionuclide transport in ocean coastal waters are simi lar to those applicable to near-shore waters in the Great Lakes.
The primary differences in behavior between the two systems results from the greater temporal and spatial variability in flow occurring in ocean coastal waters.
This variability results primarily from two factors.
The first and more readily defined factor is the major influence of astronomical tidal currents, which are negligibly small in the Great Lakes.
The second factor, whose effects are important but much more difficult to quantify, Is the influence of meteorological driving forces.
These forces include the direct effects of both meso-scale and synoptic-scale wind systems and the indirect effects of seasonal variations in heating or cooling and coastal river discharges.
As a result of these factors, the flow variability in oceanic coastal waters contains components having magnitudes and characteristic time scales greater than those of the near-shore waters of the Great Lakes.
In practice, the choice of transport modeling techniques applicable to a given ocean coastal region depends, to a large extent, on the level of knowledge of local near-shore current climatology.
A particular model choice and range of model parameters should be demonstrated to include, to the extent practical, the effects of the important scales of flow variability.
For synoptic scale fluctuations in flow patterns, it will often be necessary to perform transport calculations for conditions "typical" of various seasons or wind patterns.
For a given set of conditions, however, the choice of modeling techniques is further deter mined by the interpretation of the role of tidal currents in the mixing process.
The interpre tation depends on the averaging period used to define the velocity field.
If the averaging time is long compared to the tidal period, tidal currents cannot contribute to the advective trans port, since their contributions to the mean flow field have been removed by the averaging.
Tidal effects would be contained solely in "tidally averaged" turbulent diffusion coefficients.
This result is largely a mathematical artifact that assigns the actual advective effects of tidal currents to large-scale turbulent diffusion.
Nevertheless, if detailed descriptions of the field of radionuclide concentrations are not required, it is possible to construct quasi steady-state transport models that are valid for time scales larger than the tidal period and smaller than those associated with major nontidal fluctuations in flow.
For regular shoreline geometry, or discharges removed from the shoreline, steady-state Gaussian models based on Equation (17) may be used (Refs. 38-41).
The results based on these models require careful interpretation, however, because of the large uncertainty In input param eter values, particularly the turbulent diffusion coefficients.
Since these coefficients arise from time averaging, their values for any given case will depend on the averaging period used to define the mean velocity field.
Furthermore, there is evidence to indicate that in the ocean the rate of spread of a contaminant plume depends upon the plume age.
Hence, in general, turbu lent diffusion coefficients will be time and space dependent.
The methodology for obtaining reasonable estimates for these coefficients is based primarily on the interpretation of the results of tracer studies in the light of modern turbulence theory (Refs. 38-45).
More realistic detailed descriptions of radionuclide transport in ocean coastal waters will require the use of numerical models.
The advantage of such models is that they are applicable to fully time-dependent flow fields in receiving waters having complex geometry.
In particular, these models have the capability of treating tidal currents as advective rather than diffusive mechanisms ("real-time" models), hence removing a large element of uncertainty in the deter mination of turbulent diffusion coefficients.
Typical acceptable numerical models (Ref. 29-37) were discussed in Section 3.a.(3).
In the
"real-time" modeling approach, tidal currents are explicitly included as advective transport mechanisms.
Leendertse and co-workers (Refs. 29-34) have shown that in this case, reasonable estimates of longitudinal and lateral turbulent dispersion coefficients may be based on Elder's (Ref. 19) formulas for steady open-channel flow.
The applicability of numerical models and the techniques for establishing horizontal mixing coefficients are discussed further in Sections 4.c and 4.d.
1.113-16
4.
ESTUARIES
Transport of contaminants in estuaries differs from that in rivers because of oscillatory tidal advection and the nontidal gravitational circulation induced by salinity differences.
An important consequence of.these differences is that there is transport of material upstream from the discharge point in estuaries, the maximum upstream penetration being limited to the general region of oceanic salt intrusion.
a.
One-Dimensional Models For purposes of radionuclide transport prediction, reduction of the estuarine problem to a single dimension (longitudinal) produces satisfactory results, except in the lower reaches of the estuary, where circulation is clearly two or three dimensional.
The one-dimensional simpli fication Is accomplished by averaging over the estuary cross-section.
The resulting constituent transport equation is katJAC) + -,-(AIC) -kfi"'AE4)
XC
(23)
where
ýA(x,t).
is the cross-sectional area;
E(x)
ans the sectionally'averaged, one-dimensional longitudinal dispersion coefficient;
and
,
,
U(x,t)
is the sectionally averaged longitudinal velocity.
Both simple and elaborate methods of solving Equation (23) exist.
The simplest models depend on the "tidally averaged" approximation, in which the tidal oscillations are not included explicitly, but are considered to be responsible for large-scale longitudinal diffusion.
The more elaborate "real-time" models consider the actual tidal flow to be advective, with longitudinal-diffusion occurring through motions having time scales considerably shorter thania tidal cycle;
Each type of model is discussed below.
(1)
Analytical Model (Steady State)
The least elaborate one-dimensional model assumes a constant cross-sectional area A, a constant (tidally and sectionally averaged) longitudinal dispersion coefficient EL, and a con stant fresh water velocity Uf.
For this case Equation (23) reduces to d2C
dC_* -
(24 L dx--*'Uf 37
0
(24)
where C is the time and sectionally averaged concentration.
The solution (Ref. 46) to Equation
(24) for a source at x - 0 and the boundary conditions C - 0 at x
+
- is (U
C
U f
+
(E
L5 ME L ex p EL
14
(25 Uf The sign within the exponential is negative downstream from the source (x positive)
and positive upstream from the source (x negative).
In terms of dimensionless variables, Equation (25) reduces to r
rmax exp (N 2,'
4 C)
(26)
1.113-17
where N-
Uf r "
--
C
\\UfT+4XE1 /
X
Figure 4 Illustrates this dimensionless equation evaluated for C and N.
Several features of Equation (26) are evident from Figure 4. The dimensionless source concentration rmax depends not only on the source strength and freshwater flow, but also on the diffusivity EL and the decay constant x. This dependency is explained by the fact that a steady concentration is maintained by a balance between the discharge source, the net advective-diffusive transport away from the source, and a local sink due to radioactive decay.
The upstream and downstream curves have equal but opposite slopes for N - 0, since there is no nontidal advection where the net freshwater flow is zero.
The curves become skewed in the downstream direction for increasing values of Uf because of the nontidal advection downstream.
(2)
Releases of Short Duration For releases of short duration, the preceding steady-state model does not apply.
In the case of a time-dependent source term, the transport equation is given by
3C +
C
E
3'C -
XC
(27)
iE+Ufaxu ax The solution to Equation (27) for a time-dependent release may be obtained from the solution corresponding to the instantaneous release of a finite quantity of effluent uniformly over the flow cross-section (unit impulse function) (Ref.47 ).
The unit impulse solution is given by C N ex( (x - uft)2 A
(28)
C"AVG e xpt
4ELt
-X(8 where N is the amount of activity introduced (Ci).
For a more general time-dependent release, results may be obtained by time integration of Equation (28).
Assume that, instead of the Instantaneous introduction of a finite quantity d .s at x a 0 and t a 0, effluent is continuously discharged at the rate if Wft Cl/sec.
The concentration distribution resulting from a continuous discharge In the time interval O<T<t is given by
1.113-18
-0- Upstream Downstream -
- N-2 N -1 kN-0.6 N-0.1 N-0
at -0.
rMax 4 uf + 4XE L
Uf In2 t%
-1.5
-1
-0.5
0
0.5
1.0
DIMENSIONLESS DISTANCE FROM SOURCE, !
OIGURE 4.
DIMENSIONLESS PLOT OF CONTAMINANT CONCENTRATION VS
DISTANCE FROM SOURCE ('FROM O'CONNER ET AL. REF. 46)
1.113-19
0.5
0.4
0.3
0.2
0.05
0.04
0.03
0
CD
2 0
us
0.02
0.01
_____.x
- Uf(t -
029
-
a f(T)-exp
4EL(t r)
2 A(t - T
dr From Equation (29) the concentration distribution corresponding to a square pulse release of amplitude W and duration'tD is a[
2 c=
- AD---exp
-Uf
-T
)dr
(30)
-4wLf 4EL(t -r
~
Equation (30) may be integrated to give the following solution in terms of exponentials and error functions:
W
Ux C= exp (-)g(x~t) for 0 <t < to L
.
(31)
C -
exp (U1) [g(xt) - g(x,t - to)] for t t
where eg(xt) "
erfX +LIl t J+
1 exp(L-)
[erf tf L
1 exp
-
)
7
U2+4EL
The function g(x,t - tO) has the same form as g(x,t), with (t - tD) replacing t.
The sign within the brackets is chosen negative downstream of the source (positive x) and positive upstream of the source (negative x).
Equation (31) holds for any pulse duration to. In the limit as (t,tD)+ -, the solution reduces to the steady-state solution given by Equation (25).
Release rates other than square pulses are most easily computed by solving Equation
(29) directly, using numerical quadrature.
(See Sections 2.a.(2) and 3.a.(2) of this appendix.)
(3)
Tidally Averaged Numerical Models To simulate constituent transport in many types of estuaries, it Is necessary to include detail beyond the capabilities of analytical models.
For example, the distribution of sources and sinks (both man-made and natural) may be important.
Additionally, the estuary may have a nonuniform cross-section and tidal mixing proper ties that vary along its length.
The next level of sophistication above the analytical models are one-dimensional numeri cal models, which can account for variable cross-sections, inputs, withdrawals, and tidally averaged longitudinal diffusion.
These models solve what Is essentially the finite difference equivalent of Equation (23) in either the steady-state or transient (but tidally averaged) form.
Models similar to the EPA AUTOSS and AUTOQD models fall into this category (Ref. 48).
The estuary Is considered to be divided into variable-length segments.
Each segment is coupled to the next upstream and downstream segment, as well as to external sources and sinks.
Typically, the boundary conditions are chosen so that the concentrations of the first and the last segments are known constants.
This is the most realistic assumption for this model, pro vided the model is extended to the headwaters of the estuary and to the ocean.
In practice, the model can easily be extended from the headwaters to the ocean by fine grid spacing in the area near the discharge and by coarse spacing farther away--in the regions of less interest.
1.113-20
A useful application of this model occurs where there are recycle streams such as municipal water withdrawal and return.
The recirculation with partial or total removal of cer tain radionuclides could be important for heavily used tidal and nontidal waterways.
(4)
Intratidal Numerical Models The tidally averaged models are often subject to error because of uncertainty in the longitudinal dispersion coefficient.
A more acceptable approach is the intratidal model, in which velocity, water level, and concentration in the estuary are simultaneously solved for, the tidal velocity being retained explicitly as an advective transport mechanism.
In such a model, the longitudinal diffusion coefficient is better defined on the basis of physical princi ples and is less important than in the tidally averaged case.
The model solutions are suitable for digital computation and do not require excessive computer resources.
Included are models such as the Dailey-Harleman (Ref. 49) one-dimensional finite element model, the Lee-Harleman (Ref. 50) finite difference model, and the Eraslan (Ref. 51) one-dimensional donor cell model.
Basically, these models solve the one-dimensional equations of mass, momentum, and constituent conservation,
8 a
Source - 0
(32)
ax + +
+ g3 +
0
(33)
1a
+
__
Ia aC
-.
_(A-P-)-
XC(34)
aax(AC
axi7 ax where b
is the width of the estuary at the water surface;
Ch is the Chezy coefficient;
Rh is the hydraulic radius; and C
is the water surface location above an undisturbed level datum.
Concentration boundary conditions can be treated realistically in the intratidal formu lation.
The upstream boundary is usually the concentration at the head of the tide.
The down stream boundary, however, usually differs according to whether the tide is flooding or ebbing.
During ebb tide, the downstream boundary is chosen so that all constituents leave by advection.
During flood tide, the entering concentration must be specified.
This is determined by the physical situation assumed.
If the downstrealp boundary is the ocean, the concentration of con stituents in ocean water can be the input.
If the downstream boundary Is a bay or other water body where a discharged constituent can accumulate, an approximation of this concentration must be made.
An advantage of the intratidal model is its ability to simulate releases coordinated with the tide.
If the source of contaminant is close to the mouth of the estuary, it may be advantageous to discharge only during ebb tide to flush the contaminant rapidly out of the estuary.
Such operation could not be simulated with a tidally averaged model.
b.
Multi-Dimensional Models In very wide estuaries and embayments, the one-dimensional assumption is not realistic.
For such conditions, both transverse and longitudinal velocity components are important, and concentration gradients across the channel approach those along the channel.
To simulate this case with one-dimensional models, unreasonably large longitudinal dispersion coefficients must be used.
Two-dimensional vertically averaged numerical models are more suitable for these situations.
Typical acceptable models were discussed in Section 3 of this appendix.
1.113-21
In some cases, numerical models which simulate vertical concentration variations rather than horizontal variations may be more appropriate, for Instance, in the salinity intrusion region of an estuary, or a highly stratified reservoir.
Although three-dimensional numerical models are currently being developed, their complexity and relatively high cost of observation are rarely warranted for the purpose of computations under Appendix 1.
c.
Exchange Coefficients The sectionally averaged, one-dimensional longitudinal dispersion coefficient, E, includes a combination of several individual processes.
In the prototype, these processes include molecular exchange and flow- and wind-induced turbulent exchange.
In most cases, these processes make a relatively minor contribution to the overall dispersion, which is in part an artifact resulting from the temporal and spatial averaging of the three-dimensional transport equations.
In general, the greater the simplification of the model, the larger the exchange coefficient must be to simulate the prototype.
The simplest model is the tidally averaged one-dimensional model.
The actual three dimensional oscillating flow is drastically simplified Into a one-dimensional system in which the advective transport is determined by the fresh water flow rate.
The diffusive transport includes the effects of deviations from sectional homogeneity and "turbulence" components of time scales on the order of the tidal period or less.
In the Intratidal models, the true oscillating or unidirectional flow is simulated and is treated as part of the advective process.
The diffusive term includes the effects of deviations from sectional homogeneity of the concentration and velocity fields.
However, in this case, tidal effects are no longer included in the turbulence field.
In the case of two-dimensional intratidal models, it is, in general, only necessary to include deviations of velocity and concentration in the vertical direction since, with sufficient resolution, the lateral flow field is simulated correctly.
In all cases, the most acceptable procedure for choosing the diffusion coefficient is to adjust the model to match observed prototype conditions, usually through tracer study results.
In general, the more refined the model, the less empirical tuning is necessary because the turbu lent transport coefficients are more firmly based on physical principles.
(1)
Tidally Averaged Models If the tidally averaged model is used, the determination of the diffusion coefficient is empirical and must be based on the observed dispersion of a known tracer, with prototype and model constituent concentrations being matched.
The tidally averaged longitudinal dispersion coefficient EL may be determined from Equations (25),
(28), or (29) by a trial and error pro cedure where EL is changed until the model concentrations match observed values of the tracer.
In the case of tidally averaged numerical models covered under paragraph 4.a(3), it is possible to restructure the finite difference equations to solve for EL with input of observed concentration of the tracer.
The calculated values of EL may then be used for subsequent con centration computations.
As a rough approximation to the dispersion coefficient, lacking any field data, a formula by Hetling and O'Connell (Ref. 52) based on data in the salinity intrusion region of the Potomac River estuary may be used:
EL - 1680 Vmax 4/3
(35)
where EL
is the sectionally and tidally averaged, one-dimensional longitudinal dispersion coefficient (in ft 2/sec),
and Vmax is the maximum tidal velocity (in knots).
It must be cautioned that this equation can only be relied upon for order of magnitude estimates and is not necessarily conservative.
1.113-22
(2)
One-Dimensional Real-Time Models Less "tuning" is necessary for real-time models than for the tidally averaged models.
In the well-mixed region of the estuary, Taylor's formula (Ref.
53) for dispersion is acceptable for reasons discussed in Section 4.d of this appendix.
The salinity intrusion region of the estuary is still poorly defined on physical grounds.
Since the presence of gravitational circulation casts doubts on the applicability of sectional averaging, it is this region for which tuning is most important.
An approximation for the longitudinal dispersion coefficient that is applicable to the whole length of the estuary is based on the work of Thatcher. and Harleman (Ref. 54).
This approach is based on a combination of Taylor's dispersion formula applicable to the well-mixed portion of the estuary combined with an empirical correlation for mixing in the salinity intrusion region based on observed salinity distributions.
The dispersion coefficient is E(x,t)"
KI 00' 1 + 77nUtRh 516
(36)
-
~d(~
where L
is the length of estuary;
n is Manning's coefficient (local);
R
is the hydraulic radius (local);
- S
is the salinity (local);
So'
is the salfnity at mouth;
,Ut is the RMS velocity (local); and x
is the distance from mouth.
The factor K is given by K - 0.00215VmaLED 0 ".2 5
(37)
and Is shown in Figure 5.
The quantity ED is the so-called "estuary number" and is given:by DED
2
(38)
where F 0
Is the densimetric Froude number evaluated at the estuary mouth;
is the tidalprism, in ft 3 ;
Qf is the freshwater flow rate; and T
is the tidal period.
The dispersion formula given in Equation (36) may be used with good results as a first approximation in the tuning of a real-time model.
In an oscillatory flow such as a hydroelectric or pump storage reservoir where there is no salinity intrusion region, the Taylor formula alone may be used as a first approximation:
1.113-23
I
I
I
IuIISj
.
.
.
.1.111 B
I
I
I
liii.
B
U
I
U
10
x
04
!0
0N
WE.S2Q
ROTTERDAM I'-
POTOMAC
WES IS
WES1 DELAWARE 3 HUDSON +WE 14-0
DELAWARE 2 WES 10 0
I
I *II
£
YEII*
1 I
I
1111111 I
I
I
Il I if I
.
.
..
I
I
I
I
I
I II
a0
i I
I
I
I I I I
00
- ESTUARY NUMBER ED
FIGURE 5.
CORRELATION OF DISPERSION PARAMETER TO DEGREE OF STRATIFICATION
(FROM THATCHER, at &L, REF: 64)
I41"
0.1
10
f L
l l
l l
e
gee I
I
I
i I
- noI
ill.
D
lI
These approximations are suitable only for periodic oscillating flows and not neces sarily for unidirectional flows (as will be further explained in Section 4.d of this appendix).
Tuning of the dispersion coefficient should be performed after the friction coefficients are adjusted to simulate the observed flows, since Equation (39) is a function of Manning's coefficient.1
(3)
Two-Dimensional Models The best approximation for the dispersion coefficients in the two-dimensional estuary model appears to be the one adapted for the one-dimensional real-time model discussed above.
For example, as a first approximation in the simulation of Jamaica Bay, which can be classified as a well-mixed two-dimensional estuary,.Leendertse (Ref. 29) used Elder's formula with an additional factor for the effect of wind-induced turbulence.
As with the one-dimensional models, tuning is necessary to match prototype observations and should be performed after roughness factors in the hydraulic part of the model have been established.
In the salinity intrusion regions of the estuary, initial estimates based on the method described in Thatcher and Harleman (Ref. 54) should be adequate.
d.
Applicability of Models Choice of one of the above models involves several factors.
Although these models are classi fied as estuary models, they may be used for other types of water bodies, such as reservoirs with hydroelectric power generation flow reversals and, in most cases, unidirectional rivers.
However, the assumptions implicit in one-dimensional models may be invalid In some cases, as explained below.
Fischer (Ref. 55) analyzed the mechanics of dispersion In nontidal rivers and concluded that Elder's formula yielded dispersion coefficients that were low by as much as two orders of magni tude.
He concluded that longitudinal dispersion in rivers is primarily due to velocity variations in the lateral direction, while Elder's formula accounts only for velocity variations in the vertical direction.
An approximate diffusion coefficient for unidirectional rivers derived by Fischer (Ref.
55) is L2 E
0.3 u'
(40)
where I
is approximately the cross-sectional distance from the point of maximum velocity to the further bank;
Rh is the hydraulic radius;
u,2 is the mean squared deviation of the river flow from the sectional mean velocity V; and u*
is the shear velocity.
The one-dimensional model is valid only for downstream distances corresponding to travel times greater than the so-called "Taylor period":
t
1.8
(41)
at which point the constituent introduced at t - 0 is sufficiently well mixed in the cross-section for the transport to be considered one-dimensional.
In an oscillating tidal flow in a wide, shallow estuary, however, the tidal period is large compared to the vertical mixing time scale, but small compared to the lateral mixing time scale.
In this case, velocity variations in the lateral direction add little to the longitudinal mixing, and Equation (39) is appropriate.
1.113-25 E(x~t) - 77nUtRh 5/6
(39)
5.
IMPOUNDMENTS
There are two basic types of cooling ponds.
The first is a closed-loop system in which the thermal effluent is cooled in the pond and recirculated through the power plant condensers.
Some water ("blowdown") must be removed from the pond to limit the dissolved solids concentration to an acceptable level.
Fresh water ( make-up") must be added to the pond to compensate for evapo ration and blowdown.
The second type of cooling pond is a flow-through system in which there is little or no recirculation of effluent through the power plant.
The effluent is discharged to the pond which, In turn, discharges to a larger body of receiving water.
The pond serves as a holding reservoir, allowing effluent to cool before entering the receiving water.
The source of radionuclides may either be located on the impoundment or upstream on a tributary of the impoundment.
For the simplest models, this distinction is irrelevant because concentration is based on flow through the impoundment and does not depend on the placement of the input.
In the case of the upstream plant, the source term W is the rate of radionuclide entering with the flow at the boundary of the reservoir.
Figure 6 illustrates a closed-loop cooling pond.
Water for cooling is drawn through the intake, circulated through condensers, and returned to the pond via the discharge.
There are two important hydrological parameters of this system.
The first is the internal recirculation time constant associated with the flushing of the pond by the makeup and blowdown streams.
The second is the time constant associated with the decay of radioisotopes.
- Figure 7 illustrates the flow-through pond.
The hydraulics of this pond are simpler than the closed-loop pond, since no recirculation occurs between intake and discharge.
In this case, the only hydraulic time constant is that associated with the travel time from the plant discharge to the receiving water.
a.
Simple Analytical Models Simple models may be used to obtain conservative estimates of the radioisotope concentra tions.
Four models can be used to describe all cooling ponds:
the completely mixed model, the plug-flow model, the partially mixed model, and the stratified model.
In each case, the effect of evaporation is neglected.
(1)
Completely Mixed Model SFigure 8 shows the first case (the closed loop),
in which the pond is represented as a completely mixed tank.
All inputs of material makeup are-instantaneously mixed throughout the tank, so that the concentration is homogeneous.
By performing a mass balance on the volume of the pond, a solution for concentration is obtained, assuming zero initial concentration and complete mixing:
q b
- exp T -
I
(42)
T
where q b is the pond blowdown rate and V T
is the volume of the pond.
The concentration C0 is the steady-state concentration that would exist for a nondecay Ing substance and is given by C .W_
0
qb where W is the rate of addition of radioactivity (in Ci/sec).
1.113-26
o.
Makeup
- P
° BIowdown FIGURE 6.
CLOSED-LOOP COOLING POND
1.113-27 v,
f
I"
I
Ko FIGURE 7.
FLOW.THROUGH COOLING POND
1.113-28
Eupoati Radwaste w Makeup In a qb + Evaporation concsnt*Wtjn -0
FIGURE 9..
IaaslI
-
a
-
-
-
-
-
a
-
-
Volume
.
-
a
-
r
-
-
-
-
--
I
COMPLETELY MIXED MODEL
.S~ovwdownm Out ma mConcentration i C
j
For the steady-state concentration of a decaying substance, Equation (42) reduces to qb C
T
X
(43)
f0
qb VTX +1 In terms of the half-life, t%, of the added radioactivity, Equations (42) and (43)
reduce to CO
t
0 - exp
-
+.1n2]
(44)
(at steady state)
Co .-
l
(45)
where
""
and T
t- (ln2)/0
The dimensionless yariable - is the radioisotope half-life expressed in multiples of the flushing tiie (VT/qb).
Figure 9 illustrates the steady-state concentration defined by Equation (45) as-a function of r. This figure shows that for small half-lives (compared with the flushing time, VT/qb)S the concentration depends strqngly on half-life, but for long half-lives, this dependence diminishes.
The completely mixed tank model (see Figure 8) Is'adequate for substances with long half-lives, where the internal circulation timetis Short compared with the half-life.
In this case, the concentration in the pond is fairly homogepeous, satisfying the "completely mixed"
limitation of this model.
(2)
Plug-Flow Model For the flow-through cooling pond, the plug-flow model illustrated in Figure 10 may be adequate if it is presumed that there Is no recirculation.
The concentration is expressed as C- CO exp (-xVT/qb)
- Co exp (
ln2/r)
(46)
where qb is now the flow rate
.thrugh the pond.
This expression is evaluated in Figure 9 and compared with the completely mixed case.
Agreement is best for large r. Although not easily seen in Figure 9, the models deviate for small T.
(3)
Partially Mixed Model Where a significant part of the flow is due to both blowdown and plant pumping, neither of the above models is adequate.
A suitable model that includes both the plant pumping rate q and blowdown rate qb is illustrated in Figure 11.
The recirculation factor R is defined as Rwqb RU q p The steady-state concentration is then defined as
1.113-30
K1
K
1.(
0.I
O.I
0.?
o.e
0.5
0.4
0.3
0.2
0.1
0
- "
,v- Plg l
- ~~~w
, .YI&,,,.
-
1
111NA
I
ISili I
I
I
gillI
0
1up
10,
"HALF-LIFE/FLUSHING TIME
10)2 FIGURE 9.
STEADY-STATE CONCENTRATIONS IN COMPLETELY
MIXED AND PLUG-FLOW MODELS
\\I-
K
hi
0
lF
u z
ur-l
.
.
. .....
l
Evaporation
-
I -
Malmuo I". % + Evapoation Concetrt~OionC
=1CJO
BtOwdOwn Out - Q
Concentrationl -C
travel' time V
'lb FIGUIA2 10.
PLUG-FLOW MODEL
1 .113-32 K
t -
7ý2;
Makeup In - % + Evaporation Cl Concentmion - 0
w C3 -C 2 +
BIowdoam Out a %b Conicenmitaon -C 2 Plant Pumpin Raw %
FIGURE 111.
PARTIALLY MIXED MODEL
1.113-33 J2
+(47)
Figure 12 shows the relative concentration C/Co as a function of T and R. Notice that K
the asymptotic forms of Equation (47) for R - 0 reduce to the completely mixed case:
C
T
( 5
-C
___T"
and for R =
to the plug-flow case:
C
exp ( - ln2/r)
(46)
(4)
Stratified Reservoir Lumped Parameter Model A simple model based on an approach of Trent (Ref. 56) is useful for a gross approxi mation of the mixing processes in stratified reservoirs that have seasonal turnover.
The lake is assumed to have two layers, each totally mixed (Figure 13).
Water can flow into and be withdrawn from either layer, but the layers do'not mix during stratified flow periods.- The volume of each layer is assumed constant during the period of stratification or during unstratified floo.
Turn over is assumed to mix the two layers-totally and instantaneously.
This assumption is reasonable for systems in which the turnover-time is small compared to the residence time.
Input data needed for this model are as follows:
Stratified Period
1.
Length of stratified period
2.
Volume of epilimnion and hypolimnion (constant over period)
3.
Inflow and withdrawal (same),
aither'layer
4.
Concentration in inflow
5.
Half-life of constituent Unstratified Period
1.
Length of unstratified period
2.
Total volume of reservoir (constant over period)
3.
Inflow and withdrawal (same)
4.
Concentration in inflow
5.
Half-life of constituent The model is initialized with concentration C(o) at time t
0
0. The first period, (O<t<t,), corresponds to stratified conditions.
Concentration in the epilimnion during this period is CE =a - ra --b C(o)]e-bt
(48)
Cliqi qt a
b T- +
E
E
where Ct is the input concentration in the upper layer;
qt is the inflow to the upper layer;
VE
is the volume of epilimnion; and X
is the decay constant and is - ln2/t1/2.
1.113-34
k"
"
-I-°*/*R-Lb
0.1 q5
-
w CO
qb
>_
R-"1/4.
0.0
Pfu'
Ro, 0.1 R~~
no*,0
0.oo1 I
JL I
1
1 Rill I
I
I
l l I
1 I1l l
0.001
0.01
011 HALI=-LIFt*/FLUSHINO TIME r FIG' URE 12.
CONCENTRATION IN-PART"IAL.LY MIXED CASE
\\K
\\
a. Stratified VolVlumel VE
Conncentration CE
Volume VH
Concentration CH
¶qlC
SCH
b. Unstratified Volume (E + V0
Concentration CM
FIGURE 13.
LUMPED PARAMETER STRATIFIED
RESERVOIR MODEL
1.113-36 Ci Cif C,
q i *"
The concentration in the lower layer during this period is
.i/C
H a , -
[a ' - b 'C (o ) ]e .-
b 't H
(49)
V '
Ct'qt'
VH
where C,'
is the input concentration to the lower layer;
qi'
is the inflow to the lower layer; and VH
is the volume of hypolimnion.
During turnover, instantaneous mixing of the two layers is assumed as CEVE + CHVH
C~r
,,E'+
H
(50)
During the unstratified flow period, (tl<t4t2), the concentration is a " ' ( a "
-b " C T ) e -b
" ( t
1:)-
t l )
b"
(51)
all " C t "q t I "
a q t"1
""
T-*----- b'"* T* +.A
T
where C,"
is the input concentration for the total pond;
qi"
is the inflow; and VT
is the total volume.
Subsequent seasonal stratification cycles repeat with Equation (48), but with the latest fully mixed concentration substituted for C(o).
Simple methods such as the well mixed, partially mixed, and stratified models covered in this and the previous section are most suitable for estimating concentrations in reservoirs, ponds, and lakes that are downstream of the radionuclide discharge and consequently already par tially mixed.
In such a case, the hydraulics of the pond are less important and simple methods may suffice.
More elaborate models may be required, however, for a direct radionuclide discharge to the reservoir.
In this case, the hydraulics of the reservoir may strongly affect the way in which the radionuclide releases2disperse.
(5)
Buildup of Isotopes Using Simple Models For large cooling ponds with relatively small blowdown rates, the concentrations of the longer-lived isotopes may build up over a period of several years (exclusive of sediment uptake effects).
It may be desirable to know the rate of this buildup, since the flushing time would be a significant fraction of the useful life of the plant.
1.113-37
Since the only concern is long-lived isotopes, the completely mixed model is analyzed for transient conditions.
If the concentration in the pond is initially zero, then o .-- '
0(1
- exp(-[T + ln2Jt/t1/2})
(44)
0
Figure 14 shows the buildup to steady-state concentration CSS as a function of dimen sionless time e (time/flushing time) for several values of T.
Notice that Equation (44) becomes fairly insensitive to T for large T. This fact is illustrated more clearly by observing the time to reach some arbitrary fraction, say 99% of steady state:
1 - exp [-(T + n2) t]
0.99 and
(52)
S1(tqb\\
) 9
-
nO.OT
- gg "\\vT / g9
- r- +-T
1n Figure 15 illustrates the 99% buildup time as a function of T, clearly showing how, for very long half-lives compared with pond flushing times, the time depends only on the flushing time of the pond.
(6) Hydraulics of Ponds Using Simple Models The simple models presented here must be used with caution for several reasons.
Large portions of a pond may be unused for dilution if the pond is unstratified and irregularly shaped.
If the same pond becomes stratified during certain times of the year, however, previously unused sections may become useful because of density flows (Ref. 57) and because of the strong mixing induced by seasonal turnover.
In a flow-through cooling pond without recirculation, stratification may be detrimentalK
because the thermal effluent and the radioisotopes may be confined to the upper layer, thereby reducing the effective volume of the pond.
Thus, definition of the effective volume of a pond may be difficult.
it should be possible, however, to pick a conservative volume for a "worst case" calcu lation.
Calculation of the steady-state concentration of isotopes whose half-lives are long should cause little error because the concentrations approach that of a conservative substance w
Co qb regardless of pond hydraulics.
b.
Numerical Models Stratified reservoir models are in most cases numerical evaluations of the one- or two dimensional equations describing convection and diffusion in stratified flow.
The simplest numer ical models are the one-dimensional diffusion models, such as the MIT deep reservoir model (Ref. 57).
In such models, concentration is assumed to be horizontally uniform.
Vertical dif fusion and advection are modeled.
The flow field is calculated by the equation of continuity and by accounting for inflows and outflows such as dams, tributaries, and outfalls to and from the different layers of the reservoir.
Such models are useful where there is strong stratifi cation, especially where the reservoir is used for direct condenser cooling.
In such cases, the stratification is reinforced by the additional heat, discharge is usually to the surface, with drawal is from the hypolimnion, and vertical gradients are more pronounced than horizontal gradients.
These models are less accurate for reservoirs that have seasonal turnover and subse quent unstratified periods.
Furthermore, these models are incapabl.e of simulating certain impor tant effects, such as horizontal mixing in the vicinity of a power plant discharge.
1.113-38
TinO.1 vr- 10
CSS"C°
0 i+1n2 T
f-Iwtef4If9tmhI
time)
Vt
0
0.2
0.4
0.6
0.8
1.0
1.2
1.6
1.8
2.0
TIME/FLUSHING TIME 9 FIGURE 14.
BUILDUP OF RADIOISOTOPES IN COMPLETELY
MIXED MODEL (NORMALIZED)
K
1.0
(AD
LAP
0.6
0.4 F .4
0.2
0
,r- 0.1 wP
4 LL
0
U
wA
- I-
2
2
01
1 i tf
11 lg-.1-312
10-1
1
10,
()210
HALF-LIFE/FLUSHING TIME
FIGURE 15.
DIMENSIONLESS TIME TO REACH 99% OF STEADY-SATE CONCENTRATION
1t4 COMPLýETELY MIXED CASE
.J£
or
(
Where both vertical and horizontal effects are important, more complicated models are war Anted.
For example, the EPA Reservoir Model (Ref. 58) allows for the horizontal segmentation
"_6f the reservoir.
Each reservoir segment is solved in the vertical direction.
Inputs from upstream and downstream segments are coupled empirically to account for density flows.
Another useful model is the reservoir model of Ryan and Harleman (Ref. 59).
In this model, the one-dimensional horizontal solution in the surface layer is coupled with a one-dimensional solution in the vertical direction.
Effects of discharge mixing, surface cooling, and lateral gradients are calculated in the surface layer solution.
Vertically stratified flows and selec tive withdrawals are handled by the vertical solution.
The model is most useful for cooling reservoirs where stratification is strong.
6.
WATER USE
For identifying liquid pathways to man for realistic evaluations of the doses from normal releases from nuclear power plants, it is necessary to locate water users, identify types of uses, and estimate usage to a distance of 50 miles from a site.
Because of high usage rates along many streams and estuaries, it is also necessary to identify the effects of water usage on the spatial and temporal distribution of flows.
In addition, water usage upstream of a nuclear power plant can alter flows at or downstream of the plant.
The following is an acceptable meth odology to evaluate water usage and the consequences thereof on streamflows.
This methodology provides a realistic evaluation of the liquid transport of normal releases of radionuclides from nuclear power plants along streams and estuaries.
a.
Users A schematic diagram of the river basin that locates the following features in relation to the plant site should be prepared:
(1) surface water uses* upstream and downstream of the plant site, (2) major tributaries and their junctions, (3) streamflow gaging stations (including their period of record), and (4) major reservoirs and diversions upstream and downstream of the plant site. Approximate contributing drainage areas and types of water use for all points identified
%hould be shown on the diagram or tabulated separately.
An example schematic diagram Is shown SFigure 16.
From the diagram, key diversion and streamflow stations should be selected to provide the basis for establishing reasonable spatial and temporal distributions of runoff patterns, upstream and downstream of nuclear power plant sites.
Historical streamflows at major mainstem and tribu tary locations should be adjusted for historical diversions and reservoir effects to produce
"natural" flows (e.g., flows independent of reservoir and diversion effects).
Missing streamflow data (i.e., gaps in records) at critical stations may subsequently be synthesized by direct cor relation with nearby streamflow stations or by statistical correlation with many stations using models such as "HEC-4, River Flow Simulation" (Ref. 60).
In general, a period of at least 20 to
30 years of record, Including the historical drought of record in the region, should be used.
Monthly durations have been found (Refs. 61 and. 62) to describe adequately the fluctuations in streamflow without introducing significant errors in long-term estimates of reservoir yields.
Similarly, estimates of average annual radionuclide concentrations along a river, based on monthly streamflow averages, produced acceptable values when compared with longer flow periods (see Figure 17).
Flow periods for multidirectional estuaries, lakes, and ocean sites were dis cussed in Sections 3 and 4 of this appendix.
b.
Usage The effects on streamflows at and downstream of a site caused by reservoirs or diversions should be identified.
Reservoirs may cause significant changes in the distribution of seasonal runoff.' Operating constraints on reservoir storage, outflow, and diversions should be estab lished on a monthly basis for existing conditions of basin development and water demand and for anticipated future conditions throughout the lifetime of the plant.
Where proposed reservoirs may significantly affect flow conditions, their effects should be considered by simulating their operation using models such as "HEC-3, Reservoir Analysis" (Ref. 63).
Use types include drinking water, irrigation, process water (consumed by such users as breweries and soft drink manufacturers), recreation areas, and fisheries.
Ground water users with wells whose zones of influence extend to streams should also be included.
1.113-41
A
RES NO. 1 M & I, R, FC
42 DIVERSION NO. 2 IR
100
DIV. NO. 1 S'(FROM RES NO. 1)
GAGE NO. 1
-4-.-(1961 -
1975)
34 (RETURN FROM
SRES NO. 1. M & I)
4
4 GAGE NO. 3
(1916- 1975)
515 PLANTSITE
702 LEGEND
A RESERVOIR
V STREAM GAGE
0 DIVERSION OR USE LOCATION
-*-WITHDRAWAL
-
RETURN
50 DRAINAGE AREA (SO. MI.)
(1916- 1950) PERIOD OF RECORD
DIV. NO. 6 RES NO:6 M&IIR, P.
FC, N, R
1500
10
4 WATER USES
M - MUNICIPAL
I - INDUSTRIAL
IRW-
IRRIGATION
PI- POWER
FC -
FLOOD CONTROL
N- NAVIGATION
R-
RECREATION
L
RES NO. 2 P, FC
50
RES NO. 3 P. FC
152 RES NO. 4 M&I, R
22
__________
I
GAGE NO. 1
(1947- 1967)
73 DIV. NO.2 (FROM RES NO. 4)
DIV NO. 3
670
DIV. NO. 4
800'.
(RETURN FROM
(RES NO. 4, M & I)
I
RES NO. 5 FC
2O0
Ikt DIV. NO. 5 IR
GAGE NO. 4
(1962 - 1975) 1700
RECREATION, FISHERIES AREA
2000
FIGURE 16. TYPICAL SCHEMATIC DIAGRAM OF A RIVER BASIN
1.113-42 K
'4 NOTES
- AVERAGE
MONTHLY CONCENTRATION - DAILY FLOWS
AVERAGE MONT-HLY-CONCENTRATION
- MONTHLY FLOWS
HORIZONTAL LINES INDICATE AVERAGE ANNUAL
3 -CONCENTRATIONS
BASED ON AVERAGING PERIODS, BELOW
0
1 - DAILY (FLOW)
-
2 - MONTHLY (FLOW)
3 - QUARTERLY (FLOW)
I-
4 - ANNUAL (FLOW)
-
~2 o
U
0
Sw
- ,,
FIUR
17 T
-"
(
- K
e- m e0
.4mm
0 --JAN
FEB
APR
MAY
JUN
JUL
AUG
OCT
FIGURE 17.
EFFECT OF FLOW AVERAGING
PERIOD ON NORMALIZED
CONCENTRATION
(DATA -
1961)
k
Many alternative schemes for developing water resources may have been proposed in a particu lar region, and it Is difficult to conclude which, if any, are likely to be constructed.
The evaluation described herein should consider any Federal, state or locally authorized projects;
any projects adopted by local river basin commissions; or any other projects whose chances of being constructed are considered likely.
The locations of fisheries and recreation areas that will be exposed to normal releases of radionuclides within 50 radial miles of a plant should be identified.
Present and projected future contact by humans and fish should be estimated.
The use of river system simulation models such as HEC-3 to adjust historic streamflows and to synthesize existing and potential future water use can provide acceptable estimates of the spatial and temporal distributions of streamflows at the locations for which estimates of average radionuclide concentrations are required.
Two basic assumptions are required.
First, it is assumed that the period of recorded historical streamflow selected for simulation is representa tive of conditions to be expected in the future.
Secondly, it is assumed that it is necessary to adjust historical streamflows for the effects of reservoirs and diversions.
If both of these assumptions are not supported by historical basin water usage, no adjustments are necessary.
Furthermore, if projected water use cannot be expected to alter streamflows in a way such as to require basin simulation, no flow adjustments are necessary.
Water use should be estimated, on a monthly basis, for present and projected future con ditions.
Local, state, or regional agencies often maintain records of such use, and such infor mation should be summarized and appropriately annotated.
These same agencies have in many cases made projections of future usage; these projections should be summarized and annotated.
Where existing records or locally projected usage information is not available or is con sidered unreliable, conservative estimates may be made from population projections and forecasted per capita usage estimates of agencies such as the U.S. Geological Survey or the Water Resources Council.
Where population or water use forecasts are at variance with other forecasts submitted by the applicant, the bases for the differences should be provided.
Although conservative estimates are sometimes required to ensure that the consequences of accidents are acceptable, realistic estimates will be adequate for the normal effluent release evaluations required by 10 CFR Part 50, Appendix 1.
c.
Existing Studies Many studies of the effects of water resource development schemes have been completed in great detail.
For example, many large river basins have been studied by the Corps of Engineers and others.
These existing studies, with only minor modifications for plant water use, may be used directly.
7.
SEDIMENT UPTAKE AND TRANSPORT MODELS
The ability of suspended and bottom sediments to absorb and adsorb radioactive nuclides from solution is recognized as contributing to important pathways to man through the sediment's ability to concentrate otherwise dilute species of ions.
The pathways are by direct contact with the populace and by transfer to the aquatic food chain.
Sorption by sediments is also an important mechanism for reducing the area of influence of plant releases.
The state of the art in sediment-related effects is not as advanced as in other engineer ing disciplines.
For this reason, and until reliable models become available, the staff will rely on existing field studies and the staff's and consultants' experience to determine the conservatism or reasonableness of the applicant's analyses and results.
If the applicant elects to take credit for the removal of certain ions from the surface waters by sediment uptake, extensive verification of the techniques used will be necessary because of the lack of existing verified generalized models.
The applicant's models will be evaluated based on their adherence to physical principles and their proven reliability in simulating prototype data.
Models will be compared, in terms of physical principles, to those listed in the references, in accordance with the classification of receiving water.
However, the staff does not accept these models a priori.
Because most existing sediment uptake and transport modeling techniques are crude, the applicant should demonstrate that the model Is conservative or realistically simulates the prototype.
The model verification will be accepted based on the quality of comparison with measurements for water bodies having characteristics
1.113-44
'ilar to those at the site. Actual measurements of sorption characteristics for pertinent Aionuclides should be presented for areas of the water body within the influence of the plant.
r4 se measurements should reflect seasonal variations of sources and sinks (spatial and grain
- ize) and the physical and chemical properties of the receiving water.
Estimates of sediment movement should be supported by actual field measurements (by the kpplicant or others).
Events and processes affecting sediment movement and deposition (e.g.,
9loods, storms, wave activity, and estuarine stratification) should be considered.
Changes in
- he character of the receiving water that would influence sediment transport (e.g., dams. Jetties, Iroins, and shoreline changes) should be considered.
1.113-45
LIST OF SYMBOLS
Symbol Description A
Cross-sectional area of river or estuary b
Width of estuary at water surface Width of river C
Concentration of constituent in water CE
Concentration in epilimnion of stratified impoundment Ch Chezy resistance coefficient CH
Concentration in hypolimnion of stratified impoundment Ci Input concentration In the upper layer of a stratified impoundment Ci'
Input concentration to the lower layer of a stratified impoundment Ci"
Input concentration for the total impoundment C°
Steady-state concentration of a nondecaying substance CT
Concentration in total impoundment at time of turnover CSS
Steady-state concentration of a decaying substance K
d Depth of river
0
Diffusion factor DF
Dilution factor SE
Sectionally averaged, one-dimensional longitudinal dispersion coefficient EL
Estuarine, sectionally and tidally averaged, one-dimensional longitudinal disper sion coefficient ED
Estuary number (dimensionless coefficient)
f Coriolis parameter FD
Densimetric Froude number at downstream boundary of estuary g
Acceleration of gravity H
Depth in estuary or open coast measured from water surface to bottom K
Empirical coefficient used in description of mixing in salinity intrusion region of an estuary I Kx, Ky Vertically averaged, two-dimensional turbulent diffusion coefficients in x and y directions, respectively t
Distance from point of maximum velocity to further bank in river flow L
Length of estuary
1.113-46
LIST OF SYMBOLS (Continued)
Symbol Description N
Quantity of radioactivity released in a pulse discharge n
Manning's coefficient N
Dimensionless estuarine freshwater velocity PT
Tidal prism q
Cumulative river discharge measured from near shore Q
Total river discharge Dimensionless cumulative river discharge q b Flow rate of blowdown through the pond Qf Freshwater volumetric discharge rate in estuary qt Inflow to the upper layer of a reservoir qt'
Inflow to the lower layer of a reservoir qt"l Inflow to the total reservoir qp PPlant pumping rate qs Cumulative river discharge rate at position of point source is Dimensionless cumulative river discharge rate at position of point source qsl, qs 2 Cumulative river discharges at beginning and end of line source, respectively R
Recirculation factor for impoundments Rh Hydraulic radius S
Salinity in estuary S 0
Salinity at downstream boundary of estuary t
Time td Duration of pulse discharge T
Tidal period th Half-life of radionuclide u
Velocity in x direction uSectional mean velocity in x direction u'
Deviation from sectional mean velocity U
Vertically averaged velocity in x direction U
Sectionally averaged longitudinal velocity in river or estuary Uf Sectionally averaged fresh water velocity in estuary Ut RS velocity in an oscillating flow u*
Shear velocity
1.113-47
LIST OF SYMBOLS (Continued)
SDescription v
Velocity in y direction V
Vertically averaged velocity in y direction VE
Volume of epilimnion in stratified impoundment VH
Volume of hypolimnion in stratified impoundment Vmax Maximum local tidal velocity VT
Total volume of impoundment W
Rate of radioactivity addition, in Cl/sec x
Longitudinal coordinate x
Dimensionless longitudinal coordinate y
Lateral coordinate Ys Lateral position of a point source Yslys2 Lateral positions of beginning and end of line source In cartesian coordinates z
Vertical coordinate z S
Vertical position of a point source m
Dimensionless coefficient Dimensionless coefficient
.
r Dimensionless cross-sectionally averaged concentration rmax r at the source position SZyLateral turbulent diffusion coefficient ez Vertical turbulent diffusion coefficient Water surface elevation above undisturbed datum e
Dimensionless time (ratio of time to flushing time)
A
Radioactive decay coefficient (ln2/tN)
Dimensionless longitudinal distance from source in a one-dimensional estuary CYBUz Standard deviations of radionuclide concentrations in y- and z directions, respectively T
Ratio of the half-life to the impoundment flushing time
,T*
xi x and y components of surface wind stress x
Nondecaying concentration SxDimensionless nondecaying concentration
1.113-48
CITED REFERENCES
1.
G. H. Jirka, G. Abraham, and D. R. F. Harleman, Massachusetts Institute of Technology, "An Assessment of Techniques for Hydrothermal Prediction," U.S. Nuclear Regulatory Commission, NUREG-0044, 1976.
(Copies may be obtained from the National Technical Information Service, Springfield, Va.)
2.
W. E. Dunn, A. J. Policastro, and R. A. Paddock, "Surface Thermal Plumes:
Evaluation of Mathematical Models for the Near and Complete Field," Parts One and Two, Argonne National Laboratory, Energy and Environmental Systems Division, ANL/WR-75-3, 1975.
3.
K. D. Stolzenbach and 0. R. F. Harleman,
"An Analytical and Experimental Investigation of Surface Discharges of Heated Water," Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Rep. No. 135, 1971.
4.
K; D. Stolzenbach, E. E. Adams, and D. R. F. Harleman, "A User's Manual for Three-Dimensional Heated Surface Discharge Conditions," Ralph M. Parsons Laboratory for Water Resources.and Hydrodynamics, Massachusetts Institute of Technology, Rep. No.
156, 1972.
5.
E. A. Prych, "A Warm Water Effluent Analyzed as a Buoyant Surface Jet," Sveriges Meteorologiska och Hydrologiska Institut, Serie Hydrologi, nr 21, Stockholm, Sweden, 1972.
6. M. A. Shirazi and L.R Davis, "Workbook of Thermal Plume Prediction Vol. 2 - Surface Discharge," U.S. Environmental Protection Agency, National Env._ronmental Research Center, Environmental Protection Technology Series, Rep. No. EPA-R2-72-OO5b, Corvallis, Ore., 1974.
7.
D. W. Pritchard, "Design and Siting Criteria for Once-Through Cooling Systems," presented at American Institute of Chemical Engineers, 68th Annual Meeting, Houston, Tex., 1971.
8.
D. W. Pritchard, "Fate of and Effect of Excess HeatDischarged into Lake Michigan with Specific Application to the Condenser Cooling Water Discharge from the Zion Nuclear Power Station," Testimony at the AEC Licensing Hearings for the Zion Nuclear Power Station Operating Permit, Chicago, Ill., 1973.
9.
G. H. Jirka and D. R. F. Harleman, "The Mechanics of Submerged Multiport Diffusers for Buoyant Discharges in Shallow Water," Ralph M. Parsons Laboratory for Water Resources and Hydrodynamics, Massachusetts Institute of Technology, Rep. No. 169, 1973.
10.
J. H. W. Lee, G. H. Jirka, and D.*R. F. Harleman, "Stability and Mixing of a Vertical Round Buoyant Jet in Shallow Water," Ralph M. Parsons Laboratory for Water Resources and Hydro dynamics, Massachusetts Institute of Technology, Rep. No.
195, 1974.
11.
R. C. Y. Koh and L. N. Fan, "Mathematical Models for the Prediction of Temperature Distri butions Resulting from the Discharge of Heated Water in Large Bodies of Water," Water Pollution Control Research Series, Rep, No.
16130DW010/70, 1970.
12.
E. Hirst, "Analysis of Round, Turbulent, Buoyant Jet Discharged to Flowing Stratified Ambients," Oak Ridge National Laboratory, Rep. No. 4685, 1971.
13.
W. W. Sayre and F. M. Chang, "A Laboratory Investigation of Open-Channel dispersion Processes for Dissolved, Suspended, and Floating Dispersants," U.S. Geological Survey, Professional Paper 433-E, 1968.
14.
N. Yotsukura and E. D. Cobb, "Transverse Diffusion of Solutes in Natural Streams," U.S.
Geological Survey, Professional Paper 582-C, 1972.
15.
N. Yotsukura, "A Two-Dimensional Temperature Model for a Thermally Loaded River with Steady Discharge," Proceedings, 11th Annual Environmental and Water Resources Engineering Confer ence, Vanderbilt University, Nashville, Tenn.,
1972.
16.
N. Yotsukura and W. W. Sayre, "Transverse Mixing in Natural Channels," Water Resources Research, Vol.
12, No. 4, August 1976.
1
1.113-49
17.
F. M. Henderson, Open Channel Flow, New York:
Macmillan Company, 1959.
18.
V. T. Chow, Open Channel Hydraulics, New York:
McGraw-Hill Book Company, 1959.
19.
J. W. Elder, "The Dispersion of Marked Fluid in Turbulent Shear Flow," Journal of Fluid Mechanics, No. 5, 1959, pp. 544-60.
20.
H. B. Fischer, "The Effects of Bends on Dispersion in Streams," Water Resources Research
5(2), 1969, pp. 496-506.
21.
N. Yotsukura, H. B. Fischer, and W. W. Sayre, "Measurement of Mixing Characteristics of the Missouri River Between Sioux City, Iowa, and Plattsmouth, Nebraska," U.S. Geological Survey, Water-Supply Paper 1899-G, 1970.
22.
W. W. Sayre and T. P. Yeh, "Transverse Mixing Characteristics of the Missouri River Down stream from the Cooper Nuclear Station," University of Iowa, Iowa Institute of Hydraulic Research, Rep. No. 145, Iowa City, Iowa, 1973.
23.
G. T. Csanady, "Dispersal of Effluents in the Great Lakes," Water Research, vol. 4, 1970,
pp.79-114.
24.
Stone and Webster, "1970 Lake Temperature and Current Studies," Report to Power Authority, State of New York, AEC Docket No. 50-333, 1971.
25.
G. T. Csanady, "Response of Large Stratified Lakes to Wind," Journal of Physical Oceanography, vol. 2, no. 1, 1972, pp. 3-13.
26.
G. T. Csanady, "The Coastal Boundary Layer in Lake Ontario:
Part II.
The Summer-Fall Regime," Journal of Physical Oceanography, vol. 2, no. 2, 1972, pp. 168-176.
27.
C. R. Murthy and G. T. Csanady, "Experimental Studies of Relative Diffusion in Lake Huron,"
Journal of Physical Oceanography, vol. 1, 1971, pp. 77-24.
28.
T. R. Sundaram and R. G. Rehm, "The Seasonal Thermal Structure of Deep Temperate Lakes,"
Tellus, vol.
25, 1973, pp. 157-168.
29.
J. J. Leendertse, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume I, Principles of Computation," The Rand Corporation, No. RM-6230-RC,
1970.
30.
J. J. Leendertse and E. C. Gritton, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume II, Computation Procedures," The Rand Corporation, No. R-708-NYC, 1971.
31.
J. J. Leendertse and E. C. Gritton, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume III, Jamaica Bay Simulation," The Rand Corporation, No. R-709-NYC, 1971.
32.
J. J. Leendertse, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume IV, Jamaica Bay Tidal Flows," The Rand Corporation, No. R-1009-NYC,
1972.
33.
E. C. Gritton, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume V, Jamaica Bay Rainstorms," The Rand Corporation, No.
R-lOlO-NYC, 1972.
34.
J. J. Leendertse and S. K. Liu, "A Water-Quality Simulation Model for Well-Mixed Estuaries and Coastal Seas:
Volume VI, Simulation, Observation, and State Estimation," The Rand Corporation, No. R-1586-NYC, 1974.
35. R. B. Codell, "Digital Simulation of Thermal Effluent Dispersion in Rivers, Lakes, and Estuaries," Ph.D. Dissertation, Lehigh University, 1973.
36.
L. A. Loziuk, J. C. Anderson, and T. Belytschko, "Hydrothermal Analysis by Finite Element Method," Proceedings of the American Society of Civil Engineers, Journal of the Hydraulics Division, vol. 98 (HYll), 1972.
37.
A. H. Eraslan, "Two-Dimensional, Discrete Element, Far Field Model for Thermal Impact Analysis of Power Plant Discharges in Coastal and Offshore Regions," Oak Ridge National Laboratory, Rep. No. 4940, 1975.
1.113-50
38.
N. H. Brooks, "Diffusion of Sewage Effluent in an Ocean Current," :Proceedings, 1st Inter I national Conference on Waste Disposal in the Marine Environment, Pergamon.Press,
1960.
39.
J. E. Foxworthy, "Eddy Diffusivity and the Four-Thirds Law in Near-Shore (Coastal Waters),"
The Allan Hancock Foundation, University of Southern California, Report 68-1,
1969.
40.
J. E. Foxworthy, "Eddy Diffusion and Bacterial Reduction in Waste Fields in the Ocean,"
The Allan Hancock Foundation, University of Southern California, Report 69-1, 1969.
41.
R. E. Stewart, H. D. Putnam, R. H. Jones, and T. N. Lee, "Diffusion of Sewage Effluent from Ocean Outfall," Proceedings of the American Society of Civil Engineers, Journal of the Sanitary Engineering Division, vol.
97, SA4, 1971.
42.
H. H. Carter and A. Okubo,
"A Study of the Physical Processes of Movement and Dispersion in the Cape Kennedy Area," Chesapeake Bay Institute, The Johns Hopkins University, Report No.
NYO-2973-1,
1965.
43.
G. Kullenberg, "Vertical Diffusion in Shallow Waters," Tellus, vol. 23, 1971, pp. 129-135.
44.
G. Kullenberg, "Results of Diffusion Experiments in the Upper Reaches of the Sea," Insti tute of Physical Oceanography, University of Copenhagen, Rep. No. 12,
1971.
45.
A. Okubo,
"Oceanic Mixing," Chesapeake Bay Institute, Johns Hopkins University, Tech. Rep.
62, Docket No. NYO-3109-49, 1970.
46.
D. J. O'Conner and J. P. Lawlqr, "Mathematical Analysis of Estuarine Pollution," 55th National Meeting, American Institute of Chemical Engineers, Reprint 'Io.
31a, Pouston, Tex.,
1965.
47.
TRACOR, Inc., "Estuarine Modeling, An Assessment," Environmental Protection Agency, Project No.
160700ZV, Contract 14-12-551,
1971.
48.
R. L. Crim and N. L. Lovelace, "Auto-Qual Modeling System," U.S. Environmental Protection Agency, EPA-440/9-73-003, Washington, D.C.,
March 1973.
.
49.
J. E. Dailey and D. R. F. Harlemah,
"Numerical Model for the Prediction of Transient Water Quality in Estuary Networks," Ralph M. Parsons Laboratory for Water Resources and Hydro dynamics, Massachusetts Institute of Technology, Tech. Rep. 158, 1972.
50.
C. H. Lee and D. R. F. Harleman, "One-Dimensional Real Time Model for Estuarine Water Quality Prediction," Water Quality Office, Environmental Protection Agency, Report 16070DGW,
Washington, D.C.,
1971.
51.
A. H. Eraslan, unpublished users manual,
"One Dimensional Model," Oak Ridge National Labora tories, 1975.
52.
L. J. Hetling and R. L. O'Connell, "Estimating Diffusion Characteristics of Tidal Waters,"
Department of the Interior, Federal Water Pollution Control Administration, Middle Atlantic Region, CB-SRBP Technical Paper No. 4, 1967.
53.
G. I. Taylor, "The Dispersion of Matter in Turbulent Flow in a Pipe," Proc. Royal Society London (A),
vol. 223, May 1954..
54.
M. L. Thatcher and D. R. F. Harleman, "A Mathematical Model for the Prediction of Unsteady Salinity Intrusion in Estuaries," R. M. Parsons Laboratory, Massachusetts Institute of Technology, Technical Report No. 144, February 1972.
55.
H. B. Fischer, "The Mechanics of Dispersion in Natural Streams," Proceedings of the American Society of Civil Engineers, Journal of the Hydraulics Division, No. 93 (HY6),
1967, pp. 187-216.
56.
D. S. Trent, "Mathematical Modeling of Transport Processes in Aquatic Systems," Battelle Pacific Northwest Laboratories, BNWL-SA-5379, Richland, Wash., April 1975.
57.
P. J. Ryan and D. R. F. Harleman, "Prediction of the Annual Cycle of Temperature Changes in a Stratified Lake or Reservoir - Mathematical Model and User's Manual," R. M. Parsons Laboratory, Massachusetts Institute of Technology, Report No. 137,
1971.
1.113-51
58.
Water Resources Engineers, Inc., "Mathematical Models for the Prediction of Thermal Energy Changes in Impoundments," Walnut Creek, Calif., prepared for the Water Quality Office, Environmental Protection Agency, December 1969.
59.
P. J. Ryan and D. R. F. Harleman, "An Analytical and Experimental Study of Transient Cooling Pond Behavior," R. M. Parsons Laboratory, Massachusetts Institute of Technology, Report No.
161, January 1973.
60.
U.S. Army Corps of Engineers, "HEC-4, River Flow Simulation," Hydrologic Engineering Center, Davis, Calif., 1971.
61.
L. G. Hulman, "Regional Water Supply Systems Analysis for a Megalopolis," paper presented at the August 1971 ASCE Hydraulics Division Specialty Conference, Iowa City, Iowa, 1971.
62.
L. G. Hulman and D. 0. Erickson, "Delaware River Basin Modeling," presented at the 17th Annual ASCE Specialty Conference, Logan, Utah, August. 1969.
63.
U. S. Army Corps of Engineers, "HEC-3, Reservoir Analysis," Hydrologic Engineering Center, Davis, Calif., 1971.
1.113-52
ADDITIONAL REFERENCES
SEDIMENT UPTAKE MODELS
Selected Mathematical Models and Theoretical Development
1.
Oak Ridge National Laboratories, ORNL-TM-4751,
"A System Analysis Model for Calculating Radionuclide Transport Between Receiving Waters and Bottom Sediments," R. S. Booth, Oak Ridge, Tenn.,
April 1975.
2.
E. K. Duursma and C. J. Bosch, "Theoretical, Experimental, and Field Studies Concerning Diffusion of Radioisotopes In Sediments and Suspended Particles of the Sea," Netherlands Journal of Sea Research, vol. 4, no. 4, 1970, pp. 395-469.
3.
D. E. Fields, "Modification of the Unified Transport Model to Allow for Sediment Transport and Chemical Exchange," Proceedings of the Second Annual NSF-RANN Trace Contaminants Con ference, Asilomar, Calif., August 1974.
4.
J. F. Fletcher and W. L. Dotson, "HERMES - A Digital Computer Code for Estimating'Regional Radiological Effects from the Nuclear Power Industry," Hanford Engineering Development Lab.,
Hanford, Wash.,
December 1971.
S. E. F. Gloyna, A. A. Yousef, and T. J. Padden, "Radionuclide Transport and Responses to Organic Stress in a Research Flume," Advances in Water Pollution Research, vol. 1, no.
1, Pergamon Press, Great Britain, 1971.
6.
Geological Survey Professional Paper 433-F, "Role of Certain Stream Sediment Components in Radiolon Sorption,".E. A. Jenne and J. S. Wahlberg, U.S. Government Printing Office, 1968.
7.
Oak Ridge National Laboratories, ORNL-NSF-EATC-7,
"A User's Manual for the FORTRAN IV
Version of the Wisconsin Hydrologic Transport Model," M. R. Patterson et al., Oak Ridge, Tenn., October 1974.
8.
R. J. Raridon et al., 'Computer Model for Chemical Exchange in the Stream System," Proceed ings of the First Annual NSF Trace Contaminant Conference, Conf-730802,
1973.
9.
Geological Survey Professional Paper 433-A, "Uptake and Transport of Radionuclides by Stream Sediments," W. W. Sayre, H. P. Guy, and A. R. Chamberlain, U. S. Government Printing Office, 1963.
10.
Center for Research in Water Resources, Technical Report 19, "Radioactvity Transport in Water, Summary Report," Y. A. Yousef, A. Kudo, and E. F. Gloyna, University of Texas, Austin, Texas,
1970.
Selected Field Studies, Surveillance Programs, and Data
1.
Oak Ridge National Laboratories, ORNL-3721, TID4500, "Concentrations, Total Stream Loads, and Mass Transport in the Clinch and Tennessee Rivers," M. A. Churchill et al., (and others in this series), Oak Ridge National Laboratories, August 1965.
2.
C. Collison and N. F. Shimp, "Trace Elements in Bottom Sediments from Upper Peoria Lake, Middle Illinois River,"
Environmental Geology Notes, Illinois State Geological Survey, No. 56, September 1972.,
3.
S. Davies, F. Cosolito, and M. Eisenbud, "Radioactivity in the Hudson River," Proceedings First Symposium on Hudson River Ecology, Hudson River Valley Commission of New York,
1966, p. 289.
4.
National Academy of Sciences, "Marine Sediments and Radioactivity,' Chapter Six of "Radio activity in the Marine Environment," E. K. Duursma and M. G. Gross, National Academy of Sciences, Washington, D.C.,
1971, pp. 147-160.
1.113-53
5.
U. S. Environmental Protection Agency, RD No. 71-1, "Radiological Surveillance Studies at a Pressurized Water Nuclear Power Reactor," B. Kahn et al., National Environmental Research Center, Cincinnati, Ohio, August 1971.
6.
A. Lerman, "Time to Chemical Steady-States in Lakes and Oceans," Nonequilibrium Systems in Natural Water Chemistry:
Symposium of the American Chemical Society, Houston, Texas, February 24-25, 1970, Advances in Chemistry Series 106, American Chemical Society, Washington, D.C.,
1971.
7.
A. Lerman and G. J. Brunskill, "Migration of Major Constituents from Lake Sediments into Lake Water and Its Bearing on Lake Water Composition," Limnology and Oceanography, vol. 16, no. 6, November 1971, pp. 880-890.
8.
A. Lerman and R. R. Weller, "Diffusion and Accumulation of Chloride and Sodium in Lake Ontario Sediments," Earth and Planetary Science Letter, vol.
10, 1970, pp. 150-156.
9.
T. F. Lomenick and T. Tamura, "Naturally Occurring Fixation of Cesium-137 on Sediments of Lacustrine Origin," Soil Science Society of America Proceedings, vol. 29, no. 4, July August 1965, pp. 383-387.
10. F. T. Manheim, "The Diffusion of Ions in Unconsolidated Sediments," Earth and Planetary Science Letter, vol. 9, 1970, pp. 307-309.
11. D. K. Phelps, "Partitioning of the Stable Elements Fe, Zn, Se, and Sm Within a Benthic Community, Anasco Bay, Puerto Rico," Proceedings of the Symposium on Radloecological Con centration Processes, April 22-29, 1966, Stockholm, ed. by B. Aberg and F. P. Hungate, Pergamon Press, pp. 721-733.
12.
G. K. Riel, "Radioactive Cesium in Estuaries," Radiological Health Data and Reports, December 1970, pp. 659-665.
13.
N. I. Sax et al, "Radioecological Surveillance of the Waterways Around a Nuclear Fuels Reprocessing Plant," Radiological Health Data and Reports, vol.
10, no. 7, July 1969, pp. 289-296.
14.
U. S. Environmental Protection Agency, Radiological Health Data and Reports, (published monthly 1959-74), Washington, D.C.
15.
U. S. Atomic Energy Reports, BNWL-1341, and 1341-Appended.
"Evaluation of Radiological Conditions in the Vicinity of Hanford for 1968," C. B. Wilson (ed.), Pacific Northwest Labs, Richland, Wash. (and others in this series back to 1961), 1970.
16.
G. K. Riel, "Distribution of Fallout of Cesium 137 in the Chesapeake Bay," Second Inter national Symposium on Natural Radiation Environment, Houston, Texas, August 1972.
Selected Sediment Transport Methodology Sedimentation Committee, Hydraulics Division
1. American Society of Civil Engineers, "Sediment Discharge Formulas," Journal of the Hydraulics Division, ASCE, vol. 97, no. HY4, April 1971.
2.
U. S. Army Coastal Engineering Research Center, "Shore Protection Manual," 1973.
3.
U. S. Geological Survey, "Quality of Surface Waters of the United States," U.S. Government Printing Office, all years.
Selected Smposia
1. Proceedings, Symposium on Disposal of Radioactive Wastes into Seas, Oceans, and Surface Waters, International Atomic Energy Agency, Vienna, Austria, 1966.
Z. Proceedings, Second National Symposium on Radio Ecology, Ann Arbor, Mich.,
1967.
3. Proceedings, Symposium on Environmental Surveillance in the Vicinity of Nuclear Facilities, W. C. Reinig (ed), Charles Thomas Corp., Springfield, Ill., 1968.
4.
Proceedings, Fifth Annual Health Physics Society Midyear Topical Symposium, "Health Physics Aspects of Nucilear Facility Siting," Idaho Falls, Idaho, 1970.
1.113-54
5.
Proceedings, Third National Symposium, Radioecology,. Oak Ridge, Tennessee, May 10-12, 1971.
6.
Proceedtings International Symposium, RadioecologY Applied to the Protection of Man and the Environment, RI.,. , Sept. 1971, EUR 4800-d-f-i-e, Luxembourg, May 197Z.
1.113-56