United States Office of Radiation Programs EPA 520/6-78-005
Environmental Protection AW-459 June 1978
Agency Wash DC 20460
Radiation
Development and
Application of a
Risk Assessment Method
for Radioactive Waste
Management
Volume I:
Generic Description
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EPA REVIEW NOTICE ;
This report has been reviewed by the Office of Radiation Programss U.S. \
Environmental Protection Agency (EPA) and approved for publication. Approval
does not signify that the contents necessarily reflect the views and policies !-
of the EPA. Neither the United States nor the EPA makes any warranty, expressed
or implied, or assumes any legal liability or responsibility of any information,:
apparatus, product or process disclosed, or represents that its use would not
infringe privately owned rights. - •
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EPA 520/6-78-005
DEVELOPMENT AND APPLICATION OF A RISK
ASSESSMENT METHOD FOR RADIOACTIVE WASTE MANAGEMENT
Final Contract Report
Principal Investigators Stanley E. Logan
Bureau of Engineering Research
The -University of New Mexico
Albuquerque, New Mexico 87131
Volume I: Generic Description of AMRAW-A Model
S. E. Logan, M« C. Berbano
July 1978
Prepared for
0. S. Environmental Protection Agency
Under Contract No. 68-01-3256
Project Officer
Bruce J, Mann
Office of Radiation Programs-LVF
P. O, Box 1502?
Las Vegas, Nevada 89114
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Page Intentionally Blank
ii
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FOREWOKD
The EPA Office of Radiation Programs carries out a national program
to evaluate human exposures to radioactivity, and to promote the
development of controls to protect the environment and public health
from such radioactivity. An important part of this program consists of
the development of environmental protection criteria and standards for
radioactive waste management and disposal.
To sustain this effort, studies have been supported by EPA to
develop methods to evaluate the environmental adequacy of proposed
waste management alternatives, and this report describes one of the
first attempts to develop a comprehensive assessment model. It has
been funded at a very modest level. Much interest has been expressed
in this work, and through publication, EPA is making it available to
those involved with the development and use of models as decision-
making tools.
In order for models to be useful as tools for decision-making
concerning radioactive waste management alternatives, their
capabilities and limitations must be fully understood. It should be
noted that assessment models in themselves will not identify optimum
waste management choices. However, they can be used to compare well
defined alternatives. One of the necessary steps in any model
development and validation process is the comparison of results with
results obtained from the application of alternate models to test
cases. It is hoped that as other comprehensive assessment models become
available, comparison studies can be performed,
The methodology described herein has been applied, for model
illustration purposes, to a reference repository in a bedded salt
formation located in the southwestern United States. Any results
published in this report should not be interpreted as implying
conclusions concerning the suitability of the reference site or any
site-specific method/repository combination for the preparation and
disposal of radioactive waste,
Comments on this analysis as well as any new information would be
welcomed; they may be sent to the Director, Technology Assessment
Division (AW-459) Office of Radiation Programs, 0.S. Environmental
Protection Agency, Washington, D.C, 20460.
tf. D. Rowe, Ph.D.
Deputy Assistant Administrator
for Radiation Programs (AW-459)
iii
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Page Intentionally Blank
iv
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A Radioactive Waste Management Systems Model, developed and imple-
mented by The University of Mew Mexico under contract with the U. S.
Environmental Protection Agency, is presented. The systems model and
associated computer code called AMRAW (Assessment Method for Radioactive
Waste), has two parts. The first part, &MRRW-R, consists of the Source
Term (radioactive inventory versus time), the Release Model, and the
Environmental Model. The Release Model considers various geologic and
man-caused events which are potential mechanisms for release of radio-
active material beyond the immediate environs of a repository or other-
location; the risk analysis mode uses events distributed probabilistically
over tine, and the consequence analysis mode "uses discrete events occur-
ring at specified times. The Environmental Model includes: 1} the trans-
port to and accumulations at various receptors in the biosphere,
2) pathways from these environmental concentrations, and 3) resulting
radiation dose to man,
The second part of the systems model, &MRRW-B, is the Economic Model
which calculates health effects corresponding to the various organ dose
rates from AMRAW-&, collects these health effects in terms of economic
costs and attributes these costs to radionuclides, decay groups? and
elements initially in the waste inventory. Implementation, with calcu-
lated results, of AMRAW for Terminal Storage in a Bedded Salt Reference
Repository are presented. Preliminary demonstrations for the repository
operations phase of waste management and terminal storage in a shale
formation are described; possible applications to other radioactive and
nonradioactive hazardous materials are discussed, AMRftW uniquely links
all steps together in a continuous calculation sequence.
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Funding for this project was initially provided by the Energy/Environ-
ment Program, office of Research and Development, and subsequent funding
by the Office of Radiation Programs, EPA.
Persons at the EPA, other federal agencies, national laboratories,
federal contractors, and foreign correspondents have provided helpful
suggestions during progress of the work or through review of draft reports.
These contributions are greatly appreciated though space does not permit
acknowledgement of each individual contribution.
The work on this broad interdisciplinary program centered in- the
Chemical and Nuclear Engineering Department (Ch/NE) of the College of
Engineering at The University of New Mexico (UNM), The principal investi-
gator, S. E. Logan, assisted by M. C. Berbano and numerous graduate
students in Ch/NE. A component of the-effort concerned the Economic
Model, handled by the UNM Economics Department. Other departments at
UNM provided support in of geologic descriptions and disruptive
events, environmental pathway analysis, and computer programming. UNM
departments and personnel participating at various levels of activity and
at various times during the study are as follows:
Chemical and Muclear
Engineering Department
Faculty: S. E, Logan
M. C, Berbano
K. K. Cox
Students: W. P. Carroll
R, L, Conarty
D. L. Cox
M. W. Davis
R. D. Erickson
H. S, Ng
M. W. Young
Economics Department
Faculty:
S. Ben-David
D. S. Brookshire
A. V. Krieese
W. D. Schulze
Electrical Engineering
and Computer Science Department
Students; K, E, Patterson
C. M. Vining
Geology Department
Faculty: D. G. Brookins
A. M. Kudo
L. A, Woodward
Students; J, Iwerks
P, A. Longmire
Biology Department
Faculty; J. R, GOSE
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Econoinics Degartment Mathematics Department
Student: J. M. Dye Student; G. M. McKerney
Physics Department
Student: C. C. Herrmann
Other persons outside of UHM contributed significantly to the com-
pletion of the study through their direct participation/ the furnishing
of categories of data, or helping with critical reviews of draft versions
of the report. These individuals are listed below under AMR&W sub-models.
It should be noted that participation by these persons does not necessarily
imply their endorsement of the AMRAW methodology or any of its components.
Inventory_at^Risk (Source Term) . J. O. Blomeke of QRNL (Oak Ridge
National Laboratory) furnished ORIGEH computer output for radioactive
waste projections.
Release Model. A. Sanford {New Mexico Institute of Mining & Tech-
nology) conducted a seismic analysis for the model repository site; I. J.
Winograd (U.S. Geological Survey) and H. Lambert (consultant) provided
critical reviews,
Transport to Environment. T. E. Kelly (Geohydrology Associates)
provided hydrologic study for the model repository site; J. O. Duguid
(ORNL, now at Eattelle Columbus Laboratories) provided a description of
the Duguid-Reeves ground water transport model; R. E. Moore (QRNL) pro-
vided air dispersion computer output from the AIRDOS code; T. H. Pigford
(University of California) and H. C. Burkholder (Battelle Pacific North-
west Laboratories) provided critical review of ground water transport.
Environment-to-Man Pathways. J, P. Witherspoon (ORNL) provided food
concentration versus ground deposition computer output from the TERMOD
terrestrial code; agricultural economists at the Hew Mexico State Univer-
sity provided livestock production data; T. W. Fowler and C. Nelson (EPA)
suggested the concept of integrated concentration in foods; S» V. Kaye
and C. C- Travis (ORNL) reviewed the pathway analysis modeling and con-
firmed suggested revisions; J. E. Till (consultant) reviewed revised
pathway analysis, provided suggestions and helped in resolving dose con-
version factor questions.
vii
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Economic Model. W, H. Ellett (EPA) provided additional insight into
interpretation of the BEIR report, and B. M. Bunger (EPA) provided review
comments.
Improvements in the mathematical representation, of the model were
suggested by D. E. Cabrilla {EPA}. J. M. J. M. Briggs (EPA)
reviewed AMRAW programming and converted from IBM to a CDC system. Other
persons at the EPA who helped with extensive review of draft reports
include S, T. Bard, C* Y. Hung, J. Neiheisel, and J. J, Swift,
The EPA Project Officer during the first 1 1/2 years of the study
was S, M. Golberg (now DOE), followed in turn by R. F. Kauffmann and
B. J. Mann. The guidance and suggestions provided by these persons is
acknowledged,
Prior to the start of the EPA contract, early development of the
AMRAW model, following the framework established as part of the Logan
Ph.D. dissertation, was supported by the Sandia University Research
Program {Sandia Laboratories) and the State of New Mexico Energy Research
and Development Program (now administered by the New Mexico Energy and
Minerals Department).
The computer logistics and mountains of computer printout for the
final series of cases used in this report were handled by H. S. Ng/ the
many computer aided plots were made by C. C. Herrmann and editorial ser-
vices during preparation of this report were provided by R. L. Conarty.
Appreciation is extended to the UNM Bureau of Engineering Research,
directed by G. W. Hay, for the patient typing, most of which done
by Jo Williams, printing by M, A. Arnot, and contract administration help
by Joyce Meyer»
Last but not least, the prinicpal investigator acknowledges the
tolerance of his wife, Marjorie, during more than two years of continuous
evening and weekends contributed to successful completion of the work.
VI11
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DEVELOPMENT AND APPLICATION
OF A RISK
FOR RADIOACTIVE WASTE
VOLUME LISTING
I GENERIC DESCRIPTION OF AMRAW-A MODEL
II IMPLEMENTATION FOR TERMINAL STORAGE IN
REFERENCE REPOSITORY AND OTHER APPLICATIONS
VOLUME III ECONOMIC ANALYSIS; DESCRIPTION AND IMPLEMENTATIQt^
OF AMRAW-B MODEL
VOLUME IV AMRAW COMPUTER CODE USERS' MANUAL
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VOLUME I
TABLE OF CONTENTS
PAGE
Forward , ±ii
Abstract , , _ , v
Acknowledgements ..,,.....,.., .. [ * vi
List of Volumes ix
List of Figures. , .-.....,.,...,,..,.,.,....,... Xii
List of Tables, xiii
List of Abbreviations, Symbols
and Nomenclature, x±v
CHAPTER 1, INTRODUCTION ,,,..,,..,,.,.,,,,,,,,,, r,.., 1
CHAPTER 2, SUMMARY ....I,,,,,..,.,,,.,,*,,,.*,.,,,,,, 5
CHAPTER 3, CONCLUSIONS AND RECOMMENDATIONS,,,.,,.,.., 11
CHAPTER 4, GENERIC DESCRIPTION OF
AMRAW-A MODEL .,.....,.,.,.,,,.,,.,.,.,.,, 15
A, AMRAW-A MODEL ,,,,,,,,,.,,,..,,,.,,,.,,,,,., 20
B, SOURCE TERM ,,,,.,.,..,.,,.,.,,.,,,.,.,,.,,, 25
C, RELEASE MODEL .I.,,,..,,.,,,,,.,.,..,,.,.,,, 31
1. Release Scenarios ,,,,,,,,,,,,,,, ».,,,. 3^1
2. Release Barriers ,,,,,,,,,,.,,,.,,,,,.,,,,,, i|l
3. Leaching in Ground Water ,,,,,,,,,,,,,,,,,,,, i|2
4. Model Output ,,,,,,,,,,,,.,,,.,,,,,,,, 51
D, ENVIRONMENTAL MODEL ,..,.,,,.,,,.,,.,,..,,,,• 52
1. Transport to Environment ,,,,,,,».,,,,,,,,,,, 52
2, Environmental Pathways ,,,,.,,,,,,,,,,,, 90
E. MATHEMATICAL OF .,,,,,...,.,., 103
1, Continuous Representation ,,,,,,,,,,,,,,,,,,» 103
2, Discrete Representation ,,,,,,,,,,,,,,,,,,,,, 108
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TABLE OF CONTENTS (CONTINUED)
PAGE
CHAPTER 5, DESCRIPTION OF AMRAW-A COMPUTER CODE.,,... 113
CHAPTER 6, APPLICATION OF MODEL ..................... 119
APPENDICES
A. CONCENTRATION DISTRIBUTIONS IN
GROUND WATER TRANSPORT ..................... 121
B, RADIONUCLIDE CONCENTRATIONS
IN TERRESTRIAL FOODS ...... ...... ,,,,,, .....
bLOSSARY i i i i i i i i i i i < i i i < i i i i i i i i i < i i i i i i i i i i i i i i i i t i t
KEFERENCES • i < ..... 9 i i > i t t i • i > > i i i i i i t i > i • i t i i ( < t • i t t i JLHH
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VOLURE I
LIST OF FISURES
FIGURE
4-1 Radioactive waste management systems model,........... ig
4-2 One branch of systems model., ......................... 18
4-3 Releases from geosphere to preliminary
environmental input receptors , 32
4-4 Fault tree symbolism 35
4-5 Simple fault tree 37
4-6 Conceptual dynamic repository simulation response............ 40
4-7 Preliminary environmental input receptors 53
4-8 Dispersion to a zone during a release
time increment 54
4-9 Adjustment for inter-receptor transfers „.. 5?
4-10 Conversion of adjusted inventories to concentration 59
4-11 Sequence for residual activities in time
increments subsequent to release. » 61
4-12 Movement of leachant from disposal horizon
to upper aquifer ,,,......,» 66
4-13 Transport to air land surface environmental
input receptors in Eone 2 following volcanic
explosion release to air in 400 - 500 y time
interval , — 88
4-14 Main environment-to-man pathways 91
4-15 Basic pathway relationship. 93
4-16 Response of concentration of Sr-90 in food
to unit deposition 96
A-l Transverse distribution of concentration
of peaks at distance of 10 km for plane
and line sources ., 124
ft-2 Concentration distribution 10 km from
the source for plane and line sources
with instantaneous release 125
A-3 Concentration distributions in peak
from line source, at distances
of 10 and 20 km ... 12?
A-4 Effective plume dimensions 130
B-l Compartment diagram of the terrestrial food
pathways by which radioactivity can be
transferred to man.,.,.. ...............3-32
B-2 Linear plot of 1-129 concentrations in
response to unit initial deposition of pCi/m 139
B-3 Response of concentration of 1-129 in food
to unit initial deposition of yCi/tn^ „ 141
Xll
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VOLUME I
LIST OF TABLES
TABLE PAGE
4-1 Receptor and transfer Coefficient
Sequence in &MRAW ........................... ....... .... ..... 19
4-2 Selected Significant Radionuelicles .............. ....... , ..... 27
4-3 Fraction of Total Hazard Represented by
Groups of Selected Radionuclides f Percent ....... ............. 28
4-4 Factors Comprising Environment-to-Man
Coefficients ..... ........... ................ ........ . ....... . 94
4-5 Sample Calculations, Environmental Pathways
in Zone 2, Total Body Dose Rates from Sr-90
Following Volcanic Explosion Release to
Air in 400 - 500 y Time Interval. ...... ..... . ..... . ..... .....
5-1 Directory of AMEAW-A Output Tables ........................ ...
B-l Peak Concentrations in Food
Following Unit Deposition of 1-129 ... ...... .................. 133
XI11
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I
LIST OF ABBREVIATIONS, SYMBOLS
AND
CHAPTER 1
CHAPTER 2
AMRAW
AMRAW-A
AMRAW-B
K,
CHAPTER 3
CHAPTER
Section 4.A
Section 4.B
"th
Jth
Section 4.C.I
V A2
Al(t)
A(t)
V B2
B S C
None
(Assessment Method for Radioactive Waste) Assessment
Model and associated computer code
That portion of AMRAW which, includes Source Terms, Release
Model, and Environmental Model
The economic part of AMRAW
Distribution coefficient used in ground water transport
calculations
None
None
Thermal efficiency
Thermal energy produced
Capacity factor
Rated electrical power capacity
Duration of time period
Fault tree "and" gates
Fraction of inventory transferred to a given input
receptor if release occurs
Transfer coefficient to given preliminary environmental
input receptor
Fault tree "or" gates
Constants used in illustrating forms of P(t)
xiv
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Annual probability of release occurrence
••P
At
» etc.
n
A
o
C
C
s
t?
e
F
s
J(t)
k
K
Time at which P(t) commences change or when discrete
event occurs in using delta function
Time increment within which t lies in using delta func-
tion.
Probability factors
Section 4.C.2. none
Section 4.C.3.
Incremental amount leached for n leach period renewals
Initial total radioactivity of species subject to leaching
Concentration of mobile species at time t and space x
Uniform initial concentration of mobile species
Effective diffusivity for the species
Total exposed area of specimen
Radioactive species material flux across interface
Dissolution rate constant
Stokes-Einstein constant, 1.38 x 10 gem /see molecules
L
M
M
H
t
T
V
A
Cumulative amount of radioactive isotope leached from
solidified waste for a specified
I a
** n
m
Molecular weight of diffusing species
Molecular weight of solvent
Avogadro ' s number
Radius of diffusing particle in cm
Tine
Absolute temperature, °K
Molecular volune of the solute at normal boiling point,
cm^/g mole
-------
V
a,6
TI(X, t)
V
5
P
x
Specimen volume
Spatial coordinate in cartesian space
Spatial coordinate in cartesian space
Spatial coordinate in cartesian space
Empirical constants in leach equation
Transformation variable used is solution of diffusion
equation
Solvent viscosity at absolute temperature, T °K
Fraction of initial amount leached
Density of diffusing species in solid state
An association parameter for the solvent
Section 4.C.4 None
Section 4.D.I
T
A2
AKEAW
c
C
D'
D, .
13
DECFAC
DEP
Modified coefficient of compressibility of the medium
Longitudinal dispersivity
Transverse dispersivity
Time transfer coefficient, incorporating radioactive and
environmental decay, and transport retardation
Zone land surface area
Zone surface water area
Concentration of the dissolved species
Concentration of the dissolved species appearing as the
solution to the radio/melide mass transfer equation
Dispersion tensor
Component of dispersion tensor D"
(in AMRAW) Effective decay factor between two times
Deposition concentration for land and ground surface
(Ci/cm2) due to air deposition
xvi
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DBPGND
DEJPWTR
DISPH
E
m
E
HI
F
in
m
GNDEP
h
E
k
352
K
K
Kd
M
M'
Deposition on land surface of zone
Deposition on water surface of gone
(in &MRAW) Dispersion parameter (land surface area or
water volume)
(ADJl in &MRAW) Maximum fraction of inventory (or value
of G ) which can be transferred
m
Component along x axis of coefficient of dispersion
divided by retardation factor, R,
a
Component along y axis of coefficient of dispersion
divided by retardation factor, R.
Fraction of amount of species sorfoed on solid medium
per unit mass of medium
Fraction of amount of species remaining in solution
per unit volume of solution
{ADJ2 in BMRAW) Transfer rate constant
Storage constant
Gravitational constant
(ADJ in AMRftW) Fraction of inventory transferred from one
receptor pool to another pool per unit time
(in AMRAW) Non-accumulating matrix which retains inte-
grated deposition for current time increment for use
in calculating transfer to terrestrial food products
Pressure head
Total hydraulic head
Intrinsic permeability tensor
Hydraulic conductivity tensor
Scalar limit of K for homogeneous and isotropic medium
Distribution coefficient—a measure of retention of '
species on porous medium
Amount of particular radionuclide released by leaching
during a release time interval, Ci
Ratio of amount leached, M, to the thickness of aquifer
in which leached, Ci/m
XVIX
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o
Pressure at arbitrary datum z
Pressure at elevation 2,
o
RlJ
R2
R2CON
R2TOT
-at
U
v
V, fi V.
i 3
V
fs
V
s
V
time
y
w
a
ZONALO
ZONDEP
Retardation factor
Release increment to Preliminary Input Receptor
Environment Input Receptor inventory by zone
(in AMRAW) Concentration components
(in ftMRAW) Accumulated net total concentration in yCi
per em^ or cm^ by zone and Environmental input Receptor
(DELT1 in Time interval over which environmental
decay constant is applied? also, time increment for
which transfer is calculated
Transmissivity
Pulse velocity
Magnitude of Darcy flux
Components of the Darcy flux
Velocity of fluid relative to solid
Pore (or seepage) velocity
Velocity of solio"
Fluid velocity in the predominant flow direction (= e • v )
Coordinate axis and distance in predominant flow direction
Repository inventory for a particular nuclide at time—
input to AMRAW
Transverse distance from plume centerline
Effective width of plume
Transverse distance corresponding to average concentration
Elevation head
Aquifer thickness
Dispersion allocation factor for air concentration
Dispersion allocation factor for ground deposition
xviii
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6. .
s n
s s
a
T
9
jtection 4 .D.2
BIOPAC
CRATIQ
DELTE
DQSPAC
FAULT
Coefficient of consolidation of the medium
Fluid compressibility
Kronecker delta
Porosity
Volumetric moisture content
Radioactive decay constant
Environmental decay constant—input to M1RAW
L ' cons t ant s
Fluid viscosity
Macroscopic strain tensor
Bulk density of porous medium
Fluid density
Fluid density at pressure p
Incremental pressure in fluid
Dilatation of medium
Saturation of porous media: volume fraction of porosity
which is water-filled
Concentration or dilution to the consumed or exposed
quantity
Transfer coefficient which transforms environmental
concentration in a receptor to corresponding dose
commitment rate to a specified organ,
Subroutine in &MRAW-A for ground water transport
calculations
Same as t in Section 4.D-l time increment for which
transfer is calculated
Dose rate conversion per unit of exposure or consumption
for the specified organ
Subroutine in AMRAW-A which handles the Eelease Model
and provides transfer coefficients used to accumulate
releases to four preliminary input receptors
xix
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GMDEP
RLEACH
R2TOT
TRIHP
TRMAW
VOLINT
Section 4.E.
A2, (t, T, r)
A3l(r)
A32(r)
DC(t, T}
DS(r)
Same as defined in 4.D.I.
Subprogram in FAULT which handles leaching into ground
water
Same as defined in 4,D.I.
Subroutine provides transfer coefficients for transport
from preliminary input receptors to the environmental
input receptors
Subroutine which evaluates transfer coefficients
between environmental concentrations and population
dose rates for various pathways
Amount of exposure or consumption per year
Transfer coefficient for transfer from repository to
receptor j by release mechanism i.
Expectation value for the transfer coefficient from all
release events at time t to receptor j
Time transfer coefficient accounting for radioactive
and environmental decay between release time t and
population dose time T; can account for transport pro-
cesses in receptor j
Local dose transfer coefficient
Nonspecific transfer coefficient
Radiodecay factor between times t (release time) and
T (population dose time)
Local dispersion factor which provides uniform concen-
tration values of a radionuclide deposited in a zone
Same as defined in Section D.I.
Gm(t, T, r)
H(t, T, r)
D
k
Total transfer term to receptor j from other receptors m
Subscript denoting a release event
Environmental receptor of current interest
In subscript refers to geographical zone
XX
-------
•*•
It. (t, T, r) Transfer term representing losses from receptor j to
3 other receptors m
ffi Environmental receptor other than j
Ml{T, r) Local man. dose rate
M2 (T) Nonspecific sian dose rate
P., (t) Probability of release by mechanism i to environmental
^ receptor j during t - at to t
"*" .,.•*•
q(t, r) Activity in Ci at r from nuclide released at time t
r Space variable in rectangular coordinates Cx, y", g)
-*• '23 -*•
R(t, T, r) Activity in Ci/cm or Ci/cm at time T at r due to release
in interval t - dt to t
•*• r. •+
RT(T, r) Total activity for all release times— £ K(t, T, r)
t
S£t, T, r) Net total source term representing total activity at r
in receptor j at time T due to release in interval t -
dt to t
t Release time of radionuclide from waste site to Prelimi-
nary Environmental Receptor
t , Radioactive half-life
I/J,
T Time of interest for population doses
X(o) Amount of nuclide at some reference time
X(t) Amount of nuclide at time of release
Y(t) Radioactivity in Ci at time t for radionuclide of
interest
-+• , •*
Z(r) Fraction of released nuclide deposited at position r
a In superscript to refer to release time
0 In superscript to refer to population dose time
6 (= /dT) Period during which transfer calculation of G
is calculated
X Radioactive decay constant
T Variable r time
w Specific activity in Ci/g of a particular nuclide of
interest
Kxi
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Appendix A
f
M"
Others:
Appendix B
A
B
BIOFAC
C
D
G
M
P
R
V
Width of rectangular plane source
Ratio of amount leached during a release time interval
per unit area of a plane source, Ci/m2
See Section 4.D.I
Soil surface area required to furnish food crops for
one man (ID3™2}
Concentration of radioactivity in beef (uCi/kg)
Same as defined in Section 3.D.2.
Concentration of radioactivity in the milk
Dietary factors that correct the transfer coefficients to
man from those for "reference man" to those for the
population under study (dimensionless)
Radioactivity present in the soil below the root depth
(pci/m2)
2
Radioactivity present on the above -surf ace food per m
of surface on which the food crop is grown (pCi/m2)
Fallout source, which for this calculation was assumed
to be present only at time t = 0 (yCi/m2-d)
Ground deposition source (yCi/m2)
Radioactivity present in the grass compartment (pCi/m2)
Radioactive present in man
Radioactivity present in the subsurface pool associated
with one man's food supply
Radioactivity present in the soil from the ground
surface to the root depth of the grass (pCi/m2)
Radioactivity present at the soil surface (pCi/m2)
Fallout correction factor to account for different
depositions to the above-surface food (S ) , the soil
below this food (S ) , and the pasture (S,5 (dimension-
less) 3
Kronecker delta function '
xxi i
-------
X Turnover rate of the stable isotope of the nuclide in
man (d""-*-} except for Sr where X was isotope-dependent
e
X Radioactive decay rate of the nuclide under study (d )
T, ,. Fraction of the beef herd slaughtered per day (0.00381
beef r3~l\
mi He Transfer rate of milk from the udder (2,0 )
T Amount of meat eaten by a man each day (0,3 kg/d}
T . Amount of milk consumed by a man each day (1.0 i/d)
e/m Crop harvest rate, ra /d
T Fractional transfer rate, crops to soil surface (0.0495
e's fl~l^
2
T . Transfer rate, grass to meat, m /kg-d
2
T Transfer rate, grass to milk, m /£-d
g,c
"" * — ^ i
T Fractional transfer rate, grass to soil, 0.0495 d
Tpfd Fractional transfer rate, soil pool to soil sink, 1.096
x 10~4 d~l
T m Fractional transfer rate, soil pool to man, d
Tr ,d Fractional transfer rate, pasture soil to soil sink, 1.096 x
KT4 d*1
Tr(g Fractional root uptake rate, soil to grassr 2.74 x 10~5 d"1
Ts Fractional transfer rate, soil surface to soil pool,
0.0693, 0.006i3, and 0.000693 d*1 (each problem run three
times once for each value of T listed)
s,p
XXlll
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CHAPTER 1
INTRODUCTION
One of the major environmental concerns associated with the .pro-
jected increase in nuclear power generation is the handling and disposal
of high-level radioactive waste. During operation of a nuclear reactor,
fissioning fuel atoms result in an accumulation of fission products
within each fuel element of the reactor core. These fission products
are isotopes of lighter elements and aiany of these isotopes are radio-
active. Significant examples are Sr-90, Tc-99, 1-129, Cs-135, and
Cs-137. In addition, isotopes of actinide elements, primarily neptunium,
plutonium, americiura and curium, are created because .of neutron absop-
tions which do not result in fission. Approximately one-third of the.
energy-releasing fissions, in a light water reactor (LWR) are of plutonium.
which is created during reactor operation. Periodically, because of
depletion of fuel atoms and accumulation of neutron-absorbing fission
products, a portion of the core must be removed and replaced with fresh
fuel, Reprocessing of spent fuel recovers any remaining uranium and
plutonium for subsequent recycling as fuel. The fission products, small
amounts of uranium and plutonium that are not recovered, and the other
actinides which are not recovered (neptunium, aroericium and curium),
comprise the high-level radioactive waste. If spent fuel is not repro-
cessed, entire fuel elements, including all of the actinides contained,
ultimately become high-level radioactive waste [Ax77]. This waste,
whether from reprocessing or in the form of spent fuel, includes radio-
isotopes having very long half-lives. The waste must eventually be placed
in terminal storage repositories which prevent entry into the"environment
for up to tens of thousands of years.
Management of high-level radioactive waste must insure that the
t
risk of detrimental effects from radioactive contamination of the
environment is less than a level considered acceptable by society in
relation to the various energy alternatives available. The toxic resi-
duals and environmental disruption associated with use of the available
alternatives to nuclear power also constitute a risk to society. Placing
-------
the risk of release of radioactivity associated with nuclear power into
perspective requires recognition of the corresponding risks from the
alternatives.
Assessment of radioactive waste management may be divided into two
categories; 1} risk analysis, which considers both the probability of
occurrence of each of various radiation release scenarios and the conse-
quences of such releases, and 2} consequence analysis, which 'considers
only the consequences of various postulated low-probability potential
release events. In either category, there are various waste management
options to consider and compare: 1) storage in alternate or other type
sitesi 2) alternate waste forms, 3) fuel reprocessing versus disposal
of spent fuel, 4) efficiency of U and Pu recovery in reprocessing, and
5} partitioning of waste into different components for beneficial uses,
transmutation of actinides to fission products in nuclear reactors [Bu?5,
CK.75, Cr77] and/or different terminal storage disposition. Any flexible
assessment model must be applicable to any or all of these.
A flexible assessment methodology is needed for the evaluation of
the various long-term waste disposal methods and management options
[ERDA76a]. State and Federal regulatory and R&D agencies must be in a
position to independently evaluate proposals for waste management acti-
vities in the course of carrying out their assigned functions including
the protection of public health and safety and protection of resources.
In May, 1977, the International Atomic Energy Agency sponsored a
major international conference on Nuclear Power and its Fuel Cycle at
Salzburg, Austria [IAEA77],- which resulted in reaffirmed commitments to
nuclear power as an immediate substitute for fossil fuels and as a
mature solution towards meeting the increasing global energy needs.
The Salzburg conference also focused on the safe disposal of radioactive
wastes from nuclear power as one of the most important parts of the
nuclear fuel cycle that is yet to be fully established and demonstrated.
Presently, most countries that have nuclear power programs are
studying the use of deep geologic formations for the safe emplacement
of radioactive wastes. Only recently, two workshops were conducted to
help provide exchange of scientific information between investigators
-------
•v-.'i'nvolved in assessment work. A workshop on "Geologic Data Requirements
:'.'-for Radioactive Waste Management Assessment Models" [Lo761 sponsored by
\the Office of Waste Isolation for the D. S. Department of Energy (DOE)
/and arranged by The University of Mexico, was held in June, 1976.
'. A followup international workshop: "Risk Analysis and Geologic Modeling
in Relation to the Disposal of Radioactive Wastes into Geologic Forma-
tions," sponsored jointly by the QECD Nuclear Energy Agency and the
Commission of the European Communities, was held in Ispra, Italy in May,
1977 EOECD77],
The United States, Canada, and several countries in Europe have
started modeling and risk analysis studies fOECD77]. in the U, S., as
part of a recently-announced expanded national program in the manage-
ment of commercial nuclear wastes, the National Waste Terminal Storage
Program (NWTS) is underway by the DOE to provide federal repositories
at multiple geographic locations with differing geologic formations in
the continental United States for terminal storage of high-level radio-
active waste [Mc76]. Formations being studied for possible location of
terminal storage facilities include: bedded salt in western and mid-
western states; dome salts in gulf coast states; shales, which are
widely distributed over the country, and a wide variety of granites and
other crystalline rocks and volcanic formations. The Los Medanos area
in the Permian salt basin of southeastern New Mexico is under study for
potential installation of a Waste Isolation Pilot Plant in bedcied salt
[Wr77]. The proposed pilot plant is for DOE trans-uranium waste and
experimental retrievable emplacement of some high-level wastes. The
Battelle Pacific Northwest Laboratories have started the Waste Isolation
Safety Assessment Program (W1SAP) for DOE [Bu76a, Bu77, C£77]; the
objective is to develop methods and generate data necessary to charac-
terize the safety of generic geologic waste disposal concepts which are
to be applied in the assessment of specific sites, At the Sandia Labo- *
ratories, a study is underway for the Nuclear Regulatory Commission
(NRC) for application to repository licensing [Lo76, Ti77]»
The U. S. Environmental Protection Agency (EPA) commissioned The
University of New Mexico (UKM) to continue development and application
of a Radioactive Waste Management Systems Model initiated at in
-------
1972 [Lo74a]. This model, implemented with a computer cede, M4RAW
(Assessment Method for Radioactive Waste), evaluates long-term environ-
mental impact attributable to each phase of the waste management se-
quence. Emphasis in the study is placed on the terminal storage (dis-
posal) phase. These various assessment programs including the UNM study
for the EPA [Lo76r Lo77, Go77] have varying approaches and points of
emphasis. This provides a complementary approach to waste management
assessment and affords greater confidence in final results than would a
single centralized effort. Related work is study of the Oklo Phenomenon
[IAEA75,Bo76] which concerns several natural reactors which existed in a
uranium deposit in Gabon, Africa 1.8 billion years ago. This constitutes
a very old natural repository for radioactive wastes. Most'of the radio-
nuclides were retained in the immediate vicinities of the reaction zones.
As the studies progress, the Oklo data may serve to provide some vali-
dation of the assessment models.
This volume is one of four which report on the DMM radioactive waste
management assessment method and its application. The purpose of this
overall study for the EPA is to complete development of the model for
technology assessment of radioactive waste management, including the
AMRAW computer code, and to demonstrate the model for one model reposi-
tory site. This demonstration includes sensitivity and consequence
analyses for the terminal storage phase, a preliminary demonstration for
the repository operations phase and for terminal storage in another geo-
logic setting. The study also evaluates the feasibility of applying the
model to other radioactive and nonradioactive hazardous materials.
The scope of the study involved approximately 6.5 man-years of
effort. This was interdisciplinary, with the central effort in the
Chemical and Nuclear Engineering Department of The University of New
Mexico and a major component effort in the Economics Department. Support
was provided by the Departments of: 1} Geology, 2) Biology, and
3) Electrical Engineering and Computer Science. Additional supporting
effort was by the Department of Geoscience at the New Mexico Institute
of Mining and Technology and Geohydrology Associates, Much helpful
information was obtained front national laboratories (see the acknowledge-
ments section for details) and individuals who reviewed earlier draft reports.
-------
CHAPTER 2
SUMMARY
A Radioactive Waste Management Systems Model proposed by The
University of Hew Mexico has been developed and implemented under this
contract. The assessment model and associated computer code is called
MCRAW (Assessment Method for Radioactive Waste), She full model includes
the several phases in the waste management sequence: residuals treat-
ment (interim surface storage and solidification) » waste transport,
repository operations, terminal storage, and any other intermediate
phases which may become applicable. The effort during this study has
concentrated on terminal storage, but a preliminary application to repo-
sitory operations is included.
AMRAW is divided into two parts which are run separately;
1) AMRAW-A consists of the Source Term (Inventory at Risk), the Release
Model, and the Environmental Model, and 2) AMR&.W-B is the Economic Model.
AMRAW-&, described generically in this volume, uses externally-generated
values of input parameters for potential geologic and wan-caused release
events, transport from points of release to the environment, environ-
mental pathways to man and calculation of radiation doses.
The radiation dose rates determined by AMRAW-A are input to AMRAW-B,
described in Volume III. The Economic Model in AMHAW-B determines inci-
dence rates of health effects corresponding to calculated dose rates,
determines the associated costs, and attributes these costs to radio-
nuclides, related groups of nuclidesf and to elements initially in the
waste inventory. Initial inventory for the terminal storage phase of
waste management refers to the accumulated quantities at the end of the
repository operations phase. Up until that time, risk reduction options
of improved recovery and/or partitioning may be applied [C&75, Bu?5],
Cr77]. The allocated costs from the Economic Model provide a common
reference base for summing up the consequences of a number of health
effects associated with many different radionuclides, with consideration
of the population affected, agricultural activities, and other factors.
In addition to comparisons between disposal options, feedback of these
calculated costs to the fuel reprocessing and residuals treatment phase
5
-------
provides a basis for comparison of reprocessing and waste partitioning
options. Due to uncertainties in data values and the difficulty in
assigning dollar costs to health effects, calculated results are not
represented as being a precise quantification of damage costs. As use
of the model proceeds and improved input data becomes available, it may
become appropriate to apply the results more directly to cost/benefit
evaluations.
In the model, released radioactive material is dispersed to environ-
mantal input receptors (air, ground surface, surface water, and ground
water) in each geographic zone in a study region around a repository. The
input factors which define the dispersion are determined externally to
AMRAW. Concentrations are accumulated in each environmental receptor
but adjusted during each time increment for transfers between receptors,
radiodecay and buildup and environmental removal processes. In the
results reported in Vols. II and III, most of the cases use a conservative
environmental half-time of 30,000 years in lieu of data to support shorter
times. The corresponding token value of environmental decay constants
is believed here to be unrealistically low and leads to overestimating
the persistance of released radionuclides and the resulting dose rates.
Sensitivity analysis cases reported in Vol. II investigate the effect
of lowering the environmental half-time. Research is needed to deter-
mine nuclide-dependent environmental behavior to justify the use of more
realistic values for environmental half-times and to thereby obtain
improved calculations of estimated environmental concentrations as func-
tions of time.
AMRAW-A calculates the radiation dose commitment rate via pathways
for direct exposure of the population in each zone and for food and
drink pathways. A unique feature of the model divides the pathways and
resulting dose rates into local dose (to the specific local population
groups) and nonspecific dose. The latter is from agricultural products
which are largely exported; the nonspecific population affected is out-
side of as well as within the study region.
The remainder of this chapter applies primarily to the terminal
storage phase. As described in Section 4.C, AMRAW may be run for any
of several release scenarios. When run for a discrete geologic event
(or combination of events) occurring at a specified time, the results
6
-------
. measure of consequences associated with -the event and, time of
/--•-occurrence. Varying the events and-times of occurrence comprises a
"----;consequence analysis. In this mode of operation, the problems of
:.\--predictive geology are largely bypassed, but a number of difficulties -
; do remain. For example, if a volcano penetrates a repository, what
•-fraction of intercepted waste inventory is pushed aside or remains
./within magma in a buried..configuration and what fraction becomes ex-.
palled by volcanic ejection? Further, for the material ejected, what
particle size and chemical form distributions may, be expected? In
cases reported in the other volumes of this report, it is assumed that
one-half of intercepted inventory is ejected without reburial and that
all material ejected into the atmosphere is of small particle size
(effective deposition velocity 0.01 ia/s) , and is of a physical, arid chem-
ical form which is immediately available to environmental processes.
While it is believed here that these are overly conservative assumptions,
research has not been done to provide better data.
When AMRAW is run in a mode which distributes release events pro-
babilistically over time, the results are a-measure of risk associated
with the events and repository properties. Risk is defined as the pro-
duct of the "Probability of an Event" and the "Consequences of the
Event." Varying event scenarios, repository conditions, waste inven-
tory, waste forms, or other factors comprise .a risk analysis. In this-
mode, calculated values of environmental concentrations and dose rates
tor in AMRAW-B, health effects and associated costs) at the various times
do not represent predicted values- For example, a volcanic event with
-12
an estimated rate of occurrence of 2 x 10 /y distributed probabilist-
-12 11
ically spreads the event over l/(2 x 10 ) = 5 x 10 y» Thus, while
the probabilistic method assigns some annual probability of volcanic
explosion and obtains associated radiation dose rates and resulting
health effects to the population, it should be observed that the low
probability means there is only one chance in 500,000 (5 x 10 /I x
6
10 = 500,000) that such a volcanic event would expel material at any
time during a one million year storage period,- The calculated results,
using the probability of occurrence and consequences- of interest such as
environmental concentrations, applicable dose rates or health effects,
give the risk and provide a basis for comparing, options with an objective
-------
of minimizing risk. Another mode in which AMRAW can be run. in the
future is to use data from dynamic repository simulation (see paragraph
4.C.l.d) when results become available from persons developing the ana-
lysis concept,
There are difficulties in predicting geologic events over long
periods of time into the future, Gould [G£65a,G*65b] discusses an out-
moded term: the concept of "substantive uniformitarianisia" which
postulates uniformity of rates or material conditions. This concept,
which assumes that changes which occurred in the past continue invari-
antly through the present into the future, is considered by Gould to be
incorrect in any strict formulation, A concept which assumes spacial
and temporal invariance of natural laws has bee-n termed "methodologic
uniformitarianism." This is a basic mode of inductive reasoning in
various fields of science. Longwell [G&65b3 suggests replacing this
term by "uniformity of process through time," and Gould [Gi65bl suggests
simply; "inductive inference." Workshops dealing with geologic data
for risk assessment [Lo76, OECD77], have considered both gradual pro-
cesses and sudden discontinuous events. AMRftW input data for the pro-
babilistic mode does not depend upon any particular predictive concept
(see Section 4.C). Demonstration of the model to date has depended
largely upon projection of processes of the recent past. As advances in
predictive geology are made AMBAW is ready to accept the data. It should
be recognized that uncertainty in the results increases as the length
of time into the future increases. While absolute predictions of envi-
ronmental contamination and population dose rates are limited by the
geologic uncertainty, as well as other relevant future conditions,
results are particularly adapted to: 1) comparison of management options
for risk reduction purposes, and 2) scoping of geologic event importance
by running the model for ranges of probability or dynamic scenarios.
Uncertainties in probabilities or omissions of events which are expected
to apply equally to two cases being compared tend-to cancel when making
relative comparisons. Sensitivity analysis discussed in Vol. II demon-
strates these capabilities,
Among the various geologic disruptive events is a leaching incident,
in which ground water gains access to a portion of the waste inventory.
The leach rates following the start of a leaching incident are calculated
-------
• as a function of time within AMRAW using radionuclide—dependent input
parameters. A method for estimating the input effective diffusivity
-is presented. Subsequent transport through.the geosphere in ground
water is calculated for appropriate time intervals within AMRAW for
each radionuclide. The paucity of data for distribution coefficients
(K ) for specific sites and ground water qualities introduces uncertainty
d
into the ground water transport calculations. The ingrowth of decay pro-
ducts during ground water transport is presently handled by an approximate
method. One micliete at a time is carried through the AMRAW calculations.
When a particular radionuclide from a decay chain is considered, leach-
ing and ground water transport calculations are first made on the basis
of the average inventory of that species present in the waste during an
increment of leach time. Then the quantity at a given time and distance
is adjusted by a factor which accounts for net decay or ingrowth of the
species, considering the total waste inventory. If precursors have the
leach rate and K as the species of interest, these precursors
appear in the leachant and move along with the species; the calculation
of ingrowth in this case is exact. The method becomes approximate when
precursor leach rates and K values are different than those for the
decay product of interest.
The AM5AW model and code calculates radiological environmental im-
pact for geological and man-caused disruptive scenarios ranging up to
catastrophic events such as volcanic eruptions and meteorite impact,
Whether radiological effects or damages are important relative to the
nonradiological devastation has not been studied. AMRAW calculates
radiological effects from the moment each disruption occurs, assuming
the population stays in place and is not affected by physical violence
of the event. This is, of course, conservative and a more accurate evalu-
ation would insert a phase lag before substantial reinstatement of local
population. This is an area of research which would be very helpful to
risk analysis of natural disasters as well as nuclear risk analysis.
Volume II presents specific discussions of input data sources,
assumptions and limitations for: 1} a base case for a repository in
bedded salt, 2} other cases demonstrating sensitivity and consequence
analyses, 3) a case demonstrating application to another geologic
-------
setting, and 4) application of the model to repository operations
and ground surface storage. Volume III presents corresponding dis-
cussions for the Economic Model. It should be noted that the work coveree
by this report is not represented as being complete in regard to potential
release mechanisms but is intended to demonstrate the degree of flexi-
bility. There is a rapidly changing data base which can be repeatedly-
applied for updating the results. AMRAW is a tool to aid management:
decisions, but it does not replace the need for extensive studies at
each proposed repository site. The model can incorporate results of
such site studies for continuous refinement of results.
10
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CHAPTER 3
CONCLUSIONS AND
The AMRAW model is interdisciplinary and successfully brings together
results from several fields of study for technology assessment of each
phase of radioactive waste management. The model uniquely links each
step from an inventory of radioactive waste through releases into the
immediate environs, transport and dispersion to environmental receptors/
pathway analysis for estimates of resulting dose-to-man, and calculation
of corresponding health effects. This sequence is handled as a contin-
uous calculation with output of intermediate results providing released
quantities, environmental concentrations, doses to population, and num-
bers of health effects. The AMRAW-A. part carries the calculation sequence
through dose rates and the AMRAW-B part picks up from there and calcu-
lates health effects.
AMRAW does not replace but instead uses established models for
various segments of the problem, such as air dispersion, geosphere and
biosphere transport, environmental pathway analysis, and dosimetry. The
existing models or published results from their use, augmented by the
judgements of experts in each discipline are externally used to prepare
extensive input arrays and individual items of factors or coefficients
used in AMRAW. Individual calculation steps in AMR&W generally involve
multiplication of sequences of related factors and adding to accumulate
parallel contributions, plus use of other simple functions for time-
dependent adjustments, While the individual steps are simple, the book-
keeping is quite complex. AMRAW provides a structural means for orderly
processing thousands of data items and keeping track of intermediate and
final results for various forms of output display. Two processes, leach-
ing and ground water transport are handled analytically within AMRAW by
subprograms (KLEACH and CRATIO, respectively). These subprograms depend
upon input data from laboratory and field studies. Other subprograms do
the bookkeeping to process input data for releases (FAULT), transport to
the environment (TRINP) and pathway analysis (TRMAN). Where preferred,
the leaching and ground water transport subprograms can be replaced by
11
-------
alternate subprograms which process input data obtained by external use
of more rigorous codes. This alternate has not been done during this
study but the modular structure of AMRAW provides flexibility to do so,
Applications of AMRAW, presented in Vols. II and III, necessarily
make use of data which has been available early in assessment efforts.
Continuing studies of proposed repository sites in various geologic for-
mations , measurements of site-specific sorption properties, and advances
in predictive geology can provide updated input for AMRAW to refine and
extend the applications. The results obtained to date are not claimed
to represent all disruptive or other release processes which potentially
could occur. However, the probabilistic or risk analysis mode, with
consideration of the most disruptive events envisioned, obtains results
which suggest that only a minor risk is associated with the model repo-
sitory studied. Consequence analysis results indicate that intersection
of a repository by a volcano after 1000 y or later, through highly unlikely/
could result in population doses in areas close to the site which exceed
regmlartory limits but not at a lethal level.
The AMRAW model, developed for applications to various phases of
radioactive waste management, may also be applied to other nonradioactive
hazardous wastes or various pollutant spills. Application to seabed
disposal by redefining environmental receptors and making other modifi-
cations is a possibility through this has not been studied.
It is recommended that improved and more comprehensive data be
obtained in areas of: 1) distribution coefficient (K ) and its dependence
upon geologic media, pH, oxidation potential, and other ground water
properties, 2} environmental decay, which relates to removal and retention
mechanisms which reduce the environmental concentration of a nuclide with
time, independent of radiodecay, and 3) resuspension from land surface
into the air. In addition, improved water usage and hydrologic informa-
tion is needed. New data and improved geologic disruptive event descript-
ions should be input to AMRAW to update the earlier runs.
Preparation of alternate subroutines for leaching and ground water
transport to process data externally generated by other codes is suggested.
There are several types of AMRAW applications recommended for further
work. The model should be applied to various proposed repositories in
12
-------
different geologic media: shale, basalt, granite, and dome salt. Dif-
ferent emplacement methods such as drilled hole matrix: and conventional
mining may affect the results and should be investigated. An application
which can help to place results obtained to data into perspective is the
calculation of risk associated with an undisturbed uranium ore body.
This is a naturally radioactive "repository" of low concentration but
having a large area.
The increase in long term environmental risk if unreprocessed spent
fuel is disposed of as high-level waste, instead of disposing only repro-
cessing waste, should be assessed. Partitioning and transmutation alter-
natives, and improved reprocessing separation should be assessed*
Above all, it is recommended that important categories of .risk
assessment be completed promptly and decisions be made to resolve radio-
active waste management questions.
13
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Page Intentionally Blank
14
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CHAPTER 4
OF
The Radioactive Waste Management Systems Model (Pig. 4-1} has several
parallel paths, each representing a phase in the waste management se-
quence; residuals treatment {interim surface storage and solidification
at a reprocessing plant site)f waste transport, repository operations,
and terminal storage. If other phases become applicable, such as interim
surface storage away from a reprocessing plant site, interim storage as
spent fuel, reprocessing of waste form, and other transportation steps,
each of these simply becomes an additional parallel path in the model.
Implementation of the model is by the MiR&W computer code. The
code runs calculations separately for each branch of the model. Input
data includes a flag {IW} which designates the model branch for which the
data applies. This flag controls routing within the code to handle some
variations in calculations which depend upon the waste management phase
being studied. Most of the current effort is applied to the terminal
storage (disposal) branch (see Part 1 of Vol. II). A preliminary demon-
stration of application to the repository operations branch is included
in Part 2 of Vol. II.
The model is basically a computer simulation or systems analysis
model; a basic assumption is that each system studied is linear, AMRAW
does not replace established models which are in use for various segments
of. the problem, such as air dispersion, geosphere and biosphere transport,
environmental pathway analysis, and dosimetry. Instead, most of the
calculations within AMRAW make use of input arrays and matrices of factors
or coefficients obtained from the established models, augmented by the
judgements of experts in each discipline. Simplified versions of leach^
ing and ground water transport models are used internally, but these as
well as the major model sections (Pig. 4-2} are each contained in sub-
programs, providing for replacement should this become desired. Output
from AMRAW-A is provided at several stages through the model giving cal-
culated release quantities, environmental concentrations, and doses to
population.
15
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PLANT
7
\
RESIDUALS
DAMAGE CHARGES
ASSESSED
RESIDU
TREATM
\
ALS
ENT
/
RELEASE
MODEL
\
/
ENVIRON,
MODEL
\
/
ECONOMIC
MODEL
\
"X
WASTI
TiANSf
\
3ORT
/
RELEASE
MODEL
\
/
ENVIRON,
MODEL
\
/
ECONOMIC
MODEL
/ \
^
REPOSITORY
\
/
RELEASE
MODEL
\
/
ENVIRON,
MODEL
\
/
ECONOMIC
MODEL
L '\
j^
TERMINAL
STORAGE
\
/
RELEASE
MODEL
\
/
ENVIRON,
MODEL
—^
/
ECONOMIC
MODEL
/ \
/
A
3>
IS
I
3>
V
A
Figure 4-1. Radioactive waste management systems model,
-------
AMR&W-& interfaces the component models providing continuous cal-
•. isolations from the Source Term (Inventory at Risk}» through the Release
"Model and the two parts of the Environmental Model (Transport to Environ-
ment and Environment-to-Man Pathways), obtaining output doses to popu-
lation. This output is the major input to AMRAW-B which then calculates
health effects and the corresponding damages in economic units. The two
parts of AMSAW can be linked together for a continous .run, but it has
been convenient to maintain them separately for development purposes and
parametric studies.
Further, AMR&W is a compartment model? a compartment model assumes
that the various components of the system can be lumped into compartments
and that all changes and movements can be accounted for by transfer coeffi-
cients between compartments. The component models shown in Fig. 4-2 deter-
mine the transfer coefficients which link the various compartments and
receptors in sequence. Table 4-1 summarizes the sequence of calculated
quantities and transfer coefficients. In the model, the various compartments
and receptors are split into parallel sets: 1) the inventory divides into
a number of radionuclides, each varying with time, 2) environmental input
receptors are air, land surface, surface water and ground water, and 3)
dose commitment rates divide into local dose rates in each geographic zone
and a nonspecific category explained later, and further divide into dose
rates to various body organs. The are implied intermediate receptors which
are not specifically collected for output. An example is a contaminant con-
centration in food. This is lumped into the environment-to-man pathways
model component which includes a food intake factor and a dose conversion
factor in addition to a food concentration factor, for each pathway and
nuclide. Operated in a risk analysis mode, it is assumed in AMRAW that risk
is defined as the product.- probability of occurrence of an event, multiplied
by the consequences should the event occur,' operated in a consequence
analysis mode, consequences are evaluated for discrete events occurring
at specified times. The mode of operation is dictated by the nature of
the Release Model input data.
The following sections in this chapter describe the AMHAW-A part of
the model, and the component models in AMRAH-A in detail; Vol. Ill
17
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INVENTORY AT RISK
ACTIVITY TRANSFER COEFFICIENT
v
RELEASE MODEL
i?
TRANSPORT TO ENVIRONMENT
4
ENVIRONMENT-TO-MAN PATHWAYS
w
HEALTH EFFECTS
1
DAMAGE CALCULATIONS
DAMAGES
Figure 4-2. One branch of systems model,
18
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Table 4-1. Receptor and Transfer Coefficient
Sequence in AMRAW
Compartment or Receptor
AMRAW-A
Transfer Coefficient
Inventory, grams
Inventory, Curies
Preliminary Environmental
Input Receptors
Environmental Input Receptors
Dose Commitment Rates
Specific Activity
Release Probability and
Release Fraction
Transport to Environment
Environment-to-Man Pathways
M4RAW-B
Health Effects
Economic Valuation of Damages
Health Effect Incidence Rates
Health Effect Costs
-------
describes &MRAW-B (Economic Model).
A. AMRAW-A MODEL
The AMBAW-A part of the AMRA.W computer code may be iron for one or
more branches of the model, depending upon the number of sets of input
data provided. As stated earlier, each data set includes a flag (IW)
which designates the model branch for which the data applies. The dis-
cussion which follows in this volume is based upon the terminal storage
branch, in that the frame of reference refers to the inventory emplaced
in a repository. However, the calculation flow of the model and code
also applies to the other branches. When applications are made to other
branches, programming changes may be needed such as addition of
alternate calculation routing or additional subprograms.
The total period of time to be studied is divided into time incre-
ments each of which is identified by the time (in years} at the end of
the increment. Various time-dependent parameters are averaged in each
time increment as the calculations proceed. The AMRAW code runs one
nuclide at a time, considers one time increment, at a time for calculation
of releases, and follows the migration of each such release increment
through all subsequent time increments "in the environment." Then, for
each time increment, net concentrations are accumulated for all prior
(or coincident) release increments. The number of times and their values,
specified by input data, must be a compromise between calculation resolu-
tion (small time increments) and computer storage, output bulk and running
time limitations {large time increments), Present applications divide
one million years into 50 times with 5 y increments at the beginning,
increasing in steps to 100,000 y increments after 100,000 y,
Each branch of the model (Fig. 4~2) is entered with the mass of
each significant radionuclide in the inventory at risk at each time
(see Section 4.B). This is converted to Curies in the inventory by an
activity transfer coefficient (specific activity). It is assumed that
most of the risk associated with a given inventory of radioactive waste
can be represented by a fraction of the total number of nuclides present,
This is based on the finding that fewer than 25 nuclides represent most
of the total of a hazard measure evaluated for the total inventory. The
20
-------
handling of the nuclide inventory by SMR&W assumes that the total inven-
tory versus time is not affected by movement of portions of the inventory.
That is, as postulated migration proceeds/ the total inventory of. each
nuclide at any time is equal to the inventory if no migration occurs.
This is a valid assumption in itself but it leads to some errors in
estimates of distributions when precursors and daughters do not migrate
together»
The Release Model calculates the probability for release by each of
numerous potential release mechanisms, and the fraction of the inventory
released by each such occurrence, during each increment of time. Ss
described in Section 4.C, &MRJW may be run for any of several release
scenarios: 1} probabilistic distribution of events over time, 2} discrete
event at specified time, 3) several events each at mean time of first
occurrence, 4} dynamic repository simulation, or 5} combinations of these.
Release calculations are totally dependent upon input parameters; MfRAW
does not possess predictve capability for geologic events. Modeling
done externally to AMRAW, plus professional judgement of experts
in fields of geology and hydrology are needed to define the data input
for this part of the AMRRW model. Each event or combination of events
must be defined by the product of one or more time-dependent factors.
During each release time increment, AMR&W determines the fraction of
inventory of a given nuolide released by each event, and superimposes
and accumulates for all events as defined by the input data. This pro-
cess is repeated in turn for each of the environmental receptors; air,
land surface, surface water, and ground water. Uncertainty in prediction
of geologic events appears to be the greatest limitation of assessment
models. Leaching, following contact of waste by ground water, is calcu-
lated within AMRAW by a subprogram. This subprogram indicates relatively-
high leach rates initially, decreasing to a lower constant rate after
some time. Input parameters are based upon short-term leaching experi^-
wents, resulting in error for long-term projections.
Releases as determined by the Release Model are not necessarily
directly to the environment. This is particularly true for deep releases
to ground water. The first portion of the Environmental Model (see
Section 4.D.I) is therefore the "Transport to Environment" section. This
adjusts each release increment, obtaining the contribution-to-
21
-------
concentrations in environmental input receptors at -various times follow-
ing release. These receptors are: air, ground surface, surface water,
and ground water. It is assumed that the environment can. be represented
by these 4 receptors. Increased complexity could divide land surface
into surface and subsurface categories, for examples. The adjustment
provides for dispersion into each of the four receptors in each of the
several geographical zones comprising the study region, and then converts
accumulated activities to concentrations by accounting for dispersion
areas or volumes in each zone. The dispersion to receptors in each zone
uses factors furnished as input data. Mr dispersion factors can be
based upon runs with an air transport code or a simplified analytic
method. A basic limitation here is the predictability of long-term
meteorological conditions. Dispersion associated with direct releases
to land surface is not well modeled at this time; input for current appli-
cations used a simple exponential distribution. The adjustment also
accounts for decay from the time of release to the time being evaluated,
transfer between receptors {such as deposition from air onto ground),
retardation in ground water flow, and other environmental removal or
fixation processes. Ground water transport is calculated within M1R&W
by a subprogram which uses a simplified one-dimensional flow model with
two-dimensional dispersion. This assumes equilibrium conditions for all
related physical processes. Required data includes aquifer porosity,
longitudinal and transverse dispersion coefficients, ground water seepage
velocity, and the distribution coefficient K for each nuciide. Chain
decay for nuclides in decay series is handled by an approximate technique,
If a more rigorous treatment becomes necessary, an external code should
be used to prepare input data for AMRAW. In this case, an alternate
subprogram in AMRAW would be required to process data such as by simple
polynomials.
The last portion of the Environmental Model {see Section 4.D.2)
covers the pathways from environmental input concentrations to radiation
dose to the population, with dose rate calculations for several organs
of concern. This part of the model considers each environmental receptor
in turn and each of two main pathways for each: 1) air: immersion and
inhalation, 2) land surface: direct surface exposure and ingestion of
terrestrial food, 3) surface water: submersion and ingestion of drinking
22
-------
water and aquatic foods, and 4} ground water-, ingestion of drinking
water. In addition, each main pathway is divided into an appropriate
number of subpaths reflecting, for example, various categories of. foods.
Calculations accumulate over the several subpaths under each receptor
and results are not output for each main pathway or subpath. Dose rate
results for paths which affect residents in a particular zone are accrued
as "local dose rates." Examples are from air immersion and inhalation,
direct surface exposure, and ingestion of drinking water. Dose rates
associated with exported agricultural products are accrued under "non-
specific dose rates." Evaluation of each pathway obtains the transfer
coefficient between an environmental concentration and dose-to-man by
considering: 1) a biofactor where appropriate to account for concentra-
tions in food relative to an environmental concentration, 2} a factor
expressing consumption, exposure time fraction, or food production rate,
and 3) the appropriate dose conversion factor. Assumption of a linear
system permits superposition of effects such as environmental concentra-
tions and dose rates from several pathways.
The AMRAW code is structured with sequences of compartments linked
by transfer coefficients (Table 4-1}. The receptors represent the pro-
gress of releases, environmental concentrations, concentrations in food
and drink, radiation doses, health effects and associated economic
damages. The transfer coefficients are evaluated in subroutines using
externally-determined input data. The subroutines can be modified or
replaced, providing a modular arrangement. The philosophy is to keep
AMEAW as simple and straightforward as possible to avoid "black box"
mystery. Factors for dispersion, biological accumulation, dose, etc.,
used in the transfer coefficients, are evaluated externally by various
existing transport and dose codes. Calculation of leach rates and coeffi-
cients expressing ground water transport are both performed analytically
in subprograms in AMRAW, Each of these can be replaced by alternate
subprograms if that need develops. One example of this is the use of a
more sophisticated code for ground water transport. Such a code would be
prohibitive as a subprogram in AMRAW due to excessive computer time when
called thousands of times during a run, but a simple polynomial or other
scheme can be utilized in an alternate AMRAW subprogram to process input
parameters generated externally by the more sophisticated code. The AMRAW
23
-------
code serves SB a vehicle for bringing together data from several disci-
plines in an organized manner.
The calculation sequence used in &MRAW is to consider one nuelide
at a time, carrying each through all of ths calculations discussed above
for the release and transport to environment parts of the model, leading
to net environmental concentrations in each receptor in each sons at each
time evaluated. This is repeated for each nuclide, generating the com-
plete environmental concentration array before proceeding to the
environment-to-raan calculations. For the pathway analysis, each nuclide
is again considered one at a time, at each time o\?er the time period
studied, developing the dose rate arrays,
The following sections of this chapter provide details of each of
the sequential steps in the AMRAW-A part of the code. Section 4.E gives
a mathematical summary of the model.
24
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-B. SOURCE TERM
Assessment of potential releases from a radioactive waste reposi-
tory and the consequences of releases requires a definition of the
quantity of waste present, the quantity of each significant radionuclide»
and the variation with time due to radiodecay. The quantity of material
at risk is the "source term." This is indicated in Fig. 4-2 as
"Inventory at Risk," It should be noted that the "source term" as used
in this study represents the total inventory of each radionuclide con-
sidered, at the various times of interest, whether totally confined
within the repository or whether portions are in transit through the
geosphere and/or biosphere. In some other studies the source term refers
only to quantities released to the geosphere and/or biosphere.
If all of the radionuclides of interest were in simple one-step
decay, initial quantities as input data would be adequate, with
subsequent quantities calculated within the code. However, the actinides
and their daughters, here referred to as "heavy metals/" are in complex
decay chains. The quantities of some isotopes in decay chains increase
over time, reach a maximum and then display a net decrease through
decay as precursors decay. Instead of performing the complex calcula-
tions within AMRAW, they are handled externally by any specialized code
developed for the purpose, and the quantities of each miclide at selected
times are input to AMRAW. In this study, data calculated by ORIGEN, the
Oak Ridge isotope generation and depletion code [Bi73] is used. Currently,
fifty times are used between the start of repository operations and one
million years, with shorter time intervals at the beginning and increas-
ing time intervals later. The times used are specified as input parameters
and may have any desired values, in years. The number of times are
limited only by computer storage, running time, and output cost consi-
derations .
In general, sources of nuclide quantity data do not correspond to
the desired times for AMRAW input. Codes such as ORIGEN calculate gram
quantities at specified times but available output from other studies
usually has different times than those selected for an &«RAW application
and/or have insufficient intermediate values. Adjustment of these times
25
-------
and addition of intermediate values may be accomplished with any adequate
curve-fitting method. Cubic spline functions are a recent mathematical
development and provide an excellent method for curve-fitting. Basically,
the technique involves interpolation by cubic splines such that a cubic
polynomial function is formulated between each pair of data points.
Coefficients are chosen so that the second derivative is continuous
across adjacent points. A cubic spline curve-fitting computer program
developed by Holer (The University of New Mexico Mathematics Department)
and Malcolm [Fr77] was obtained and slightly modified for time adjustment
of nuclide concentration data for this study. The auxiliary program for
the purpose is called "POLYEPA."
The inventory of radioactive waste from spent nuclear fuel initially
includes up to several hundred radioactive isotopes. Many of these are
present in small quantities or have short half lives and do not a
significant contribution to the total hazard, a screening method [Lo74b]
is applied to select the most significant radionuclides over the time
range of interest, to reduce the calculations by AMRAW to a itiore manageable
level. The screening method uses a hazard measure defined as the activity
in Curies of a given radionuclide in a quantity of waste (such as from one
metric ton of fuel) divided by the corresponding Radiation Concentration
Guide {RCG} value [CFR20]. Ingestion hazard uses values for water and
inhalation hazard uses RCG values for air. The ORIGEK code outputs
tables of these hazard measures. Briefly, the screening method consi-
ders numerous times over the full time range of interest. The three
fission product elements and three heavy metal elements with the highest
hazard measure are selected at each time considered. Then the isotopes
are selected which collectively comprise over 99% of the hazard for
each selected element. This method provides representation from the
two major categories of elements in the waste and representation over
the entire period of time studied. During initial work on this study,
a waste blend 80% from enriched uranium fuel and 20% from self-sustaining
Plutonium recycle fuel was assumed. The screening method applied over
a time range of 10 years to one million years selected 7 fission product
isotopes of 6 elements and 16 heavy metal (actinides and daughters)
isotopes of 7 elements. Because of special environmental interest in
26
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C-14 and 1-129, these were added for the repository assessment, making
a total of 25 radionuclides for assessment, listed in Table 4-2.
Table 4-2, Selected Significant Radionuclides '
Fission Products
C~14a Sr-90 Zr-93 Tc-99 1-129 Cs-135
Y-9Q Nb-93m Cs-137
Heavy Metals
Thorium
Series
Cm- 2 44
Pu-240
Neptunium
Series
Pu-241
Ara-241
Np-237
Th-229
Ra-225
Uranium
Series
Am-242m
Cm-242
Pu-238
Th-230
Ra-226
Eb-210
Actinium
Series
Am-243
Np-239
Pu-239
The activation product C-14 is included with fission products.
Table 4-3 summarizes the percentages of total ingestion and inha-
lation hazard measures represented by the two major groups of the 25
selected nuelides and their total. It may be noted that the selected
nuclides represent 96% or more of the total hazard for the fission pro-
ducts group, the heavy metals group and the total of all miclides over
a range of waste age up to one million years. This tine range includes
the peak buildup quantities and the start of net decay for the most
persistent of the selected nuclidesf including Ra-225 which peaks at
between 600,000 and 700,000 years. The small balance from all of the*
nuclides not selected represents less than a few percent of the total
hazard. Values of 100% indicate a contribution from all other nuclides
of less than 0.05%. &MR&W may be applied over any appropriate time-
range i the one-million-year range used in this study does not necessarily
indicate a required isolation period for stored radioactive wastes but
was arbitrarily chosen as a starting basis for calculations.
27
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Table 4-3, Fraction of Total Hazard Represented by
Groups of Selected' Radionuclides, Percent
10
Ingested Hazard
Fission Products 100.00
Heavy Metals 99.5
Total 100.0
Inhalation Hazard
Fission Products 98.2
Heavy Metals 99.8
Total 99 . 7
10
99
99
99
99
100
100
2
.6
.2
.5
.6
,0
.0
Waste Age, Years
3 -4 *5
10 10 10
100.0
97.4
97,4
98.1
98.3
98.3
100.0 100.0
96,7 96,1
96.7 96.2
100.0 100.0
97.7 98.8
97.7 98.8
io6
99.
95.
95.
100.
98.
98.
0
6
6
0
9
9
The activation product C-14 is included with fission products.
Next, discussion of the relationships between the nuclear
power generation scenario and the corresponding waste accumulation is
necessary. Some variation of constituent nuclides in spent fuel occurs
with variations of irradiation history and with the type of fuel. Light
water reactors (LWR) are fueled with enriched uranium in which the
fissile isotope is U-235. However, about one-third of the fissions in
LWR's are plutonium fission, primarily fission of Pu-239 formed by con-
version of U-238 by neutron capture during the fuel lifetime in the
reaction. Recycle of plutonium recovered by reprocessing of spent fuel
results in an increased fraction of fissions of plutonium in an LWR.
A high temperature gas-cooled reactor (HTGR) is initially fueled with
0-235 and utilizes conversion of thorium"into fissile U-233. Slight
differences in the fission yield spectrum for the several fissile species
results in a minor effect on the fission product accumulation as com-
pared to the LWR case. The main result from fuel cycles involving in-
creased plutonium utilization, as in Pu recycle in LWR's or the liquid
metal cooled fast breeder reactor (1MFBR), is an increase in the amount
of heavier actinides such as americium and curium produced by non~
fissioning neutron absorption. If there is no reprocessing of spent fuel,
28
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-:-the spent fuel itself becomes radioactive waste [Ax7711 increasing the
•'•'amount of 0 and Pu to be disposed of by a factor of approximately 200
-:over the 0.5% assumed for reprocessing waste; reprocessing is generally
•assumed to recover 99.5% of 0 and Pu. The amount of waste from nuclear
'••power generation is, of course, proportional to the thermal energy pro-
duced, which be expressed as
where
P = rated electrical power capacity
t = duration of time period
F — capacity factor (average operating fraction of
rated capacity during period)
e,_ = thermal efficiency.
th
-.Any consistent set of units may be used. Fuel burnup is expressed in
terms of thermal energy produced per metric ton of heavy metal in the
fuel loading, A typical design value used for LWR's is 33,000 Mw-d/MT.
-For more detailed discussions of the relations between fuel cycles and
corresponding waste accumulations, the reader is referred to projections
of waste generation by Blomeke, et al. [Bk74, KeC76].
The source term for AMR&W input is preferably based upon a scenario
which details installed capacity of each reactor type versus time,
reprocessing status, interim storage periods, and other factors which
determine the quantities of significant constituent radionuclides [S£77j
placed in a repository to be assessed. The projected quantities versus
time accumulated in the repository are required for assessment of the
"repository operations" phase. The total accumulation is required for
assessment of the "terminal storage" phase. Results calculated for the
repository can then be normalized and presented in terms of damage
(environmental concentrations, dose rates, or other calculated results)
per unit of energy production, per unit of fuel, per reactor year, or
per unit of waste emplaced. It should be noted that estimation of pro-
babilities for disruption of events depends upon the respository size
or area involved for storage of waste. This dependence upon repository
29
-------
size makes it difficult to rim AMRAM for, say, waste from one metric
ton of a particular fuel type. Comparisons between different reactor types,
fuel cycles, reprocessing conditions or other consiaerations can be
accommodated in AMRAW by assuming a modal repository is filled, in
turn, by waste from each system to be compared.
In summary, the source term for AMRAW is a matrix of grams of each
significant radionuclide over a sequence of specified times. This
matrix is prepared externally to AMRAW in accordance with, any nuclear
power scenario to be assessed and furnished to AMRAW as input data.
If this matrix includes the times during which waste is being placed
in a repository, AMRAW may be operated for the "repository operations"
phase as -well as for the "terminal storage" phase. Conversion to Curies
of activity is accomplished within AMRAW by multiplying an item in the
source term by the corresponding specific activity (activity transfer
coefficient in Figure 4-2 } which is input to the code for each nuclidie
considered.
30
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'RELEASE MODEL
first step in the assessment calculations is to determine the
phenomena and man- caused events which are potential mechanisms
: 'release of radioactive materials from the repository. One radian tie lide
•:.:&t-.-a:time is routed through AMRAW-A., The Release Model (see Figure 4-2)
•jajjpvieles transfer coefficients which denote the fraction of the reposi-
'.'i.'tpEy inventory which is released during each time increment; tills be-
.:'. comes input to the Environmental Model. Environmental pathway analysis
vin: -the Environmental Model, described in the next section, uses input
---concentrations in four "receptors"; air, land surface, surface water,
.'•••.arid; ground water. It is convenient for calculation purposes to con-
.::.s.'idar the releases from the geologic formation during an interval of time
';-to-:;four corresponding "preliminary environmental input receptors,"
••;. (figure 4-3} . Release to air represents the initial ejection into an
'-.:-:air, suspension. Release to land surface and surface water is the
^."initial commitment to these areas, and release to ground water is the
^-transfer by leaching into ground water at the point of ground water
.•-'-contact. The "OR" gate symbol in Figure 4-3 indicates that any one or
.'•-'.any combination of inputs constitutes a release from the repository.
;.':Mpre specifically then the Release Model provides values for transfer
^.coefficients to each of the four preliminary environmental input recep-
• -'to'rs. These preliminary receptors should be visualized as being in the
{ :elose vicinity of the repository as a step toward subsequent calcula-
:-'tion of dispersion to the various geographic zones in the study region.
-.'•''-. Careful siting of a waste repository initially provides isolation
.'.-from circulating ground water and chooses a region with predicted long-
;'-.t.enn stability to avoid disruptive changes. There are geologic proces-
•;-;s.es which can occur to disrupt a repository and lead to transport of
-waste inventories, denuding of deposits, or exposure of deposits to ground
-'_-water» Gera and Jacobs [Ge72] considered the following categories:
. -I) catastrophic events, including meteorite impact and volcanism,
2} slow geologic processes, including faulting, erosion, glaciation and
.leaching (followed by ground water transport), and 3) plastic deforma-
tion of the disposal formation by salt or shale diapirism, Man-induced
processes include accidental or deliberate penetration by drill holes
31
-------
w
(0
TO
AIR
A
KLEASETQ
PRELIMINARY EWIFWOTAL
INPUT
OR
1
TO
LAND
RELEASE TO
A
A
RELEASE TO
A
Figure 4-3, Releases from geosphere to preliminary environmental input receptors,
-------
::which provide ground water access , failure of shaft seals left after
'.repository operations r and thermal response to waste emplacement.
The transfer coefficient as a function of time to a given prelimi-
.nary environmental input receptor for a given release mechanism and
radionuclide may be defined as
- PCt) ftl(t), y~ . (4-2}
.Multiplication of this coefficient by the length of a time increment
considered gives the fraction of radionucli.de inventory which is trans-
-f erred during the time increment. As explained in subsequent paragraphs,
there is a flexible interpretation of the two factors in Eg, 4-2,
•depending upon the release scenario. Al (t) generally is the fraction
of inventory transferred if a release occurs, This is the sudden trans-
fer by a rapid event (specified by input data) or the accumulated
-transfer during the time increment of interest by a slow event such as
leaching into ground water (calculated within AMRAW} , P(t) is the
.annual probability of occurrence of release and is expressed as
P(t) = P.(t)P0(t) -•« P (t). {4-3)
1 f. n
To provide flexibility, each component factor of P(t), treated as being
.statistically independent, may be any of five functions:
1} Constant; p {t) = C. Most presently available data on pre-
diction of geologic events are accommodated by this simple
repre sentat ion.
2) Step Function: P (t) = C if t < t
n P
P {t) = C + B if t 2L t ,
n p
where t is the time of change by amount B- This function
applies, for example, to initiation of continuous leaching
following a discrete offset faulting event.
3) Ramp Functions P (t) = C if t < t
n p
P (t) = C + B(t - t ) if t > t
n p - p
33
-------
where t is the time of start of change and B for this
P
function is the slope. This function or the exponential
function (described next) is useful for a gradual process
such as erosion which has a most probable rate and there-
fore a most probable time until exposure (and hence release
via weathering) but also decreasing probability of
exposure earlier by higher rates of erosion.
4} Exponential Function; P (t) = C if t < t
n p
P (t) ~ C + exp[B(t - t )] if t 2-t
n p p
where t is the time of start of change with exponential
P
constant B,
5) Delta Function; P {t} = O for t < t
n p
and t > t
P
P (t) = I/At for t = t
ii P
where t is the time of occurrence of a discrete event and
P
At is the time increment within which t lies. Subsequent
multiplication by At then generates a unity probability
during the increment. This function applies to discrete
events,
Input data used by the Release Model in AMRAW consists of the fol-
lowing for each of the four receptors: 1) the number of release events
or event combinations (currently dimensioned for up to nine events),
2} the number of factors P (t) comprising P(t), specified for each event
{currently dimensioned for up to four factors), 3) specification of the
function type and corresponding values of parameters C, B, and t for
each factor and 4) release fraction Al(t) for each event. For release
by leaching into ground water, an input value for Al{t) is overridden
by a time- and nuclide-dependent value calculated by an AMRAW function
subprogram (DUEACH},
1. Release Scenarios. The structure of the Release Model provides
for making AMRAW computer runs for several release scenarios; 1} proba-
bilistic distribution of events over time, 21 discrete event at specified
-------
/time, 3) several events each at mean time of first occurrence* or
;4-)' dynamic repository simulation. In addition,, combinations of these can
'be accommodated. Available geologic data at the present time provides
/for only the first two of these scenarios.
(a) Probabilistic Distribution. Running AMRAW in a mode with
potential release events spread out over time by probability density
-functions provides a measure of long-term risk, where risk is defined
as
n• v _ / Probability of 1 / Consequences of
I Occurrence I I Occurrence
'.•This mode accrues components of risk from a variety of events during
'.each time increment over the range of time considered. Low probability
events, though not likely to occur within a study period such as 10
/years, are given weighted consideration in evaluation of risk and pro-
• vide for relative comparisons of various waste management alternatives.
Systematic analysis of geologic and man-caused events which may
combine in various ways to result in release of radioactive material
from a waste repository is necessary. Fault tree analysis provides a
'.systematic method for organizing M1BAW input data, through any technique
..which combines events into sets may be used. Symbolism used in fault
trees is shown in Figure 4-4. A simple fault tree, illustrating how
•probabilities combine at AND gates and OR gates is shown in Figure 4-5
.Each path through a fault tree which leads to a release represents a
'. set of conditions existing at a given time which together can permit a
"'.release to occur. Each such path comprises a "cut set," All of the
cut sets in a simple fault tree can be identified by inspection. Each
'•cut set can be represented by a series of probability factors. For
..example, one cut set in Figure 4-5 consists of the right hand input
.'to gate B and, say, the middle input to gate 8 , resulting in outputs
'/Of the OR gates B, and B , satisfying the AND gate A causing output
ii. £, JU
of the top event. The overall probability for the cut set can be ex-
pressed by X1 • X2 • X3» or if preferred &2 • X3-
Fault tree analysis usually considers a constant probability for
•each gate input. In this study, the method has been extended with a
capability to represent each factor in a cut set as a function of time.
35
-------
o
System component or basic fault event.
OUTPUT
INPUTS
OR GATE gate Is In the failed state if
at least one of its Inputs is in
the failed state.
AND GATE This gate is in the failed state
only If all, of its Inputs are
simultaneously In their failed
states.
EVENT DESCRIPTOR. The rectangle is used to
describe the event represented by
a gate.
TRANSFER SYMBOLS. These symbols are used
to transfer an entire part of
the tree to other locations on
the tree.
INHIBIT CASE, This represents an event
which occurs with fixed
probability of occurrence. The
inhibit gate is in the failed
state only if its inputs are in
the failed state and the inhibit
condition has occurred. It is a
special type of AND gate.
Figure 4-4. Fault tree symbolism.
36
-------
OUTPUT
EVENT
I
n
Jl
.„£>
Figure 4-5. Simple fault tree,
3?
-------
The overall probability of each cut set is P{t) with component factors
P (t), previously described. Fault trees prepared for a demonstration
n
application of AMRAW are presented in detail in Volume II of this re-
port and were presented at a geologic modeling workshop at Ispra, Italy
in May, 1977 [Lo77]. The present status of available geologic data
results in large uncertainties ia estimates of probabilities which
affects the calculated risk, but doesn't preclude relative evaluation
of various management options.
Complex fault trees can involve up to hundreds of cut sets; the
number of cut sets increases rapidly with the use of OR gates. MOCOS
is a computer code [Pu?4] which may be used to obtain the cut sets for
fault trees if they are of sufficient complexity to require computer
selection of cut sets. It possesses the capability of determining the
cut sets for up to twenty gates in the fault tree per run. These cut
sets are grouped in the output according to the top gate specified in
• the input and the number of input components which comprise the cat
set. This type of code reduces the possibility of errors and the time
consumed in the determination of cut sets. The output is also easier
to interpret for anyone who is not familiar with fault tree analysis.
The cut sets and failure probability for each input event of the cut
sets may be punched out on cards. This capability of MOOTS allows the
overall failure probability of each cut set to be subsequently deter-
mined and ranked by the use of an additional computer program. This
procedure may provide the ability to consider only those cut sets with
overall failure probabilities above a specified cut-off value. In this
study, fault trees are simple enough to reduce by visual inspection
and the use of MOCUS is not required,
(b) Discrete Events. Running AMRAW in a mode with discrete re-
lease events forced to occur at specific times provides for analysis
of event consequences. Calculated results must subsequently be
weighted by judgment which considers the probability of each such event
actually occurring. This mode does not require estimates of proba-
bilities, but fault trees serve as a convenient display of event rela-
tionships and assist in selecting events or combinations of events to
be considered in consequence analysis. The probability function input
38
-------
^provisions in AMR&W provide for specifying discrete events. A rapid
'•.•'e'^ent occurring at a specific time is simply input as a delta function
v:'.jpius the corresponding release fraction Al. Repeated occurrences are
•'ih'ajidled by additional pseudo cut sets, each with the appropriate 'delta
'-/-•function, to offset faulting event which initiates exposure to ground
:•' : ' ' /
.•falter and results in leaching is input as the appropriate step func-
,-tion, assuming that once initiated the leach incident continues until
•'a.'given radionuclide is depleted by decay and/or leaching removal,
/:X-f rock mechanics studies indicate that a fracture should be considered
-.-.as- closing up or healing after SOUK time elapses, this is handled by
//another factor with reverse step function to "turn off" the leach inci-
dent at the appropriate time.
:/:. ;•'••''• (o) Statistical Mean-Time OaauTrenee, A possible mode of opera-
/-'•tion of AMR&W is to estimate the mean time to first occurrence for each
•postulated event by statistical analysis and then input each of these
-:/as discrete events at appropriate times. No work has been done on
•••this approach during this study? it is expected that more geological
-.-research is first needed,
'•/.:'•'• (d) Dynamic Repository Simulation. This involves geologic mod-
/--.e/ling of tectonic movements, rock mechanics and waste/rock interactions,
/.'to.- represent the gradual geologic processes and thermal effects of
••':waste emplacement. Work on such modeling is beyond the scope of this
••.Study but was started recently at Bat-belle Pacific-Northwest Labora-
-;.;-tories arid at Sandia Laboratories. Preliminary concepts were presented
yby Burkholder (Battelle) and Tierney {Sandia) at the Ispra, Italy geo-
"/.logic modeling workshop in May, 1977 [OECD77, Bu77].
•:':• ;. It may take another year before results from dynamic modeling are
•:ready for input to assessment models, but the flexibility of the AMRAW
-.;.Eslease Model provides for dynamic input now. It is visualized
•'•.here that the results of a large effort in dynamic simulation will ,
^.-produce a graph of release rate, perhaps in Ci/y, versus time. There
/pan-, be such a graph for release to each environmental receptor, and
-,for.-different radionuclides. The graph can be restated as fraction of
-instantaneous repository inventory released per year. Figure 4-6
^arbitrarily illustrates a possible graph in which no release is expected
-;until some future time when small releases occur followed by increas-
ingly disruptive events. This can be input to ABRAW as one "cut set"
39
-------
o;
-
a:
LU
Q.
O
h-
U-l
ce.
10
10"
Figure 4-6
10
TIME (years)
10'
10
Conceptual dynamic repository
simulation response.
with a sequence of step, ramp, and exponential factors represented by
factors P (t) described earlier. An alternate is to break the curve
n
into two or more additive components. Each of these components can then
become a separate cut set with appropriate defining factors.
(e) Example of Release Model Calculations, As an example of
the calculation through the Release Model, consider data from the proba-
bilistic mode presented in Volume II and release of Sr-90 to air as a
result of a volcanic explosion sometime during the time interval 400 -
500 years (after start of repository operations). AMRAW calculates the
average inventory during a time increment as the arithmetic average at
the beginning and end of the increment as illustrated by the example.
This is considered to be more valid than using inventories at the ends
of the time increments. The average inventory of Sr-90 at risk comes
from the source term for times of 400 and 500 years; (7.82 x 10 + 7,85
23 2
x 10 )/2 = 4.30 x 10 g, Multiplying by specific activity, 1.42 x 10
Ci/g obtains 6.11 x 10 Ci. The Release Model obtains from data input
for the volcanic explosion cut set: one factor, a constant, for P{t) =
-12
2.4 x 10 , and the expected value of release fraction Al(t) = 0.075.
40
-------
transfer coefficient becomes
_i y
= P£t)al{t) = (2.4 x 10 ) (0.075)
= 1.8 J£ 1Q~13,
.the release going to the air preliminary environmental input
is
(6.11 x 105Ci>£1.8 x ItT^/yXlOQy) = 1.1 x 10~5Ci -
" 2. Release Barriers. A multi-barrier concept is applied in a
•••gesologie isolation repository to prevent or impede release to and
•••transport through the geosphere to the biosphere. Each of these is
briefly in the following paragraphs.
;••: !';.-•'; ' (a) Geologic S-bz*uatw?&. A site for geologic isolation of ra-
•:;eti.oaetive waste is chosen to provide a stable geologic formation with
rock free of circulating ground waters. In AMEAW, potential dis-
are considered which could change the initial conditions and
waste material or allow ground water to reach the repository
:•::;.'•. : ' (b) Container, Most of the waste emplacement methods under
'/••'.consideration utilize a sealed metal canister to contain a solidified
yfojm of the waste. For rock-melting concepts, the canister is sacri-
/.ficial and is only a temporary barrier. For non-melting concepts, the
.•;caiiister provides a barrier for up to tens of years. In &MRAW, this
vCpntainer is neglected for terminal storage analysis for which a geo-
;iogical time frame is involved.
:';•/. '••[.:•-. (o) Leaah Resistance. A major barrier to release of ncclides
•-into the geosphere is the use of a leach resistant solidified form of
:;wa,sts , such as glass. Leaching occurs only if events occur which per-
:-.irti'-t::f round water to come into contact with laced waste. The next
•.•section of this chapter describes the calculation of leach rates in an
••MiflAW subroutine.
•••."•'. fd) Nualide Retention by Sorption. If release to the geosphere
,• by.; leaching occurs, entry to environmental input receptors requires
;. transport via ground water movement to the biosphere. During the
41
-------
migration, sorption processes such as: adsorption, ion exchange, col-
loid filtration, reversible precipitation, and irreversible minerali-
zation occur, retarding nuclide movement. The ground water transport
model is in the Transport-to-Environment portion of the Environmental
Model, described later in this chapter (Section D.I.).
3, Leaching in Ground Water. Leaching of a waste deposit followed
by transport in aqueous solution is an important process that occurs
prominently in the Release Model and subsequent Environmental Model
particularly for an underground repository storage. The calculation of
leach rates in an AMRAW subroutine applies the leaching model presented
in following paragraphs .
Many studies on the incorporation of the radioactive waste in
solid media [Br74, Gd69, Me73, Me?2, Ra72, Sm69] have included the effect
of time on leaching. The time law expression fA£61, Lu70, We67]
1/2
L = at f + Bt {4-4}
which was developed from studies on the leaehability of commercial
glasses by aqueous solutions [Gv66» Me73] has been used to character-
ize the cumulative amount, L» of the radioactive isotope leached from
the solidified waste for a specified leach period. Here, it is assumed
that the glass matrix does not undergo devitrification. In Bq, 4-4
a and 0 are empirical constants and t is time.
Equation 4-4 shows that the amount leached follows a parabolic
relationship with time at short times and approaches linear kinetics at
longer times. Differentiation of Eq. 4-4 with respect to time yields
which shows that the rate of leaching varies with the reciprocal of the
square-root of time at short times and becomes constant at long times .
It must be pointed out that an accurate evaluation of Eq. 4-4
will require experimental leaching tests to determine the constants a
and P {Gci74, We67, A£61, Lu70] . However, experimental tests may not be
available in measuring a and (J for a specific leach process, in which
case an approximation for L may be employed. For example, various
42
-------
investigations have made use of Fick's laws of diffusion
, Br74, Gd69, Gd74, Gf74, Me73, Ra72, Rt73a, Sro69] as a means of
JJ. Consequently, the diffusional transport model by Gpdbee
[Gd74| , which considers Fickian diffusion with a concentration-
Dependent dissolution rate for sparingly-soluble species , has been em-
ployed in this analysis to describe the amount of radioactive species
•'leaving the solid waste matrix.
•v':/''-- The governing equation and the accompanying limiting conditions
;':'a|S': -.'developed by Godbee and Joy [Am72, Gd74] for the diffusion of radio-
•'•'activity from the semi -infinite solid waste are given by
ox
- c) (4-6)
€ = C t=0rx>0 (4-6a)
C=0 t > 0, x = 0 {4-6b}
C=Cs t > 0, x = » (4-6c)
;.yvhere C is the concentration of the mobile species at any time t and
-::-space x, V is the effective diffusivity for the species, k is a disso-
'.:•..••;••.•.' e
:;'."fut.ion rate constant, and C is the uniform initial concentration of
-.mobile species. The initial concentration of mobile forms of a species
yrt-C-} may be assumed to be at saturation for these forms in the matrix,
•/jnX'addition, the rate of transformation of less mobile forms of the
ysp.ecri.es to more mobile forms can be taken as linearly related to the
•{•concentration driving force {C - C) which is the difference between the
ysaturation concentration and the average concentration of mobile
-visj3ecd.es at any time. The rate referred to is the second term on the
Bright .side of Eq. 4-6. The dissolution rate of the waste matrix
-•-itself is also assumed to be low compared to the migration rate of
.-'.species to the matrix surface, so that essentially there is no moving
,'vbpundary.
'.';.-";••'•:• Equation 4-6 does not consider radioactive decay which takes
..place in competition with the diffusion process and also occurs in the
-------
leachant. Leaching during an increment of time is determined on a basis
of the average inventory of a particular radionuclide as listed in the
source term. Following leaching, a decay factor is applied to account
for radioactive decay. Evaluation of the factor (DECFAC) and its appli-
cation are described in Section D.I. of this chapter.
A method of solution [Da70, Gd74] of Eq. 4-6 involves the intro-
duction o£ a transformation variable
n{x,t) = c - c(x,t)
s
(4-7)
into Eqs, 4-6 to 4- 6c to yield the following corresponding expres-
sons
n = o
t = 0, x > 0
(4-8a)
n = c
t > 0, x = 0
{4-8b}
n = o
t > 0, x = m .
(4-Sc)
Equations 4 - 8 to 4 - 8c may be solved analytically [Da?0],
yielding
n =
1/2
-x
erfc
t)
1/2
1/2
+ exp
1/2
erfc
t)
1/2
+ (kt)
1/2
(4-9)
where erfc y = 1 - erf y
y2
»-2
erf y = — I e dz.
/JT-'o
The error function (erf) is a monotone increasing function ranging
from 0 to 1. Properties and tabulated values of the error function and
44
-------
complementary function (erfc) can be found in texts and handbooks of
' mathematics [Sb70, Kr67 ].
(a) Pv&dictov Equation for Leashing, Direct substitution of
-Sg..' '4 - 9 into lq. 4 ~ 7 gives the concentration of the mobile species
:':'':iii':':the medium as a function of time and space, which is
c- Cs ll~ -exp
exp
k
k \1/2~
iT~ i
e'
sx*f c
-
,_
er~iC
x
2 CO t)I2
e
t /-j_ ^ \ '*•
2/*n A* \ JL^ •**
(V t)
e
- (kt)
1/2
(4-10)
The rate at which the radioactive species diffuses into the leach-
ing, can be obtained by computing the flux J(t) across the interface,
i.e.' -at x = 0. Thus, from Pick's first law [
J(t) = - V
3C
e 3x
(4-11)
x = 0
. total amount of activity accumulated in the leacharit over a period
y'of'•'_-'time is then equal to the time integral of the flux, i.e.
n ft
I a = F | J(t}dt
L n s J
(4-12)
::.y:Wiiere'- a is the incremental amount leached for n leach period renewals.
-v;;:(Notej each time increnent in AMRAW is divided into n subdivisions for
;:::ie;aehing calculations.}
';::::r;:;:;;;-'-^Differentiating Eq. 4-10 with respect to x, evaluation of the gradi-
i^fe^ x ~ °' inss-ting into Pick's Law, Eq. 4-11, and integrating over
x:t;ime.,;_:Eq. 4-10 eventually leads to the following resultant expression :'
(4-13)
:Wftere Lp ~" i &n- The parameter P is the total area of speci-
:;inen, V is the specimen volume, and a is the initial total radioacti-
•'••'.,' O
,.vx-ty of the species subject to leaching. To obtain the corresponding
45
-------
fraction, £, of the initial amount leached, L in Eq. 4-13 is divided
by AQ, i.e.
1/2
o s
1/2 -kt
e
(4-14)
Equation 4 - 13 is thus the predictor equation for the amount of
radioactive species leached from the solidified waste for a specified
leach period (L in Eq. 4 ~4 ) . It should, again be pointed out that
radioactive decay is applied subsequently by use of a decay factor.
Godbee and Joy [Gd74] interpret the application of Eq. 4-13 to that
of a "stable isotope."
It is important to examine Eq. 4 -13 to determine whether its be-
havior is consistent with that predicted by Eq. 4 - 4 . At short times,
Eq. 4 - 13 becomes [Da70, Gd74]
C4-15)
which, for small kt, follows a parabolic relationship as in Eq. 4-4.
1/2
For very long times, erf (kt) approaches unity and Eq. 4-13 becomes
[Da70, Gd74]
L * -2- A CO k)
P V o e
1/2
(4-16)
for the amount leached. As was observed in Eq. 4 - 4 the above equa-
tion (4- 165 also follows a linear relationship with time. Much of
the available results from work on the leaching of glasses [Rt73b, SmG9] ,
especially silicates, reveal that the total amount leached varies with
the square-root of time at short times and approaches a linear relation
at longer times. This is the behavior predicted by Eq, 4-13.
Differentiation of Eq. 4-15 with respect to time when kt is very
small yields
1/2
dL
_E
dt
fP.
-1/2
V o
s
(4-17)
and the differentiation of Eq. 4- 16 with time correspondingly yields
46
-------
<3L F
T^ s ~ A (t? k)1/Z W-18)
dt V o e
s
tiroes Eq. 4-1? predicts the leach rate as a function of the
of the square-root of time; Eg. 4 ~ 18 predicts a constant
at long times. Both cases are consistent with the predic-
Eq. 4 - 4.
use of the effective diffusivity "P as it is applied in
g.:/.;4:-- 6 is appropriate since it is implicitly assumed that the dif-
of the species from the solidified waste can be characterized by
"concentration changes on the diffusing species, in which case
. diffusion is the controlling mechanism, and P can henceforth
to be independent of time, position, and concentration.
this analysis t? is estimated using Eq. 4 - 23, discussed in
l owing section. Subsequently the estimated t? is utilized in
the dissolution rate constant k by iteration via a. curve-
procedure. The value of k is adjusted until the theoretically
profile (e.g., L vs. t plot of Eq. .4 - 13) adequately coin-
with experimentally measured leach data [Gd?4] , Leach data from
-glass by Mendel and MeElroy [Gd74, Me72J is used in this iter-
-procedure. Comparison plots of the experimental amounts of Cs-137
and those predicted by Eq. 4 - 13 from a phosphate -glass product
.'';;av. cement-sludge matrix are presented by Godbee and Joy [Gd74] ,-
is very good,
Estimation of Diffusivity. The kinetic theory of liquids
vis..-;iipt.-as developed as for gases, where the kinetic theory of gases is
:^i^Jtnown [Da70, Pe63, Pr58] . It is not surprising, therefore, that
::;.fJ|isi5re-:-are no satisfactory methods of predicting diffusivities in liquid
v^SteiBsyfrom first principles. Diffusivity coefficients in liquids are
:vabo'Qt;>:fou-r orders of magnitude smaller than in gases and are more diffi-
: -measure [Pe63] .
y::;:;;j::y:y;--Estiination of the diffusivity coefficients is done with the use of
••th^.'/;:St:okes-Einstein relation [Bi60] , given by
47
-------
1 /" 2
where K is the Stokes-Einstein constant equal to 1.38 x 10 g cm /
2
sec molecule °K; |J is the solvent viscosity at absolute temperature
— ^
f °K (2,35 x 10~ g/cm sec at 523°K for water); and it is the radius of
the diffusing particle in can, Eq. 4-19 considers the diffusing par-
ticle to be spherical in shape and also assumes that the solvent, here
taken as water, appears to the diffusing species as a continuum [Bi60].
Using an average temperature of 250°C (523°K), Eq. 4 - 19 simplifies
to
ft 1.88S x 10"17 cm2 .
^e ~ I~ ~d~ (4-20)
The radius FL of the diffusing species is approximated using the
Loschmidt method. Present [Pr58] adequately describes this method,
which assumes that the molar volume in the solid state (M/p) is of the
order of magnitude of N (2R. } , i.e.
* I (4-21)
where N is Avogadro's number (6,025 x 10 - ) j M is the mole-
cular weight of the diffusing species; and p is the mass density in the
solid state in g/cm . Eq. 4-21 simplifies to
-9 3nr
Rk = 5,92 x 10 f - cm {4_22)
which is combined with Eq. 4 - 20 to yield
Pe ~ 3.18 x 10"9 ^*|~" ZSL.' (4-23)
It should be pointed out that Eq, 4-23 provides merely a rough
approximation for the diffusivity coefficient. The Wi lice -Chang semi-
empirical equation [Sk74] , given by
M } 2
f) f Tn irt™-" s era
£e = 6.39 x 10 ^6 -j- (4-24)
u v
is a better relation to use where the solvent is water. Here, T and p
are defined as before (except that \i will have units of centipoise) ,
48
-------
'-is the molecular weight of the solvent, V is the molecular volume of
: i _ 3
solute at the normal boiling point in cm /g mole, and x is an
.^''association" parameter. The association parameter x refers to the sol-
:xysnt and is 2.6 for water [Da?0|. However, there is apparent rigor in
0-enploying Bej, 4 - 24, particularly where it is applied beyond simple
•-Vspbstanees. For example, in estimating V, the contributions of the
Sterns in the molecule are added up in the case of complex substances» and
:'varie subtracted in the case of ring-compounds [Ba?Q], Specific details
••':bf waste form and chemical composition are beyond the scope of this
"•.study, necessitating use of the StoJces-Einstein approximation for deter-
;...mining effective diffusivity D instead of the more accurate Wilke-
:-Chang equation,
'••.• • (G) Example of Leashing Calculations. An offset fault which
;:-results in ground water coming in contact with a portion of the canis-
::ters in the repository inventory constitutes a leach incident, 1MRAW
"•calculates the amount leached during a given release time increment and
.'Obtains the corresponding release fraction Al(t). An example is pre-
sented here to illustrate the steps. Consider a leach incident during
.the/ 'time increment 900 - 1000 years (after beginning of repository
operations), and consider release of C-14 by leaching. The average
V'Wiwentpry of C-14 corresponding to these times, obtained from the source
/term, is {3,64 x 1Q4 + 3.59 x lQ4}/2 = 3.62 x 10 g. This is multiplied
•.:.by;.:.its specific activity, 4.45 Ci/g, to yield the radioactivity, i.e.
(3,62 x 104)(4.45) = 1.61 x 105 Ci.
If this-activity is evenly distributed in a total canister inventory of
62,500 canisters but only one row of 250 canisters is subject to leach-
ing at a time (both values are input to AMRAW), then the C-14 exposed
to leaching, A , is 1.61 x 10 (250/62,500) - 6,44 x 102 Ci. Section
6.B, Vol.. II, describes the canister dimensions, where the total surface
4 2
area per canister exposed, F , is 4.38 x 10 cm (this value assumes
that the;-canister disintegrates into ten parts) and the specimen volume
ET *2
per canister, V , is 2,22 x 10 cm (both values are input to AMRAW).
S
Proctor [Pc66] describes a typical composition of radioactive
wastes from the reprocessing of spent reactor fuel. If, for example,
49
-------
C-14 Is present In the solidified waste matrix as carbonate, for cal-
cium carbonate M = 100 and p = 2.71 g/crn [Pe&3] can be substituted in
Eq. 4-23 to approximate D . *Chus, from Eq, 4-23
V = 3.18 x 10"9 V1PF = 9.S5X1Q"10 2L_-
e I 100 d
This estimated I? is used to determine the dissolution rate constant k
e _3
as described in Section 4.C.3, and is found to be 4.96 x 10 /d. This
determination of $ and k is done externally to AMSAW and the values
e
are furnished as input data. Finally, use of Eq, 4-16 yields the
predicted activity of C-14 leached during the time Interval, t = 100 x
365 dayst
-
2.22 x 10
4 I'" ...... ' ' """ ....... ' •••' •• ' -•'
* 10 (6.44 x 102) {9,55 x 10~10) {4.96 x 10~3)
x
1
100 x 365 + ~
2 4.96 x 10~3
=• 10.1 Ci,
This is the activity leached into the ground water preliminary input
receptor during the time increment of interest.
As performed within AMRAW, the calculation sequence is rearranged
for programming convenience as follows;
2
1) Calculate mass leach rate, gm/cm -d, in a subprogram (RLEACH),
2) Multiply by the areas exposed to leaching, P , and, by the
time interval, t = 100 x 365 d, obtaining grains leached during
intervals.
3) Divide by average inventory during interval (grams), obtaining
dimensionless release fraction, Al{t). This value, calculated
as grams released per gram inventory, also represents Ci re-
leased per Ci inventory.
4) Multiply by annual probability of leach incident, P(t), obtain-
ing the transfer coefficient, A(t).
5) Multiply A(t) by average inventory (1.61 x 10 Ci) and by time
50
-------
increment, t, (100 y), obtaining the release to the ground
water receptor.
:/;--:-'. The calculation may consider either a discrete leaching event com-
•'•:Kiencing at a specified time or may be distributed probabilistically. For
':_•;& 'given time increment, t, an input probability of 1/t when multiplied by
'^duration t generates a unity probability for occurrence, therefore,
•'•'if the probability is 1/t, a leach incident occurs (or continues) and
::.the amount released becomes the 10.1 Ci calculated above. In a
".'probabilistic mode where P(t) is the probability of offset faulting
>'-'(5t»ch as 1.4 x 10 y~ ) , the release on a probabilistic basis is cor-
.':respondingly less.
'/.•;•. • More specifically, the calculation in AMRAW divides a given re-
-'.--lease time increment into 10 sub-intervals (5 if increment is 100 years
;::Q'r- less) , and calculates the average of leach rates obtained for each
-'-.sub-interval}.
-','-.;.'-; 4, Model Output. In suaroary, the Release Model in AMRAW provides
•:.values of transfer coefficients used by AMHAW, for each radionuclide in
vturn, to generate a matrix (denoted by the computer variable R1J) of
^releases in Curies to each of the four preliminary environmental input
'.-•receptors (air, land surface, surface water, and ground water) , during
':-.each of the time increments considered. Subsequent transport to envi-
•','rpBHiental receptors in each geographic gone, adjustments for decay pro-
-ioasses and accumulations for all release increments is handled by the
';:'finvirontnental Model.
-------
D. ENVIRONMENTAL MODEL
The Environmental Model is divided into two parts: 1) Transport to
Environment, and 2) Environment to Man Pathways. The first part uses
releases to the four preliminary environmental input receptors from the
Release Model output matrix and calculates the corresponding concentra-
tions in the environmental input receptors for each of the geographic
zones. The second part of the Environmental Model performs the pathway
analysis and calculates dose to man.
1. Transport to Environment. The Release Model calculates quanti-
ties of each radionuclide, in Curies, released during each time interval
{by probabilistic, discrete event, or other modes}, The releases are
initially collected in Preliminary Environmental Input Receptors {Pig.
4 - 7 ) representing four categories of environmental input: air, land
surface, surface water, and ground water. Several steps are required to
calculate environmental receptor net concentrations for the subsequent
pathway analysis. These steps are summarized as follows and then dis-
cussed in detail:
1} Calculate dispersion of the release increment to the several
geographic zones,
2) Adjust for transfers from each receptor to the other three
receptors,
3) Calculate average concentrations for the activity remaining
in each receptor.
4) Calculate residual activity during each time increment sub-
sequent to release.
5) Accumulate concentrations in each time increment from all
current or prior releases,
(a) Dispersion to Zones, The first step in obtaining environ-
mental concentrations is to allocate the initial releases to each geo-
graphic zone. The relationships for one zone during the time increment
coincident with the release time increment are illustrated in Fig, 4-8.
AMRAW terminology, with subscripts omitted, is shown as labels where this
can be helpful in relating this discussion with other material describing
52
-------
RELEASE TO ENVIRONMENT
LAND
SURFACE
SURFACE
WATER
CI
GROUND
WATER
CI
Figure 4-7,
Preliminary environmental
input receptors.
53
-------
ZONALQ
ZONDEP
OEP
RZ
AIR
ci
LAND
SURFACE
C!
i
f
1,0
^
f
ci/cr
AREAG
DEPGND
Ci
INTEGRATED AIR
CONCENTRATION
IN ZONE, Cly/cm3
RELEASE TO LAND
IN ZONE
Ci
AREAW
UEPWTft
SURFACE
WATER
Ci
Ci
T
RELEASE TO
SURFACE WATER
IN 20H6, Ci
GROUND WATER
IN ZONE
C!
Figure 4-8. Dispersion to a zone during a release time increment.
-------
the code. The first factor, A2, accounts for retardation,, radiodecay, and
.environmental decay effects. Data statements in the program set these
values equal to unity for the first three receptors (air, land surface, and
surface water) for the environmental time increment which is coincident
with the release time increment. For ground water, A2 is evaluated by a
ground water transport subroutine (CRATIO), described later.
The dispersion allocation factors, ZQNALQ, are not calculated
within AMSAW but are determined by application of existing dispersion
models or codes, considering the effective surface areas of land and
iwater in each zone, and are furnished to AMRAW as input data. First,
consider the receptor for air. Any of several codes calculate air
concentrations and ground deposition as a function of distance and
direction from a release point. For a continuous uniform release rate
{in Ci/y}, air concentrations, (Ci/cm }/(Ci/y), and ground deposition
2
rates, (Ci/cm -y)/(Ci/y) can be obtained. The ground deposition rate
is approximately equal to air concentration multiplied by an effective
deposition velocity but the effects of wet deposition cause some vari-
ation from this relationship. If an acute release occurs at some time
within a given release time increment and involves activity equal to
the integrated chronic release for the release time increment, inte-
grated concentrations result which are numerically equal to the chronic
case. Integrated air concentration, (Ci-y/cm )/Ci, and integrated ground
2
deposition, (Ci/cm )/Ci can therefore also be obtained. Acute releases
are assumed in Fig. 4-8 and in AMRAW programming, but it should be
pointed out that the corresponding integrated dose during a time incre-
ment is numerically the same whether a release is treated as chronic or
acute. The air concentration factor, ZONALO, and ground deposition
factor,...ZONDEP, in Fig. 4-8, are simply the area weighted average
values for each zone obtained by an air dispersion code, e.g. [Mo75].
Time increments in AMRAW are generally set to be at least several
years. Therefore, air deposition is relatively instantaneous following
-a release. This is shown in Fig. 4 - 8 as a deposition concentration,
DEP, in:units of Ci/cm . The corresponding deposition on land surface
area in; the zone, AREAG, is ground deposition DEPGND, in Curies. The
deposition on surface water area, AREAW, is DEPWTR, also in Curies.
55
-------
deposition on surface water area, &KE&W, is DEPWTR, also in Curies.
Bext consider the receptors for land surface and surface water.
In addition to air deposition, the fault tree model includes direct
release to land surface and water surface. Mechanisms include ballis-
tic trajectory dispersion from violent events, lava flow, etc. Again,
the allocation factors, ZQNALO, are determined by external modeling
furnished to as input data. Models for this purpose are not well
developed and approximations are necessarily used for current AMRAW
implementations,
The allocation factor, 3QN&LQ, for the ground water receptor is
used as a flag to denote whether or not there is discharge or well water
withdrawal in the with flow front the repository area, a value of
0.0 indicates a direction of the zone relative to the repository such
that contaminated water cannot enter the zone or that other factors
preclude such water from entering the biosphere in the zone, ft value
of 1.0 indicates discharge or use in the zone. In this case, the factor
A2 is the ground water transport factor, calculated by a subroutine
(CR&TIO) for the distance from the repository to the average discharge
point in the zone and for the accumulated transport time for the release
increment. The ground water transport model is described later in this
section.
The initial values of releases after allocation to the zones are
represented by p-2 in Fig. 4-8. At this stags, the inventories are
retained in Curies because further adjustments are required before
conversion to environmental concentrations.
(b) Intev'TQoepto'f Adjustment, Simultaneously with the dis-
persion to the four receptors in each zone, transfers between receptors
occur. For example, surface deposits can be partially resuspended into
the air, or washed off into surface water, ground water can discharge
to surface water, and ground and surface water can be deposited on land
surface by irrigation. These and other transfer processes for a given
zone are shown in Fig. 4 - 9. Resuspension from surface water and
ground water is included in Pig. 4 - 9 as dashed lines; AMRAW checks
for input data related to these transfers but they are expected to be
noncontributors. Air deposition to surfaces is included in the
56
-------
VI
RESUSPENSION
RECHARGE
IRRIGATION
AIR
C i y/cnr
A
LAND SURFACE
Ci
RESUSPENSION
SURFACE WATER
Ci
RUNOFF
GROUND WATER
Ct
t\
LEACHING
DISCHARGE
IRRIGATION
RESUSPENSION
, J
Figure 4-9. Adjustments for inter-receptor transfers.
-------
dispersion calculations previously discussed and does not require fur-
ther treatment in the adjustment sequence. Each transfer process is
visualized as transferring a fraction of one receptor pool, with cal-
culated radionuclicte content, per unit time to another receptor pool?
the untransferred balance then becomes more diluted. The fraction of
inventory transferred from one pool to another (ADJ in AMRRW) is there-
fore represented by the exponential expression
G = E
ra m
1 - expf-Q.5F At)
tn
(4-25)
where E (designated ADJ1 in MffiAW) is input data representing the maxi-
m
mum fraction which can be transferred (<_ 1.0), F {ADJ2 in AMRAW} is a
m
transfer rate constant, and the average time for transfer of portions of
the inventory (average of transfer to the beginning and to the end of
the time increment considered) is one-half of the time increment At
(DELTE in M4RAW). If the rate constant is large, a step transfer
G = E is used. Resuspension into air uses a modified expression
mm
(G is multiplied by land surface inventory and At and divided by land
area} to obtain integrated air concentration, consistent with the units
for that receptor. In this case, E is the resuspension factor. It
should be noted that AHRAW uses input constants developed by externally
applied models or rationale. The result from exercising this step is
the adjusted receptor inventories, R2, in Fig. 4 - 10 .
fa) Convert to Conoentrat-ions, After calculating dispersion
to zones for each environmental receptor and adjusting for inter-
receptor transfers during the release time increment, a simple step
is taken to convert the inventories, in Curies, to concentrations in
each zone, as shown in Pig. 4-10. The dispersion parameter, DISPH,
is land surface area or water volume as appropriate. For ground water,
the dilution volume for the leachant is the effective volume of the
ground water plume flow during the time increment. It is convenient to
convert from Curies to micro-Curies in this step. The concentrations
are accumulated in the matrix R2TOT, The pathway analysis, discussed
later in this section, makes use of the integrated deposition during
each release time increment for terrestrial food products. For this
purpose, deposition is retained in the non-accumulated matrix, GNDBP.
58
-------
'-(APJUSTEp);
R2CON
R2TOT
. ;;y\ -::-- :: :;::;:::;::;:-:;-: ::c-^:ve:v:.:-
^1
uCi y/cm
yCj y
cm
--.-."--.-..-; .'-.-'-•"":""•-.-
.::;:;v:"-:;;-;V::' - '-LAND' SURFACE *
ci
(
106/D
"" """X
SPN
j>
)
.../ 2
yC i/crn
GNPEP
2
yC i /era
2
pC i /cm
Ct
C ,oS,sPN )
Ns . S
7
yC i/cm
(
GROUND WATER
Ci
1/DISPN
yCJ/cm
yd/cm
yd/cm
Figure 4 -10, Conversion of adjusted inventories to concentrations.
-------
(d) Residual Activity in Subsequent Time Increments. The above
discussion describes the step in calculating the net concentrations asso-
ciated with the time increment during which a calculated release occurs.
The next step is to determine the average residual activity during all
subsequent environmental time increments. This requires accounting
for physical and environmental decay and additional transfers between
the environmental receptors. This is followed by summing up, within
each environmental time increment, the residual activities from the cur-
rent and all previous release increments. The sequence for doing this
between two time increments is illustrated in Pig,4 - 11 . The transfer
coefficient A2 is evaluated in a subroutine (TRINP - Transfer to envi-
ronmental input) and includes two factors: radiodecay, and environmental
decay, applied over the time interval from the middle of the previous
time increment to the middle of the time increment being evaluated. The
method used for determining these factors is described in the following
subsection. There are removal and fixation processes that gradually
remove each nuclide from effective environmental movement; these pro-
cesses lead to the concept of environmental decay. It is difficult to
obtain appropriate decay constants to fully implement this provision in
the model.
The air suspension from a release is fully accounted for within the
release time increment and there is no direct residual during subsequent
times (A2 = 0.0, via input of a large environmental decay constant).
That is, any release to the air is deposited on the surface or is swept
out of the study region by air movements within a few days. This is a
very short time compared to time increments of several years or more,
and there is therefore no subsequent direct residual. There is, however,
a resuspension component fed back to the air by inter-receptor adjustment
(land surface to air) for each time increment,
For ground water transport, the factor A2 for each environmental
time following release is evaluated for the cumulative time since re-
lease. This is detailed in a following subsection.
After accounting for the decay processes and the delay associated
with ground water transport, each quantity R2, carried forward to the
subsequent environmental time increment is then adjusted for interreceptor
60
-------
cr>
RZ
RZCON
R2TOT
PHYSICAL ANO
IMVIRONHEMTAL
DECAY
0.0
PHYSICAL AMD
ENVIRONMENTAL
DECAT
ci
6ROUND yATEft TRANSPORT
COEFFICIENT FOR TOTAL
TIME SINCE RELEASI
CI/CI
Ci
CI
ADJUST FOR INTERRECEPTOR TRANS F-ER
CONVERT TO CONCENTRATION COMPQNENTS
_L
ACCUHULATE, INTO TOTALS FOR TIME INCREMENT
wCi"y/cro
nC(/cra
vCI/cm
REPEAT FOR NEXT TIHE INCREHENT
Figure 4-11. Sequence for residual activities in time increments
subsequent to release.
-------
transfers (described earlier and illustrated in Fig. 4-9), converted
to concentration components R2CON (also described earlier and illustrated
in Fig. 4-10), and accumulated in the net matrix of environmental input
concentrations, R2TOT. As indicated in Pig. 4-n , this sequence is
repeated from time increment to time increment, over all time subsequent
to each release increment considered,
Transfer between zones of the region following the initial disper-
sion is not provided in AMRAW, with the exception of ground water which
can have withdrawal for usage in any appropriate zone. Programming for
interzonal adjustment can be added to AMRAW with a sacrifice of addi-
tional computer storage, running time, and input data requirements. At
this time, the unavailability of appropriate data for this additional
model refinement does not justify the additional complexity. However,
transfer from any zone to areas putside_ of the study region can be simu-
lated in &MRAW as presently programmed by appropriate adjustment of the
environmental decay constants. Also, it should be noted that environ-
mental effects which accrue to the population in one zone include any
components which would otherwise accrue to the populations in other
zones if inter-Eonal transfer were calculated.
(e) Decay Factors. The physical and environmental decay fac-
tors used in the calculation of residual activities in environmental
time increments subsequent to a release are described here.
Radiodecay is handled in RMRAW by a decay factor, DECPAC. If all
of the selected nuclides had simple one-step decay to a stable form, an
exponential calculation could easily be used in AMRAW. However, many of
the actinides have complex decay chains with daughters first displaying
a buildup with time followed eventually by a decline. In AMRAW, the
effective decay factor between two times is determined as simply the
ratio of inventory quantities for the two times from AMRAW input data,
This may be done since the decay behavior of any released fraction is the
same as that for the total repository inventory. That is, the complex
decay-buildup equations are done externally by the ORIGEN code, or equi-
valent, which is more accurate than any simple model which could be used
within AMRAW. specifically, the radiodecay factor for carrying
forward the residual activity from one time increment to the next time
increment is the ratio of the average inventory in the two adjacent in-
crements. For example, consider two ten-year increments ending at 80
62
-------
:90 years respectively, and evaluate the radiodecay factor for Sr-90.
-'aver age repository inventory during the first time increment is CX
" )/2, where the X values represent input data: grams of Sr-90 at 70
BO
years (after start of repository inventory), respectively, Simi-
the average inventory during the next time increment, using data
cases in Vol. II, is {Xon + X )/2. Then the decay factor becomes
;.•:: ;•• • • Ow :?U
„__„„ X80 + X90 1.91 x 107 + 1.4B x 1Q?
DECFAC = = - ;£-= — = - 7 - J {4-26}
70 80 2.43 x 10 * 1,91 x 10
= 0.781,
•'jljsing the basic exponential decay relation [My67J , activity - exp (-Mt) ,
lathis factor for a ten-year interval, corresponds to a decay constant of
.,-A-v».;itJ 0.781/(-10) » 0.0247 y"1 and hence a half life of £n 2/0*0247 =
;.v2-0.Q y. This is a reasonable approximation of the literature value of
::;27.'7. It should be noted that the decay factor is dimensionless and
Devaluation by use of nuclide mass is the same as use of activity. When
-;:l5uildup of a radionuclide occurs over a time interval this is automati-
:':;G;ally- accommodated by this method; a DECFAC value >1.0 indicates build-
oli;.,': Also, it should be noted that this method properly evaluates an
?:jej|fective decay factor for nuclides in equilibrium with longer lived
".pa-cents .
iS;:::-;; '/; ground water transport calculations are from the time of re-
• to the beginning and to the end of the subsequent time increment
'jiiriterest and then averaged. The decay factor in these instances is
with inventory values for the corresponding times,
ground water calculations where the time increment of interest
the increment is subdivided and the intermediate values obtained
n the average for the whole time increment. The inventory
each intermediate value of DECPAC is determined by linear inter-
-between inventory values for the beginning and end of the whole
above discussion applies to the terminal storage phase which
- '.releases only after a fixed initial inventory has been accumu-
hen AMRAW is run for the repository operations phase, potential
are calculated only for the repository accumulation period,
-------
Evaluation of DECFAC for environmental times which follow the end of
the accumulation period proceeds as discussed above. However, during
repository operations, the accumulation process masks decay processes
and a modified evaluation of DECFAC becomes necessary. For this condi-
tion, the decay factor is based upon the factor for the first time
increment after closing the repository, with adjustment for the size of
the time increment of interest relative to the reference increment.
This may be illustrated with an example. Consider: 1) a release during
a time increment from 20 to 25 y after start of the repository, 2) re-
pository closing at 30 y, and 3) time increment immediately after clos-
ing is from 30 to 40 y. Then,
DECFAC .
(X40/X3o)
0.5 (1
For Sr-90, this becomes
DECFAC = 0.5 (1 + 4.91 x 1Q7/6,2S x 10?) = 0.891
which for the five year time interval is within 1% of the 0.882 value
which would correspond to the literature value of 27.7 y half-life.
For a long lived nuclide, X, = X , DECFAC becomes 1.0 as it should,
The environmental decay factor is simply exp{-A At), where A is
e e
the environmental decay constant and At is the time interval over which
the factor is to be applied. A is input to AMRAW as ECD with values
for each combination of radionuclide, zone, and receptor.
(f) Ground Water Transport Model . In Section 4.C.2, a multi-
barrier concept is discussed as it applies to a geologic isolation
repository. By selecting a stable geologic structure free from water
penetration and by using a high-integrity container, the initiation of
release of radioactivity can be prevented or impeded. For a hypothe-
tical breaching of the container, the rate of release can be reduced
by selecting a low-leachable solid waste matrix (such as borosilicate
64
-------
- Into which the nuclides are incorporated. In addition to these
'barriers , there is a fourth barrier provided by the geologic
||i^|!uBl--surrounding the repository which can inpede the migration rate of
lcies through the geosphere to the biosphere. Here, an analysis
'-- transport processes of the last barrier is the domain of ground
: transport s t ud ie s .
In considering movement of solutes (dissolved nuclides) through the
geologic medium it is well understood that generally solutes move due
to the connective movement of the transporting solution, in this case
water. In addition, other complex physico-chemical interactions such
as solid~phase sorption, hydro-dynamic dispersion and diffusion also act
to control the movement of solutes relative to the solvent |Br?4] .
effect of these interactions is thus to cause the nuclides to at
generally lower velocities compared to the velocity of the water and*
also taking into account radioactive decay, result in the consequent
reduction of releases to the biosphere £Bu76] .
(1) Flow in Saturated-Unsaturated Porous Media. Consider
the case of instantaneous release of radioactive waste frosts a storage
tank. Essentially this type of release first brings the waste into
contact with the soil moisture moving as unsaturated flow. The pre-
dominant direction of unsaturated flow is vertically downward until the
flow reaches the saturated zone where the moisture content on a volumetric
basis, 6, has reached effective porosity e (i.e., 0 = e) and flow is
mainly lateral, in some sites [EP&75] the unsaturated zone (i.e., 6 < e)
way be sufficiently thin so that interactions during transport may be
considered small. In other sites, like the Los Alamos low-level burial
site {EPA75J , the unsaturated zone may be so thick that it may be diffi-
cult to characterize an interaction between the burial ground and the main
asjoifer underneath,
Consider further a different type of release whereby interconnection
of aquifers by offset faulting (Pig. 4-12} introduces ground water into
the disposal horizon and allows it to come into contact with the inven-
tory of waste (container failure is assumed here for purposes of ana-
lyszs) , -pjje contaminated ground water leachant may then move through
the disposal formation and into the upper aquifer as shown in Fig, 4-12.
65
-------
SURFACE
I
t
AQUIFER
DISPOSAL
DISPOSAL HORIZON
LOWER AQUIFER
FAULT
Figure 4 - X2. Movement of leachant from
disposal horizon to upper aquifer,
For this release scenario, the upward movement through the disposal for-
mation can be considered equivalent to the downward movement unsaturated
flow described previously in the release from the waste tank storage.
(2} Generalized Formulation for Ground Water Transport.
The equations governing ground water transport through saturated-
unsaturated media may be formulated in the most general form by first
assuming that, where flow of both air and water is involved, the air
phase is continuous and is at atmospheric pressure; therefore, there are
66
-------
no air pockets trapped in the main ground water flow system CRe?5j.
The. generalized formulation for flow in saturated-unsaturated porous
media as developed fay Duguid and Reeves [Re75, Du?6, MS] consists of
the following: a) equation of continuity of the fluid, b) equation of
continuity of the solid, c) equation of motion of the fluid, d) consoli-
dation equation for the medium, and e) equation of state for the compressi-
bility of water. Combination of all of these equations will yield one
governing equation for flow through porous media [Re75].
The equation of continuity of the fluid [Co66J is given by
31
where JS is the saturation i.e., volumetric fraction of porosity which is
Bolid, and v is the velocity of ths fluid relative to the solid [Re75J.
j~S
Bird [Bi&O] defines v_ as the superficial velocity, i.e., the volume
rate of fluid through a unit cross sectional area of solid plus fluid.
The velocity of the solid, v is carried here to keep the equations gen-
eral but this parameter is not retained for the simplified formulation
presented later. The term velocity is used here interchangeably with the
Darcian- flux of fluid relative to the solid. The equation of continuity
for imcompressible solids is
JL
at
(1 - e) + 7 • (v (1 - e)) = 0. (4-28)
» s *
Here, the term (1 - e) represents the volume concentration of the solids,
For anisotropic media the equation of motion of the fluid is repre-
sented by Darcy's law [Sc74] given by
v = - K • VH (4-29)
ishere E is the hydraulic conductivity tensor and H is the total hydrau-
lic bead. Generally, the tensor K accounts for directional properties
{anisQtropy} that arise in formations such as layered sediments. It is
defined as
6?
-------
k Pf9
(4-30)
where k is the intrinsic permeability tensor, g is the gravitational
factor, and V is the fluid viscosity. If a continuous sattirated-
unsaturated flow domain exists, then the total hydraulic head H at ele-
vation z, relative to an arbitrary datum z c
manner defined by DeWiest [0w65, Re75], i.e.,
vation z, relative to an arbitrary datum z can be expressed in the
Tj __ __
Z p
O Q
The term p, is the pressure at elevation z,, and p is the pressure
at the arbitrary datum z . Thus H may be written, using consistent units,
as
H = 2 + h (4-32)
where
Pi ~ Pm
where CF represents the incremental pressure in the fluid. Substitution
of Eq. 4 - 32 into Eq. 4 -29 yields the resulting equation of motion
V = - K • (Vh + Vz). {4-34)
X S
Although Eg. 4 - 28 considers the grains of the solid medium to be
incompressible, the granular skeleton of the medium as a whole is con-
sidered to be compressible, in which case the geometric quantities
describing porous media may be functions of certain dynamic quantities,
notably of the existing stress [Sc74J. Thus in a study on the consoli-
dation of porous media, Biot [Bm40] developed the three-dimensional
consolidation equation [Re75] given by
(X + 2n ) ?2T - 72o (4-35)
s s
where X and n are the Lame1 constants, i is the dilatation of the
s s 2
medium, and the term V a represents the total stress. The dilatation
68
-------
is defined as
T = E
Tek
•where 5. . is the macroscopic strain tensor, i.e. of the bulk of the
ium. (In a study of flow through porous media, the flow of fluids
not the consolidation of the medium is of primary interest in gen
;::;..;-. The equation of state for the fluid compressibility g* [Dn68J is,
ifor: ;an isothermal case
Pf = Pf e 1 o = pf e
I' = lpfg. (4-37)
• ' 4>
;3;he.:'p-,, here is the fluid density at pressure p , and 3' is the modified
of compressibility of water. The term h is defined in
: this point a number of functional relationships should be noted
-continuing with the formulation of the generalized flow equa-
-As indicated by Eq. 4-37, the fluid density p is a function of
::j3r.ejs'sure heacL The hydraulic conductivity (often called permeability
;-;piay-:seepage coefficient) and the porosity e are both functions of posi-
pressure head [Re75] , i.e.,
K = K(x, h) (4-38)
e = e{x, h) (4-39)
a position vector. In saturated regions the dependence of
is due or»ly to nonhomogeneity of the medium, and in unsatur
g K varies both with position and time even in homogeneous
to its dependence on pressure head [Re?5].
K and saturation 0 (Eq. 4-27) may be used to define
moisture content 6, such that
69
-------
0{x, h) = 0(x, h) e(x, h) , (4-40)
Eq. 4-40 simply shows that as the medium approaches saturation (0 -> I) ,
the moisture content approaches the numerical value of the porosity of
the medium.
Equations 4-27 and 4-28 can be written first in expanded forms
and then combined to yield the resultant expression
f s £ s
+ ? */p v ) + EV 7 « (0P-) =0. (4-41)
V A itS ' S \ f/
The last term in Eq. 4 - 41 is essentially a higher-order effect and
may be neglected [Re 75], thus
EPf
* p
f vfgj =o. (4-42)
The equation of motion (Eq, 4-34) can be multiplied by p and
the divergence of the result obtained to give
f • (p
f
p K • C?h
(4-43)
When Eq. 4-43 is substituted into Eg. 4-42 the following equation
is obtained
Epf If + ^e if + 0Pf ? ' Vs
p K • (7h -f 7z) - (4-44)
f 1
Eq. 4 - 44 can be simplified by searching for a relation for the
gradient V • v . The porosity may not vary considerably with the
pressure head h, in which case chain-rule differentiation on Eq, 4 - 40
yields
70
-------
30 3#
5T = E 3? ' (4-45)
from which it also follows that
d§_ 3h 30 3h 30 ,„ _
dh a? = E 9k ^ = E 3^ • (4'46)
Assuming a constant modified coefficient of compressibility of water,
3', the fluid density given by the equation of state (Eg;. 4 - 37 ) is
differentiated with respect to time to give
3t H \Kf 3t
(4-47)
The equation for consolidation of the medium {Eg, 4 - 35 ) is seen
as a second-order derivative, and when integrated twice, yields
s + 2ns) T = Q + f (4~48)
where f = f £x, t) , The function f here must satisfy the Laplace equa-
2
tion V f » 0 for all time [Re75] , i.e. this condition enables Eq. 4-48
to transform back to Eq. 4-35 when Eg. 4-48 is double -differentiated
The Lame' parameters A and n are considered constant. For the case
where all the displacement u is in the vertical direction, e.g. u =
u , it was shown [Dw69, Re75] that f = 0. Thus from Eq. 4-48
zz
3T _ ^£
at ~ a 3t
^s+ s
2r\ }. (4-49)
s f
The lumped parameter a is the coefficient of consolidation of the
medium.
Introduce the transformations
71
-------
~ T = ? - u. (4-50)
Now
but since u is considered a continuous function, the operational order
on Eq. 4-51 is immaterial, thus
7 . v = JL (tf • u) « — . (4-52)
The expression for h in Eq. 4 - 33 can be written
a - pfgh
which is substituted into Eq. 4 - 49 to give
T~ = a p g v|- {4-53}
or
a: = a p g, (4-55)
Here, a1 is the modified coefficient of compressibility of the medium.
Eq. 4 - 54 is next combined with Eq. 4 - 52 to obtain V • v , i.e.
, 3h
?- vs » a' ~. (4-56)
Finally, Eqs. 4 - 40, 4 - 46, 4 - 47, and 4-56 are substituted
into Eq. 4 - 44 to yield the governing equation for saturated-unsaturated
flow in porous media
72
-------
dh
—- = 7 ' K • (Vh + Vz)
dt I
{4-57}
terms'a' and p' are defined in Eg. 4-55 and Eq. 4-37, respec-
tively; z is the elevation head defined in Eq. 4-33,
Inspection of Eq. 4-5? shows that it is nonlinear on acccount of
the dependence of both the moisture content 0 and the conductivity tensor
K on the pressure head for unsaturated flow. Furthermore, the disadvan-
tage of such a nonlinear formulation in three dimensions is that in a
large-basin oriented study, the added numerical computational complexity
practically restricts the size of the region that may be modeled.
The following is a discussion of a simplified version of the Duguid-
Beeves solution [Re75] of the generalized flow formulation, giving a one-
dimensional flow with two-dimensional dispersion relation which is adapted
in this analysis,
(3) Simplified Formulation for Ground Water Transport.
Strictly, the governing formulation for saturated-unsaturated flow in
porous media (Eq. 4-57) is .valid for both saturated and unsaturated flow
because the unsaturated region is considered in the movement of the
species from the point of release through the unsaturated zone to the
water table (saturated zone) where flow is mainly lateral. The Duguid-
Reeves transient model [Re7.5, Du76, ANS] is first discussed here before
presenting a simplified version of that model, which is used in AMRMf,
This model and a number of one-dimensional models [Ch69, Kn64, Ls74, Rt72]
were studied to ascertain which predictive method to use in determining
the effects of solid-liquid phase interactions on the movement of dis-
solved nticlides in porous media. The Duguid-Reeves model is now in
"Standards for Evaluating Radionuclide Transport in Ground Water at Nuclear
Power Sites/" American National Standards ANS-2.17 (in review} CANS],
For saturated-iinsaturated flow, both a vertical dimension and a
horizontal dimension are considered, generating a vertical plane. The
equation of motion for the fluid given by Eq. 4-34 along with the govern-
ing formulation for flow (B<5- 4-57} are written together to form a coupled
set of equations
73
-------
- K
(Vh
(4-34)
— a'
e
ee'.fl
3h
dh 3t
= ? • K
(Vh 4-
(4-57)
Prom these equations, a single equation can be written in which the
Darcy flux (v ) appears as a variable, i.e.
3h _
3t " ~ ? ' Vfs'
(4-58)
For a defined position vector x, the conductivity tensor K is a
function of pressure head, namely K = K{h>; this is verified by the form
of Eq, 4 - 38. When flow interactions in the unsaturated zone are
considered negligible (i.e. the unsaturated zone is sufficiently thin),
then only saturated flow in the lateral direction is considered. Thus,
from Eg. 4 - 40 , 0 ->• s as 0" -*• 1» and Eq. 4 - 5? becomes
(a1
3t
K
{Vh + Vz) .
{4-59}
As was pointed out in an earlier discussion in this section, the
conductivity tensor accounts for directional properties (anisotropy) .
If the coordinate system is selected such that it is made parallel to
the principal components of conductivity, then only the principal com-
ponents of the tensor are required [Re75]. Assuming further that the
solid medium is homogeneous and isotropic/ in which case the conducti-
vity will not vary with direction, the tensor K reduces to a scalar
[Bi60, Kr67] , i.e. K •* K. Equation 4-34 thus becomes
fs
and using this result, Eq. 4-59 takes the corresponding form
(4-60)
(a' + 93
3h
- K V - (Vh + ?z)
(4-61)
where a' and B are defined in Eq. 4-55 and Eq. 4 - 37 , respectively
apfg
(4-55)
74
-------
e = epfg (4-37)
In dealing with saturated flow, a generalized storage coefficient
F is defined such that
F = a1 + 6$'
or, using Eqs. 4-55 and 4-37,
F = pfg (a + 68) (4-62)
Substituting Eg. 4-62 into Eq. 4-61, the result is
F ~ = K V •
-------
Consider a confined aquifer of thickness w. Next define a storage
constant P and a transmissivity T such that
F = Fw T = Kw. (4-66)
Substituting these definitions (Eq. 4-66) into Eq, 4-65 yields
Eq. 4-67
V2 H - 5* || . !4-67)
o
Duguid and Reeves note that in using this predictor relation, the boun-
dary conditions of leakage should be applied when appropriate.
For the case of flow through an unconfined aquifer, the modified
compressibilities of both the solid medium («*} and the water ($ ) are
not significant compared to the vertical movement of the free surface
(water table) [Re75]. Thus Eq, 4-67 simply reduces to
7 H = 0 (4-68)
which is the Laplace equation {Kr67J. Equation 4 - 68 is valid for
steady-state flow in confined and unconfined aquifers [Re75].
A further approximation of the equation of motion {Eq. 4 ~ 60 ) for
the fluid velocity v- (also termed Darcy flux in this analysis) can be
obtained next. If the predominant bulk flow is in the x-direction,
Eq. 4-60 along with Eq. 4 - 32 can be written
v
fs
dH
(4-69)
The gradient dH/dx relates to the basic concept of a continuum. Thus,
from elementary calculus [Kr67] Eq. 4 - 69 can be approximated
v
fs x
(4-70)
term AH/^X is the approximate hydraulic gradient in the direction of
the flow {ic-direction); it is constant over the increment Ax for a homo-
geneous, isotropic solid medium.
76
-------
The pore velocity (also called seepage velocity) is obtained by
x
, by the effective
dividing the fluid velocity in the x— direction , vf
porosity [Bi60, Re75].
(4) Simplified Formulation for Radionuclide Mass Trans-
port. A formulation for the general movement of the carrier fluid (water)
has so far been discussed. In order to completely describe the uiove-
ment of dissolved constituents (radionuclides) in ground water through
porous media, a formulation for the mass transport of the radionuclides
must also be obtained.
It was pointed out at the beginning of this section that, with
respect to the migration of radionuclides, these rmclides may have com-
plex physico-chemical interactions with the geologic medium fBt»76] ,
These interactions, which fall tinder the general category of sorption,
can cause the nuclides to move at velocities lower than the carrier
water itself. In general, nuclides (e.g. Th-229, Th-230) are
very strongly sorbed on many geologic media; others (Sr-90, Np-23?) are
moderately sorbed, while nuclides like 1-129 and Tc-99 are sorbed very
poorly, if at all {Bu76, Rt73a],
A measure of the retention of the species on the porous medium is
called the distribution coefficient K, [Bu76, Gf74, Gv66, Lv?2J, In
a
general, K is a function of the pH of the ground water, the concentra-
d
tion of dissolved salts (e.g. sodium chloride), solution temperature,
and in cases , concentration of the dissolved nuclides themselves
{Bu76J « Equilibrium condition are assumed for all relative physical
processes.
Symbolically, K can be represented by
f
m
K = - (4-71)
where f is the fraction of the amount of species that is sorbed
on the solid medium per unit mass of the medium, and f is the fraction
of the amount of species remaining in the solution per unit vol-
ume of solution. The usual units of K are in cm /g. Simply, a higher
K, strong sorption, and conversely; Th~229, for example, has a
d
K, over 10,000, while 1-129 has a K, near zero [Rt73a] .
a a
77
-------
A retardation factor R, is defined such that
d
PK
Rd = 1 + e (4~72)
where p is the bulk density of the porous medium and e is the solid
porosity defined in Eg. 4-39. Here, p must have units of g/cm to
obtain a dimensionless R . The pore velocity is normally divided by R
to obtain a measure of the approximate rate of travel of the radionuclide
(see Eq. 4 - 80 in subsequent discussion).
The most general form of the single species radionuclide mass trans-
port equation for saturated-unsaturated media as developed by Duguid and
Reeves [Du76, ANS] is given by
RJ e IT ~ v ' (8D • ?c) + V • (v,, c)
d 3t fs
*\ a
* (Rd at + A6Rdc) = ° (4"73)
where c is the concentration of the dissolved species, 5" is the dis-
persion tensor, and X is the radioactive decay constant.
In general, for simulation of radionuclide transport, Eq. 4 - 73
may be used together with either Eqs. 4-34 and 4 - 58 or Eqs. 4-34
and 4 _ 59 . Duguid and Reeves {Re75] observed that in a numerical solu-
tion of Eqs. 4-34 and 4 - 58 in conjunction with Eq. 4 - 73, the com-
ponents of the flux will be discontinuous where the advective-transport
term V • (v c) is comparable to or greater than the dispersion term
(second term in Eq. 4 - 73). In the case of fine-grained sediments
where the coefficient of dispersion is small, Duguid and Reeves recom-
mend using Eqs. 4-34 and 4 -59.
The Duguid-Reeves transient model [Re75] employs a finite-
element Galerkin method to numerically solve Equation 4-73 along
with Eqs.4-34 and 4 - 59, for instance. The method was shown to be
superior to other numerical methods previously used, in that stability
was significantly increased. As a result of improved stability, Duguid
and co-worker were able to increase step increments in size and time
accordingly, thereby reducing the computer time and storage core re-
quired. However, the average computing time for this procedure is
approximately 4 1/2 minutes. Because of the computational nature of the
78
-------
ftMRAW code itself, this numerical method was not adapted for use in the
ground water transport calculations in AMRAWj instead, a simplified ana-
lytical solution ie the basis of the ground water transport algorithm
employed in this analysis.
In the mass transport equation (Eq. 4 ~ 73) , it should be pointed
out that the dispersivity D is generally a fourth-rank tensor which
4
contains 3 or 81 components. If isotropy is assumed, however, it can
be related to two constants: namely, longitudinal and transverse dis-
persivities [MIS] , The longitudinal and transverse components of dis-
persivity can be obtained from tracer studies conducted in the aquifer •
under investigation.
The component, D. ., of the dispersion tensor for isotropic media
has the general form' [Re75]
& (a - a }
C4~74)
where 6 . , is the Kronecker delta [B160, Kr67}, am and a are the trans-
it J? i> >
verse and longitudinal dispersiviti.es, respectively? }v is the mag-
nitude of the Darcy flux, and v. and v, are the components of the Darcy
flux. Note that the subscript fs in the previous Darcy flux term (v )
has been dropped for simplicity.
The following major assumptions provide a simplification to the
radian uclide mass transport equation (Eq. 4 - 73) , and form an important
basis for the simplified Duguid-Reeves two-dimensional model itself;
1) the porous medium is infinite , homogeneous , and isotropic with sim-
ple boundary conditions; 2} porous region is fully saturated; 3) sorp-
tion of the dissolved radionuclide species is governed by a linear
relationship; 4) mechanical dispersion is dominant over molecular dif-
fusion; 5) chemical reactions are rapid such that instantaneous equi-
librium exists between the dissolved and sorbed constituents, 6} fluid
flow is uniform and steady; 7} flow is parallel to the x-axis;
8} concentration of the radionuclide species in the soil region is zero
at time equals zero; and 9} a single species without a decay source is
considered.
The use of the second assumption above yields 8-»-e as $-*•!, and
Eq, 4-73 becomes
-------
R . |f- - 7 • CD « 7c) •*• ? • (- c) -f XR e = 0. {4-75}
Q ot, e d
Also, from assumption 6, the Barcy flux v can be considered constant t
thus Eq, 4 - 75 reduces to
R , rr ~ V • (D * 7c) + - • ?c + AR,c = 0. (4-76)
a at e a
If the dispersion tensor is assumed to ' apply to a homogeneous but
anisotropic solid medium, then using assumption 1, Eq. 4-76 aiay be written
in a form giving two-dimensional dispersion with one-dimensional flow as
where the components of the coefficient of dispersion are given in
Eq, - 74 as
v v
D=aT~ D = a — . (4-78)
xx L e yy T e \ i
The term v is the fluid velocity (as distinguished from pore velocity
which was defined earlier as fluid velocity divided by the effective
porosity) in the predominant x-direction of flow; a and a are the
I» T
longitudinal and transverse dispersivities, respectively, and should
be determined from in-situ studies in the aquifer. Dividing Eq. 4-77
by R yields
D. , j v
Ei"Tf U = i~ii- (4-80)
a a
Here, U is called the pulse velocity, and is the approximate rate of
travel of the dissolved radionuclide and can be used to estimate the
approximate travel time of the species [AHS].
Eq. 4-79 can also be written
2 2
DC ^,3c ^3c ,
^ ' \ ~2 ~ Ey 7~2 + Xc ' ° H-81)
3x 3y
80
-------
where
DC _ _§£ _3£
Dt "" 3t 3x *
Hie term Dc/Dt is a special kind of total derivative and is called
the "substantial derivative" or, more logically, the "derivative follow-
ing the motion" of the radionuclide in the x-direction.
Although for saturated~unsaturate<3 flow with two-dimensional dis-
persion the vertical and horizontal dimensions must be considered, the
resulting rectangular plane source approaches that for a line source as
the distance from the source becomes large compared to the source width
[ANS]. Appendix A provides development of the equivalent line source
equation from a plane source equation- Hence, for the instantaneous
release from a vertical line source through the point
-------
this chapter. Separate calculation for one rmelide at a time with Eq.
4-83 or Eg. 4-84, followed by adjustment for decay (or buildup) by DECPAC,
needs some interpretation. If the radionuclide of interest has no radio-
active parent, has a short-lived radioactive parent, or if a radioactive
parent has the same K, as the daughter, the simplified method described
here correctly accounts for decay and for a decay source with no further
adjustment, A short-lived daughter of a long-lived parent may be appro-
ximated by setting the K, value for the daughter equal to K, for the
a a
parent,- the daughter inventory in this case is dependent upon the parent
and in effect, moves with the parent. If both parent and -daughter are
long-lived/ the method described here overstates daughter concentrations
if the daughter faster than the parent and understates daughter
concentrations if the daughter moves slower than the parent. An inter-
mediate value of K assigned to the daughter in such a case can provide
an approximate corrected representation. A complete interpretation of
the validity of these simplified calculations depends upon inspection
of the K, values determined for a specific site for the nuclides in
a
decay groups to be considered in conjunction with water velocities/.
travel distances, and other aquifer parameters. For nuclides where the
travel time to a usage or discharge point exceeds the time range to be
calculated (i.e., K, exceeds a "border value?" see Section 7,A.2,a. in
a
volume II), the calculation method becomes moot.
The definitions given in Eqs. 4 - 72 , 4 - 78 , and 4-80 are used
to write Eq. 4 - 84, relative to the point (x^ = D, y^ = G)
2
(x-k_v t]
2 D
exp -
v t
P
k,v t
3 p
(4-84)
where
M1 1 r
k ^ k = k 4 _±
4ir(aa)VR, 2 Rd 3 Rd
jLi j. ci
k = 4 — M pKrt
4 R. M' = — R. = 1 + —& (4-84b)
d a e
Here, v is the pore (or seepage) velocity (= —I, and z is the aquifer
p \ e / a ^l
thickness. Eq. 4-84 is in a subprogram CRATIO in AMRAW.
82
-------
Equation 4-84 obtains the concentration in ground water at time t,
distance x from the source, and at a distance y from the plume centerline
for specified aquifer and nuclide parameters. At y » Q, the concentra-
tion is a maximum and it drops off rapidly with distance from the center-
line. It is shown in Appendix A (Eq. A-15) that there is a value of y,
where
y = yy = 2.08(aTK}*5 , (4-84c)
at which the concentration calculated by Eq, 4-84 is equal to the average
concentration across the plume width (in the •vicinity of the peak with
respect to time). This is the basis of input to AMR&W-A for the corre-
sponding zone-dependent parameter YY. appendix A also shows that the
effective width (width ~ 2y) of plume where the concentration drops to
0.1% of a valne at the peak, from Eg. A-14, is
t,
y = 10.5 (a x) a , (4-84d)
The value y is input to AHB&W as the zone-dependent parameter YW. The
w
subprogram CRATIO in AMR&W first determines the average concentration
across the plume pe_r Ci released, by using y = y as explained above,
•* 3 y
This concentration is (yCi/exn )/Ci or (Ci/m )/Ci. Next, CRATIO calcu-
lates the volume of water with the calculated average concentration which
seeps past the location of interest during a time increment {or sub-time
intervals). This volume (denoted in CRATIO as GNDD1S or GND1NG) is cal-
culated as the product of the effective plume width y t aquifer thick-
ness z , seepage velocity v , porosity e, and the duration of the time
a p 3
increment. The product of concentration per Ci released, (Ci/m }/Ci;
and the associated water volume, m , is diinensionless (Ci/Ci), repre-
senting Ci passing the location of interest during a time increment, per
Ci released at an earlier time. This product, denoted as CRATIO in sub-
program CRATIO, is returned to subprogram {see previous Section
4.D.l.d and Pig. 4-11) where it is averaged for sub-intervals in the
time increment (see a following paragraph for discussion of sub-intervals)
and adjusted for radiodecay. Finally, the transfer coefficient A2 (Fig.
4-11) emerges for use in the main program, where multiplication of A2
by a quantity released in Ci obtains the quantity in Ci passing the
83
-------
location of Interest during the time increment.
An example calculation is presented here to illustrate application
of Eq. 4-84 and the subsequent calculations in predicting radionuclide
concentrations at usage point, e.g., at 10 km from the repository
area, consider an offset fault which results in ground water coming in
contact with a portion of the canisters in the repository inventory, and
that this event constitutes a leach incident. Consider further that this
leach incident takes place during the time interval 900 - 1000 years
(after beginning of repository operations), and release of C-14 by leach-
ing is being studied. Then, as was determined in the example calculation
for leaching given in Section 4.C.2, the activity leached into the ground
water preliminary input receptor during the time interval of interest is
10.1 Ci. However, first calculates a transfer coefficient norma-
lized to a 1 Ci release and then applies the coefficient to the calcu-
lated release.
Next consider that the contaminated ground water, normalized to a
1 Ci release, enters an unconsolidated aquifer with the following pro-
perties taken from the application in Volume II: v =1.46 m/yi e =
3 -P 3
0.15; a = 50 m; a = 6 m; p =2.3 g/crn ; z ~ 50 m; and K = 1.4 cm /g.
Ij T ad,
The C-14 concentration is to foe determined at a usage point x =* 10,000 m
after a time in the environment, assumed here for illustration, of
k
160,000 years. From Eq. 4-84c, y = 2.08{6 x 10,000) = 510 m. The
retardation factor can be immediately estimated using Eq. 4-72: R =
1 + (2.3) (1.45/0.15 = 22.47. Then from Eq. 4-84: M1 = 1/50 = 0.020
k 7
Ci/m; k = (0.020) (22.47)/(4 TT (50 x 6} 2) = 0.00208 Ci/m ; k2 « i/22.4?
- 0.044; k, = (4) (5Q}/22,47 = 8.9 m; k = (4) {6)/22.47 = 1.07 m.
-J ^J
Substituting these values in Eq. 4-84, yields the C-14 concentration
prior to accounting for decay.
c = 0.00208 Ci/m J [10,000-(0.044){1.46}(160,000)J2 m2
(1.46 m/y)(160,000 y) '" |(8.9 m){1.46 m/y){160,000yj
[510]2
(1.07 ra)U.46 ra/yHl&Q,ODQ
-9 3
(8.90 x 10 Ci/m ) (0.340)
84
-------
= 3,03 x 10~9 ci/m3
= 3.03 x 1(T9 yci/cm3 .
The example calculation is continued after first discussing travel time
and the use of sub-intervals of time in AMRAW.
The travel time of the C-14 at the emergence point can be approxi-
mated using the pulse velocity U defined in Eq. 4-80:
U - v /R = (1.46 m/y)/22.47 = 0.065 M/y. Then,
approx, travel time = ^~^e—7~~ ~ 154,000 y.
Thus, it would tales approximately 154,000 y for the maximum concentration
"peak" of C-14 to occur at a distance of x = 10 km.
It is helpful to describe the procedure in estimating the average
radionuclide concentration in ground water in MLEAW. Presently, as
specified by input data for applications in Volume II, fifty times are
used from the start of repository operations up to a time horizon of a
million years, with shorter time increments such as 5, 10, 100 and 1,OOO y
at the beginning anfl increasing time increments later, such as 10,000 and
100,000 y. Results of preliminary sensitivity analysis runs on the ground
water transport model discussed in Section 7.a of Volume II indicate that
generally the width of the radionuclide concentration peaks at half-
height is more than 2,000 y. This means that for time increments up
to 1,000 y (e.g., 9,000 ~ 10,000 y), the average nuclide concentration
is simply taken as the arithmetic average of the concentrations calcu-
lated at the beginning and end of the time increment (e.g., at 9,000 and
10,000 y). When the time increments are 10,000 y or higher, however,
this simple averaging procedure would be in error because for these large
time increments, narrow peaks associated with low K, values can be
d
"missed," Hence, in each time increment of >_ 10,000 y is sub-
divided into 1000 y sub-intervals if K, < 1 and each increment > 100,000
d
y is subdivided into 1000 y sub-intervals if K < 1 and into 20,000 y
sub-intervals if K > 1 (broader peaks permit longer sub-intervals)» The
concentration is calculated at the end of each time period, and the
average concentration is obtained by dividing the sum of all these
85
-------
calculated concentrations by the total number of time periods in the
increment. AS discussed in earlier Paragraph 4.D.l.e/ a decay factor
DECFAC is applied to account for radiodecay in all of the components for
average concentration calculations. To illustrate the application of
DBCPAC, continue the example calculation where it is found that the aver-
age concentration of C-14 in a plume 10 kin from the repository after
160,000 y following release of 1 ci during a leaching interval from 900
-9 3
to 1000 y, and prior to accounting for decay is 3,03 x 10 yCi/cm .
The inventory values for C-14 at times of 1000 y, 100,000 y and 200,000
4 -1 -6
y are 3,59 x 10 , 2.26 x 10 and 2.28 x 10 g, respectively. By linear
interpolation, as performed within &MR&W, the approximate inventory at
-2
160,000 y is 9.04 x 10 g. The decay factor beeouses siatply
DECFAC = 9-04 x lo" /3.59 X 1Q4 = 2.52 x icf
and the concentration corrected for decay during transit becomes
. C «* (3.03 x 10~9}(2.52 x 10" } = 7.64 x 10 pCi/cm (or Ci/m )
still normalized to a 1 Ci release.
The effective plume width, from Eq. 4-84d is y = 2,570 m. The
w
time sub-interval for the 100,000 to 200,000 time increment and K =
1.4 > 1.0, in accordance with the above discussion, is 20,000 y. Hence,
the associated water volume is
H 3
GNDINC = 2,570 x 50 x 1.46 x 0.15 x 20,000 = 5.63 x 10 m .
Multiplying by the average concentration obtains the activity passing
during the internal,
CRATIG = (5.63 x 10 ) (7.64 x 1Q~15} = 4.30 x 10~° Ci
=4.30 uCi .
In subprogram TRINP, the above calculation is called for all sub-intervals
in the time increment and averaged to obtain the transfer coefficient
(A2) for the time increment. If we consider only the sub-interval for
illustration, the main program obtains the corresponding activity trans-
ported following the 10.1 Ci calculated release as simply
86
-------
(10.1}(4.30 x 10 6) = 4.34 x l(f5 Ci .
Also, the main program establishes average ground water concentra-
tions, after accumulating contributions from all releases and adjust-
ing for transfers to other receptors, by dividing the net activity by
the associated water volume for the time increment of interest.
(g) Accumulate Conoentyat-iona. The product of the Transport-
ta-Ejwironmerrfc portion of the Environmental Model is a matrix, R2TOT,
of net total concentrations accumulated for each of the four environ-
mental input receptors, and the land surface deposition matrix, GNDEP,
for each zone of the study region, at the end of each time increment
considered. This matrix furnishes the environmental concentrations for
use by the second part of the Environmental Model which performs the
pathway analysis and calculates dose to man.
(h) Sample Calsulations, In Section 4.C.1, a sample calcula-
tion is given for the probabilistic release to the preliminary environ-
mental input receptor for air during the 400 - 500 y interval as a
result of volcanic explosion. The release is 1.1 x 10 Ci, representing
a quantity, RlJ, released to the air in the immediate vicinity of the
repository from either an instantaneous pulse or a slower release over
period of time within the time increment. A sample calculation is now
given to illustrate the steps in obtaining the corresponding environmen-
tal input concentrations in Zone 2, using data from the base case des-
cribed in Vol. II, by the Transport-to-Environment part of the Environ-
mental Model.
Figure 4-13 uses appropriate portions of Pigs. 4 - 8,
4-9, and 4- 10, and illustrates this sample calculation. Consider
first, the airborne component. A2 has a value of 1.0 indicating no decay
for a time interval coincident with the release interval. Use of an air
dispersion code, externally to AMRAW, obtains the integrated concentra-
tion per unit release in Ci-y/cm -Ci, in various grid subdivisions
of Zone 2. The weighted average in the zone in this example is ZONALQ -
5.31 x 10 , a value input to &MRAW, which represents the average
integrated concentration from a diffused unit release pulse moving across
87
-------
I1J
A2
ZQMALO
R2
ADJUST
K2
ADJUSTED
*
1. 1
AIR
x 10-*
C i
. I '
r
IOKOEP
^
t
i.f3 x IfT15
Ci
cm2-C!
2.12 « ID"20
AREAG
R2TOT
RESUSPEHS !OM
(2,1k x 10'27!
RELEASE TO LAND
IN ZONE,
2.14 x 10'6
CI
X 10
Ci
^6
03
M I
O
+J O
U
J-I-H
4J M
J3 -H
C
-H O
-M
r-i
W Q)
d W
0) 03
O
G-H
0) CO
o
CP r-J
U 04
Vj
P O
tfl -H
^ W5
rt O
•H >
M 3* Vi
-H o a>
r0 ^1 -M
H C
O O -4
fl)
4J CM g
M -H
O 0) -M
|*5, g
W O >!
d ^*3
rt o
J-i C o
EH -H in
- 1
«=}•
3)
M
fc*
8,81 E-20 (x 32.6}
8.7S E-1J U 40.3)
88
-------
—5
the zone. Then, for the given release of RlJ = 1.1 x 10 Ci, multiply-
ing by A2 and ZGNALO obtains the integrated air concentration in the
—2& 3
zone of M2 = 5.84 x 10 Ci-y/em . Next, this is adjusted for any
transfers in from other receptors, in this case as resuspension from
land surface. Removal from the air need not be performed at this point
since this taken into account by the external air dispersion code,
The resuspension integrated concentration {explained below) is 2.14 x
-27 3
10 Ci-y/cm which when added to the airborne plume component yields
-27 3
a total or "adjusted" value of R2 = 2,70 x 10 Ci-y/cm . Note in
passing that resuspension dominates the air concentration. Multiplying
by 10 converts units and obtains concentration of R2COH = 2.70 x 10
yCi-y/crn , also accumulated into the net total air concentration R2TQP =
-21 3
2.70 x 10 yCi-y/cm , The term "accumulated" is used here because
the code goes through this process for each receptor. For air, however,
integrated concentrations do not carry over to a subsequent time incre-
ment ? the code sets R2 = 0 to accomplish this beyond the present illus-
tration.
Next, consider the ground deposition onto land surface, again
referring to Pig. 4-13. From air dispersion code calculations, the
average deposition per unit release is the input value ZONDEI1 = 1.93 x
—15 •? —5
10 Ci/cm -Ci. Multiplying this by the release RlJ = 1.1 K 10
~20 i
Ci obtains ground deposition DEP = 2.12 x 10 ci/cm2 . Multiplying
14 2
by the area of ground, AREAG = 1,01 x 10 cm (equal to dispersion
area for acne, DISPN) yields the total deposition in the zone, DEPGND =
2.14 x Id""" Ci, which is carried into the receptor R2. It is here that
any other events releasing directly to land surface are added to R2
(omitted from this example for simplicity). The "adjust" step transfers
a small fraction of the land surface inventory into the air, This re-
3 2
suspension factor is Ci/cro air concentration per Ci/cm ground concen-
-9 -1
tration. The value input as flDJi (E in Eq.3 - 25) is 1, K 10 cm ,
m
and it is applied as a step transfer by making ADJ2 (F in Eq.4 - 25)
sufficiently large (= 20), Then, the integrated resuspension eoncentra-
-6
tion is the zone land surface inventory, R2 = 2.14 x 10 Ci, divided
14 2
by the zone land area, 1.01 x 10 can (giving ground concentration),
-9 -1
multiplied by the resuspension factor, 1 x 10 cm (giving air con-
-------
centration}, and multiplied by the duration of the time increment, 100 y,
giving the integrated concentration, 2.14 x 10 ei~y/em » which is
consistent with the units used for the air receptor. Continuing with
the land surface receptor, the small amount of material which continu-
ously cycles through a resuspended status is a neglible removal and the
"wf-%
adjusted R2 for land surface is also 2.14 x 10 Ci, Multiplication by
*r -| A O
10 and division by land area DISPN = 1,01 x 10 can obtains the eon-
-14 1
centration, R2CON * 2,14 x 3.0 pCi/cm . This concentration is the
current time increment deposition, GNDEP, used subsequently for terres-
trial food pathway calculations, and is also accumulated into the net
total land surface concentration, S2TOTt used subsequently for direct
exposure pathway calculations. Residuals from each previous release
increment are carried forward (see Pig. 4-11 for the steps) , consider-
ing physical and environmental decay and inter-receptor transfers, and
the release increment discussed here is carried forward to subsequent
environment time increments. Each such increment makes an additive
component to the resuspension air concentration, and the net total,
R2TOT, increasing the air and land surface concentrations to larger
values than shown here in this sample calculation for one release incre-
ment.
Similar calculation steps apply to releases to the other environ-
mental receptors. The deposition to land surface illustrated above is
handled in the same way for deposition onto surface water of area,
(see Fig. 4 - 8), giving deposition onto water, DEPWTR, which when
divided by the water volume yields the concentration in water,
A sample calculation for transport in ground water is included in the
earlier Section 4.D.1- (f).(4).
2. Environmental Pathways. The second part of the Environmental
Model is the Environment-to-Man Pathv/ays Model, in which pathway analysis
is performed and dose equivalent rates to man are calculated. In dis-
cussion that follows, frequent use of AMRAW nomenclature is used as an
aid in correlating with associated input data which is required. This
model is entered for each increment of time with the calculated con-
centrations for each environmental input receptor. These concentrations,
90
-------
TO m
AIR
-.-y
O
K
UJ
T
""s5*
O
H-
<£
1C
2
n 1
r
i'_
O
UJ
DC
["•"*)
LAND
SURFACE*
U4
ee
o
O,
X
UJ
z
o
H
til
t£>
*--L
_
UF i
SURFACE
WATER
_J
I-
I
\
t
i
f
f
t
h
r
zf
™_l
"V*
5§
"V trnlt-1
JJ
^jy
o
CO
QC
•tl
A
^»
q
s-
u
GROUND
WATER
Q
O ss:
O
UL
u
fr— 4
J
o
1—
CO
LU
to
«z
«
1
w
DOSE TO MAN
-For Land Surface, the net total accumulated concentration applies to the Direct Exposure pathway,
and current deposition concentration applies to the Terrestrial Food pathway.
Figure 4 - 14, Main environme.nt-to-man pathways.
-------
as determined in the Transport-to-Environment Model discussed previously,
are:
1} Air. Integrated air concentration, R2TQT, uCi-y/cm ,
2) Land Surface.
2
a. Accumulated ground concentration, R2TOT, yCi/cm ,
b. Integrated deposition for current time increment,
GNDEP, pCi/cm ,
3} Sur£_ace^Water _. Accumulated water concentration, R2TQT,
yCi/on , and
4) Groun_d^Hater_, accumulated ground water concentration at
point of use, R2T0T, pCi/cm .
The matrix, R2TOT, contains the net total concentrations accumulated
for each of the four environmental input receptors, for each zone of
the study region, at the end of each time increment considered. Simi-
larly, GNDEP is the land surface deposition matrix for each current time
increment.
There are a number of potential pathways through the environment
from the input concentrations to radiation dose commitment to man,
Fig, 4-14 shows the main pathways. For each of the first three recep-
tors , the first main pathway (mode 1) involves external dose sources and
the second main pathway (mode 2} involves internal dose sources. For a
specific site, the ingestion pathways from ground surface and surface
water to food and drink are each subdivided into a number of subpaths
for the various categories of terrestrial and aquatic foods as appro-
priate. In fact, in AMRAW any of the main pathways may be divided into
subpaths if needed.
The basic pathway relationship (Fig. 4 - 15} is that a transfer
coefficient is used to transform a radioactive material concentration
in a receptor to a corresponding dose commitment rate for each specified
organ. The transfer coefficient, C, must contain elements to represent:
1} Concentration or dilution to the consumed or exposure quantity
(BIOPAC).
92
-------
2) The amount of exposure or consumption per year (VOL1KT),
3) Dose rate conversion per unit of exposure or consumption, for
the specified organ (DOSF&C).
Hence, the transfer coefficient is expressed as
x VOLINT x DOSFAC
14-85}
where C and the component factors use a set of units consistent with
the environmental concentration to obtain, dose or dose rates in the
same units for all pathways, to permit smnmation. Table 4-4 details
the units for each factor in AMRAW for the main pathways. Any siabpaths
follow the scheme of the corresponding main pathway.
ENVIRONMENTAL JMPUT
RECEPTOR CONCENTRATION
TRANSFER COEFFICIENT
DOSE COMMITMENT RATE
Figure 4 - 15. Basic pathway relationship,
-------
Table 4 - 4 . Factors Comprising Environment-to-Man Coefficients
ENVIRONMENTAL
INPUT RECEPTOR
CONCENTRATION
Main Pathway
ftode
Biofactor
BIOFAC
X
Consumption,
Exposure (
or Food
Production Rate
VOLINT
X
Conversion of
Integrated
Value to
Average Rate
I/DEL TE
X
Dose Factor
DOSFAC
Transfer
Coefficient
C
Dose Rate
AIR
R2TOT
Immersion
1
y/y
i/y
mrem/y
pCi/cn.3
mrem/
pCi-y/cirr
mt otn/y*
Inhalation
2
cm /y
i/y
nucem
pCi
_jmrem/y_
pCi-y/cm-*
, 4*
mrefli/y
LAHD SURFACE
R2TOT QSDEP
Direct
Exposure
1
y/y
—
mrem/y
pCi/cirr
mrem/y^
,Ci/om2
mre»/y
Ingestion
Terrestrial
Food*
2
pCi-y/g
.Ci/c.2
9/f
i/y
mrem/y
uci/y
pCi/cm2
inrem/y*
SURFACE WATER
pCi/cm3
R2XOT
Submersion
1
y/y
—
yCi/cm
jrrein/y_
mrern/y
Ingasti
Drinking
Water
2
(dimensionless)
cwVy
rorgm/y
pCi/cn
mrera/y
on
Aguatio
Food*
2
uCi/gr
pCi/cm
f/y
mrem/y
uCi/y
JSSIk-X
pCi/cm3
mretn/y
GROUND WATER
R2TOT
Ingestion
1 or 2
nCi/cm3
(dimensionless}
cin^/y
grem/y
"jJcT/y
JEESl/i
yCi/cm-*
mrem/y
10
*.
*Food pathways divide into sub-paths (not shown).
tTransfer coefficient yields average dose commitment rate during time interval in which integrated dose commitment
occurs.
-------
The air pathways involve integrated air concentration and the ter-
restrial food pathway involves integrated food concentrations. These
are converted to average dose rates during a time increment by dividing
by the length of the time increment, as shown in Table 4 - 4 to provide
consistent units for summation with other pathways which directly pro-
duce average dose rates. The use of dose rates instead of the corre-
sponding integrated doses during each time increment permits inspection
of output tables for trends where the size of time increments varies.
(a) Integrated Food Concentrations* Before describing the
component factors of the transfer coefficient, a discussion of food con-
centrations will be helpful. If there is a uniform and continuous de-
position rate, equilibrium concentrations of each radionuclide are
approached in various components of the terrestrial environment and in
terrestrial foods. Following an acute deposition, there is a transient
response for food concentrations. Fig. 4-16 illustrates the response
of concentration of Sr-90, in uCi/g, in above-surface crops, milk and
2
meat following a unit acute deposition of 1 pCi/cm . These curves are
typical in general characteristics to those for other radionuclides,
ftbove-surf ace-food crops have a maximum concentration initially, due to
foliar deposition, followed by decay through wash-off. Milk and beef
are initially at zero and increase with contaminated food intake, Move-
ment of radionuclides down through the soil horizons eventually removes
them from further intake, and biological elimination, processes produce
an exponential reduction of the concentrations in foods. The peak con-
centration for the example illustrated occurs at approximately 2d for
milk and at 50d for meat. Appendix B presents a detailed analysis of
the equations from the TBRMOD code [K176] and the food concentration re-
sponses for several radionuclides. The area under each curve for a given
radionuclide, integrated in terms of years, represents the integrated
food concentration, yCi-y/g. The analysis (Appendix B) shows that the
time constants for transfer downward from, foliage through soil horizons
to the soil sink (beyond root zone) override the significance of physical
half-life such that virtually complete integration is attained in less
than five years, even for the longest half-lives. Therefore, as AMRAW is
typically implemented with time increments greater than five years, a
calculated release accumulated during one release time increment, treated
95
-------
3n _.
c
O
c
Si
O
c
O
Meat [=] yCi/kg
Mi!k =
Above-surface food [=] yCi/m
Above-Surface Food
2
10
100
Time, days
1000
_ 4
- 3
_ 1
5000
Figure 4 - 16, Response of concentration of Sr-90 in
food to unit deposition.
-------
as an acute release, results in terrestrial 'food consequences which are
completed within the following environmental time increment. It is ad-
vantageous to base the terrestrial food on the concept of integrated
concentration following an acute deposition. There is an equivalence
of the ratio of the equilibrium concentration in food (uCi/g) to a unit
•>
continuous surface deposition rate {pCi/cm~-d} with the ratio of the in-
tegrated concentration in the food {uCi-d/2) to a unit acute surface
2
deposition (yCi/em ). This equivalence provides for a simple application
of terrestrial code output {converted from unit of day to year) to obtain
integrated concentrations.
Cb) Local Dose and Nonspesifia Dose, Some, of the pathways {or
subpaths) discussed above have a direct effect on populations within each
geographic zone considered. These ares immersion in air, inhalation,
exposure to contaminated land surface, and submersion in and ingestion
of contaminated water. Dose to man by organ resulting from these path-
ways, in mlllrems per year per individual, is collected as "local dose
rate" for each zone. All of the pathways concerned with production of
agricultural commodities produce effects which are not localized to the
zones in which the food is produced; most of the food is exported, Dose
to by organ resulting from these pathways is collected as manreros of
population dose per year as "nonspecific dose rate." Accordingly, for
this last category, food production rates are involved instead of indi-
vidual consumption rates. Data input to AMRAW for each subpath includes
a flag which identifies the dose category to which the calculations accrue.
(a) Component Faetovs foT Transfer Coefficient. The three fac-
tors: BIOFAC, VOLIHT, and DOSFACf are obtained from output tabulations
by existing computer codes or other sources and supplied to AMRAW as in-
put data for each subpath, along with data designating the number of sub-
paths under each receptor and mode (see Table 4 - 4 ) and designations of
dose category.
The first factor, BIOFACr expresses the concentration or integrated
concentration in food and drink per unit concentration in the associated
environment. For terrestrial food, this is the integrated concentration,
2
uCi-y/g per unit of acute deposition, pci/cm , as discussed previously.
Codes such as TERMQD [Ki?6] or FOOD [Ba76] may be used to perform calcu-
lations for preparation of AMRAW input.
97
-------
For aquatic foods, BIOFAC is simply the nuelide-dependerit bioac-
eumulation factors for each class of aquatic food considered, pCi/g in
3
the food per yCi/cm of water concentration. Tabulations such as those
by Thompson et al. [Tp72] and OKNL [OHN1.75] provide this information.
For ingested water BIOFAC is xmity fdimensionless), although it could be
set at less than unity if water treatment may be assumed.
Contamination of meat and milk from contaminated drinlcing water
uses BIOFAC obtained for each radionuclide as the product of the stable
element transfer factor (meat or milk as appropriate) and the water con-
sumption rate. With unit conversions this becomes (yCi/g)/{jiCi/cm ) , as
with aquatic foods in Table 4-4.
The second factor, VQLINT, expresses the consianption, exposure or
food production rate for each zone and subpath. For immersion in air
or water, or direct exposure to contaminated land surface, VOLINT is
the average fraction of a year during which individuals are so exposed.
For inhalation, the value is respiration rate, cm /y, and for ingestion
of water by people it is the intake rate, can /y. As explained above,
pathways concerned with production of agricultural commodities produce
effects collected as "nonspecific dose rates." Accordingly, VOLINT for
these paths are food production rates/ g/y-
The last factor, BOSFRC, is the dose commitment conversion factor
for each radionuclide, organ, and exposure mode combination. External
exposure modes are air immersion, land surface direct exposure, and
surface water submersion. Internal exposure modes are air inhalation,
and ingestion of food or drink. Dimensions are as shown in Table 4 - 4.
Codes such as EXRBM 111 [Tr73, Kl?6] and INEEM (Kit75, K176] provide dose
conversion factors for external and internal sources, respectively, AMRAW
is presently dimensioned to handle up to eight organs, including total
body,
(d) Operation of Code, Each subpath is provided with a flag
to denote whether results are to be accumulated as local or as non-
specific dose rates. For each time increment, zone, and organ, the AMRAW
main program: (1) considers each of the four environmental receptors in
turn, {2) calls subroutine TKMAN to obtain and return the summation trans-
fer coefficient C for all subpaths associated with the respective receptor,
98
-------
contributing to local dose rate, arid then calculates the corresponding
dose equivalent rate, and (3) repeats for nonspecific dose rates. This
process is repeated for all organs for the given zone, for all other
semes, and for all other time increments. The nonspecific dose category
accumulates from all zones.
It should be noted that the Environment"to-Man Pathways Model is
fully dependent upon input data determined by other external models and
codes, fhe model within AMBAW serves to perform the arithmetic for the
many combinations of parameters to produce the output dose rate matrices.
The dose rates calculated in the environmental model are the last items
of output by AMRAW-S. They are subsequently entered into AMBAW-B, the
economic model, where consequences of dose are evaluated, beginning with
the application of health effect incidence rate factors for each organ
dose rate.
(e) Sample Calculations, In Section 4.D.I, a sample calcula-
tion is given which obtains environmental input concentrations of Sr-90
for air and land surface receptors in Hone 2, associated with probabi-
listic volcanic release during the 400 - 500 y interval. Continuing,
using data from the base case described in Vol. II, a sample calculation
is now given to illustrate the Environxnent-to-Man Pathways Model part
of the Environmental Model (Fig. 4 - 14),
Table 4-5 shows the calculation sequence for the air and land
surface receptors, for one zone (Zone 2} and one organ (total body),
This table is the applicable portion of Table 4-4 , with typical numeri-
cal values (see Vol. II) indicated. As pointed out in the earlier
Transport-to-Environment sample calculations, the receptor concentrations
shown represent only the quantities from the sample release increment;
in AMRAW, residuals from previous release increments are accumulated,
increasing the land surface total (R2TOT), and the corresponding resus-
pension increases air concentration (R2TOT). In Table 4 - 5 / modes 1 and
2 under each receptor represent external and internal main pathways/
respectively. There is one subpath under each main pathway for this
example. For other zones, additional terrestrial food subpaths {above-
surface-crops, milk, and hay-fed-meat) are included under mode 2 for
land surface.
99
-------
Table 4-5. Sairple Calculation, Environmental Pathways ia Zone 2, Total
Body Dose Rates from Sr-.90 Following Volcanic Explosion Release
to Air in 400 - 500 y Time Interval
Environmental
Input Receptor
Concentration
Main Pathway
Mode
Subpath
BIQFJVC
X
VOLINT
x
1/DELTE
X
DOSFAC
Transfer
Coefficient C
AIR
R2TOT = 2.7 x 10~21
f 3
yCi-y/cm
Immersion
1
Immersion
_ — .
l-o y/y
1/100 y
mrem/y
pCi/em
mrem/y
u» u "~ 4
]4Ci-y/cm
0. 0 mrem/y
Inhalation
2
Isolation
— _.
7.3 x 109 caj}3/y
1/100 y
i a v in3 mrem
J» * »3 X 4-v/ ^
pCi~y/cra
3.5 x 10 mrem/y
= 2.1 x 1(T14
2
pCi/cm
Direct Exposure
1
Direct Exposure
™
0.4 y/y
inrew/y
0.0 • ""••' TT "
pCi/cm
/
pCi/cm
0,0 fflrent/y
-14
= 2.1 je 10
. , 2
pCi/cm
Ingestion Terrestrial
Food
2
Meat (Range Fed)
Q r^ pci-y/g
yCi/cm
1.2 x 10 g/y
1/100 y
1 7 x 102 ^S?^
i , .. in!0 mrem/y
i . JL X 1U "
pci/cm
-4
2,3 x 10 mrem/y
o
o
-------
A subroutine in AMRAW (TRIKP) calculates the transfer coefficients,
C, for each mode under each receptor (for given radionuclide, zone,
organ, and duration of environmental time increment). The main program
then multiplies the respective receptor concentrations at the time of
interest by the transfer coefficient values to obtain dose commitment
rates. To illustrate the calculation of C, consider the subpath for
meat in Table 4-5 (last column), Note that C = BIOPAC x VOLINT x
DOSFAC/DELTE. Here, BIOFAC is the integrated concentration of Sr-90,
2
(pCi-y/2}/EpCi/cm ), in range-fed meat animals following & unit deposi-
tion of Sr-90 on the land surface. VOLINT is the total meat production
rate, g/y, for the zone considered. The quantity represents mass added
during grazing in the zone and does not include meat added in feed lots
after export from the contaminated zone. With use of total meat pro-
duction, the subsequent dose rate is routed to the nonspecific dose
category by input of the appropriate flag values in AMRAW. If local
dose rate to an individual is preferred for ingestion pathways, the
individual meat consumption rate is used for VOLINT and the appropriate
route flag is used. DOSFAC is the dose conversion factor for dose com-
mitment for ingestion, mrem/yCi, or rates, (rarent/y)/{pCi/y). DELTE is
the duration of the time increment, used for conversion from an integrated
value to an average value. The subroutine (TBMMJ) calculation of c
accumulates for all subpaths under a mode and does not preserve component
subpaths nor intermediate values for a given subpath. It is of interest
here to trace the intermediate values implied by the calculation sequence.
-14 . 2
First, multiplying the ground deposition quantity, 2.1 x 10 pCi/cra ,
-14
by BIOFAC obtains the integrated concentration in the meat, 1.1 x 10
yCi-y/g. Then, multiplication by VOLINT obtains the total contamination
-4
activity in meat produced during the time increment, 1.3 x 10 pci.
—6
Division by DELTE converts to the average rate, 1.3 x 10 yCi/y. Finally,
-4
multiplication by DOSFAC produces the dose rate, 2.3 x 10 mrem/y. When
routed to nonspecific dose rate, due to use of total production rate, the
_4 -7
result is 2.3 x 10 rnillimanrem/y, converted to 2.3 x 10 manrem/y.
It should be noted that the location of the division by DBLTE in this
sequence has no effect or the numerical result. If the division is left
until the end, it can be shown that the result after multiplying by DOSPAC
is integrated dose, 2.3 x 10 mrem, which when divided by DELTE becomes
101
-------
—4
dose rate, 2,3 jc 10 mreffi/y, as before.
The other subpaths in Table 4-5 are similarly calculated. In
this example, since Sr-90 has no gamma emission, there is no external
mode exposure (DOSFAC = 0.0). Factors which <3o not apply are assigned
a value of unity within aSB&W. In the main program, the dose rates for
each mode under each receptor are routed to the appropriate category
(local or nonspecific) in accordance with routing flags. As indicated
above, nonspecific dose rates to the population become stated as man-
rams /y. Vol. II discusses the sources of input data for the several
factors for an iinp lament at ion example.
102
-------
E. MATHEMATICAL SUMMARY OF MODEL CG. M. McNERNEY)
This section gives a mathematical development of the portion of the
Waste Management Systems Model upon which the AMR&W-A coiaputer code is
based. It is necessary for computational purposes that all of the inde-
pendent and dependent variables be discrete. However, a continuous
representation with the transformations At •*• dt, Axay -*• dxdy of the
equations involved are given first, This facilitates an easier under-
standing of the model by replacing subscripts with continuous variables,
After the continuous representation is discussed, the corresponding
discrete equations are given as they appear in the AMRAW code,
1. Continuous Representation. The variables and subscripts have
the following meanings; T is the variable time, t is a release time of
radionuclide from the waste site to the Preliminary Environmental Recep-
->
tors, T is time of interest for population doses, r is a space variable
in the rectangular coordinate system (x, y, z) in which the origin of
coordinates is the land surface directly above the waste site, i is a
subscript denoting a release event, j is a subscript for the environmen-
tal receptor which is of current interest, and m is a subscript for any
environmental receptor other than j, Generally, the space variable
representation may be considered two-dimensional since we are mostly
concerned with concentrations on the land or in surface water.
The starting point of the computation is the introduction through
data statements of the quantity of the radionuclide in grains as a func-
tion of time, X{t). For simply decaying miclides [My67] (i.e., no radio-
active parents)
X(t) = X(0) exp(-At) (4-86)
where X(0) is the amount of the nuclide at some reference time, and the
radioactive decay constant, A, is related to the half-life,
A = ,693/t ,_. If u is the specific activity in Ci/g of the particular
1/2 o
radionuclide of interest, then
Y(t) = X{t) *
is the radioactivity in Ci at time t for the radionuclide.
103
-------
Nuclides in decay chains, like many transuranic isotopes, have com-
plex simultaneous buildup and decay. The time-dependent quantities for
these nuolides have been previously computed in the ORIGEN computer
code, and are provided to the AMRAW code for each time t in data state-
ments. A radiodeoay factor DC(t»T) between two times t, and. T may be ex-
pressed as the ratio of nuelide quantities for the two times. For
nuclides released at time t, the subsequent distribution and radio-
active decay is computed by means of the transfer coefficient &2{t» T,
r), to be discussed below.
The next phase of the computation relates to the release model
which determines release mechanisms moving the nuclide from the reposi-
tory to the preliminary environmental receptors.
A versatile method for computation with release mechanisms is to
introduce a probability density function P..(t) which represents the
probability of release by release mechanism i to environmental receptor
j during the time interval (t-dt, t), The resulting generality allows
computations to be made either with acute release from mechanism i by
setting P, . (t) , for example, equal to the delta function
-------
for each instance. Information is provided to subroutine FAULT by in-
put data from externally computed data values. Consequently, the fol-
lowing result
= j P, . £t) * Al, , {t} (4.-871
3 f J i} iU '
gives the expectation value for the transfer coefficient from all re-
lease events at time t to receptor j.
Since we are considering the contribution to population doses
from each different environmental receptor in turn, the subscript j may
henceforth be dropped for simplification, except where confusion is
possible. It should be noted here that the four receptors are treated
slightly different. This is due to deposition onto land surface arid
surface water of material which is released to air. This is discussed
in detail in Section 4.D. The following discussion is- for the receptor
ground water as an illustration; the other receptors are handled by
adding appropriate terns,
Let Z(r) be a dimensionless function which gives the fraction of
-j- ->-
released nuclide deposited at position r. In AMR&W, Z(r) is a discrete
function for the zones, giving the fraction of the release which ends
up in each zone. This zone allocation factor involves external calcu-
lations with air and land dispersion models. For ground water the fac-
tor serves to indicate delivery via a ground water path to a given
geographic zone. The space dependent source term is then
q(t, r) = Y(t) • - 2(r) (4-88)
->
giving the activity in Ci at position r from nuclide released at time t.
The sum over release events is finite; therefore, q can be considered
to be an expected value. Similarly, all functions developed in the
following sequence of equations (except G in Eq. 4-89) can also be »
considered to be expected values. However, in AMRAW, the summation
occurs at the step represented by Eq, 4-87, Therefore, the expected
value symbol is omitted from the subsequent equations*
105
-------
The next step of the calculation involves transfer from the recep-
tor of interest at release time t to population dose tine T, and to the
receptor of interest from other receptors. The introduction of two
transfer coefficients, Al (already discussed) and A2, requires further
explanation. Each environmental input receptor is a volume of air or
-water, or area of land surface. Some potential release events may pro-
vide initial depositions which serve as concentrations at environmental
input receptors. However, other potential release events may involve
secondary distribution processes, An example is leaching of a waste
deposit process by circulating ground water. This release process re-
quires a geologic faulting event to cause a major non-healing fracture
through the deposit, coupled with the presence of ground water, for
leaching to occur. However, particularly with deep burial, release by
leaching to ground water is not in itself a release to the environment.
In addition, transport is required before contamination concentrations
accrue in an aquifer contributing to the biosphere. The use of the two
transfer coefficients, Al and A2» then provides the flexibility to cope
with the physico-chemical aspects of such two-stage release and trans-
port processes. Section 3-D. provides a detailed description of these
coefficients.
The coefficient A2.(t, T, r) is a time transfer coefficient, account-
ing for radioactive and environmental decay occurring between release
time t and population dose time T. In addition, the coefficient can
account for special transport processes within one receptor. The coef-
ficients A2 are computed from AMRAW input data in subroutine TRINP. For
the receptors air, surface water, and land surface, the calculations
are done completely within this subroutine. For ground water, subroutine
TRINP calls function CRAT1Q for ground water transport calculation of
concentration ratios.
Some quantity of the nuclide enters the receptor j from the other
•*
receptors, and it is thus necessary to add terms to the A2.ft, T, r) to
•> J ->-
account for these processes. Two sets of functions E (r) and P (r)
mm
account for transfer between receptor terms and are provided to the
AMRAW code as input data. E (r) is the maximum fraction of the nuclide
m
in receptor m which can be transferred to receptor j. F (r) gives the
f racfcional rate of transfer of the nuclide from receptor m to receptor j.
106
-------
Then, the transfer fraction term of nuclide from receptor m to
||iceptor j is given by
G
Itt
(t, T, r} = E (r) 1 - expf-P (r) - 6J (4-89)
IT) j_ \ Kl /J
v-.v/here 6 = /dt (range of integration is period during which transfer
'.;'• is considered) .
If rapid transfer is expected, F (r) is given a large value, while for
slow transfer, Pm<3r> takes a smaller value,
Thus , in the following equation ,
H(t, T, r} = I G (t, T, r) • &2 (t, T, I) • q . -j. ->
R(t, T, r) = S(t, T, r) • DS(r), (4-93)
where R(t, T, r) is the activity in Ci/oa or Ci/cm at time T and posi-
->•
tion r due to release in the time interval (t - dt, t) ,
107
-------
Integrating over all release times prior to T, Eq, 4 -93 becomes
T T
RT(Tf r) = |R(t, T, r)dt = DS(r) " /S(t, T, r) • dt. 14-94)
Here, RT(T, r) corresponds either to the total activity per unit volume
for ground water or surface water, activity per unit area for land
-4"
surfacer or integrated activity for air, at time T and position r due to
all previous release events,
The coefficients for transfer from environmental receptors to popu-
lation dose are now considered. Pathway analysis considers two cate-
gories of pathways from environmental concentrations to population dose:
1} local dose rates for persons in the vicinity of position r, and 2)
nonspecific dose rates to persons at undefined locations from foods grown
->• ->
xn the vicinity of position r. The coefficient A3i(r) is the local dose
-»-
transfer coefficient, and A32(r) is the nonspecific dose transfer coef-
ficient. These two coefficients are discussed in Section 4.D. and are
computed in subroutine TRMMi, The dependence of A3l and A32 on various
organs of the body is suppressed here but is included in the complete
calculations.
The local dose rate at time T is then
Ml(T, r) * RT{T, r) • A3l(r) (4-95}
and the nonspecific dose rate at time T is
M2
(t) = //RT(T, r) • A32fr) • dr. (4-96}
The quantities Ml and M2 given here represent population dose rates
only from receptor j for a specific radionuclide. The total dose rates
are obtained by summing over all receptors and radionuclides. The double
integral in M2 is to obtain the total contribution to the nonsoecific
dose from all spatial locations.
2, Discrete Representation. The discrete equations may be obtained
from the continuous equations by replacing the continuous variables with
, iperscripts and subscripts, and integrals with finite sums- To prevent
108
-------
confusion, time-dependence is represented by superscripts, and all other
independent variables are represented by subscripts. Release time t is
labeled by the superscript a, and population time T is likewise
-»-
labeled by the superscript g. The space dependence, or the variable r
is replaced by zone dependence denoted by the subscript k. It should
r* R
be pointed out that the time increments At and At are not uniform in
the AMR&W calculations and the superscripts are thus necessary. The
discrete form of dr is not needed; all other subscripts retain their
original meaning.
The final objective is to represent JSqs, 4-95 and 4-96 in the
continuous representation in discrete notations. The resulting expres-
sions explicitly contain all the calculations in the AMRAW code for
ground water, except the transfer between receptor calculations. As
mentioned in the discussion of the continuous representation, the other
receptors are slightly more complicated and need minor modifications.
The quantity of radionuclide assumed available for release in the
ct
time increment At is the average of the radionuclides available at time
t and time ta~ . Thus X° = — [X(t°) + X(ta~ }] , and the activity cor-
•£
responding to Eq, 4-86 for the continuous representation is
01 a
Y = X • UQ. (4-9?)
The probability density function at release time t is P,,» and
ot
the first transfer coefficient is Al.,,
13
Thus, corresponding to Eq. 4 -87,
I P3. Ala, (4-98}
I 30 13 f
is the expectation value for the transfer coefficient.
The term 2 is the zone-dependent factor which gives the fraction
jK
of the amount released to receptor j that ends up in that receptor for
Zone k. The zone-dependent source term is then» corresponding to
Eq. 4 -88,
109
-------
In the continuous case, the second transfer coefficient was intro-
-»•
duced as a given function A2(t, T» r}. In the discrete case, the com-
putation of the second transfer coefficient is rather complicated, and
its representation as a continuous function needs some justification,
FY ft -A, fa Q
Let A2.f be the discrete analog of A2.(t, T, r) . Then A2.^ is deter-
3 aB -1 -1
mined as follows, A quantity, S, , is computed in subroutine TRINP for
jfe
each population dose time greater than or equal to the release time
\T >. t / For the case where population dose time equals the release
time (T = ta),
.
3k
t
Subsequently, A2 p is defined recursively by
JS.
or, in general,
^«P TT *«y
A2. = it A, r
where « I represents product summation and y ranges from a to fJ.
Thus, for example,
_^4 11 jy 11 12 3,3 14
n 1c 1 ^ *V.^>. ^t n Ic T V" T Ic ™i Ic *i 1?
This computational form was chosen since it can be easily used to
handle radioactive decay.
Now, letting E . (r) , F , (F) , G . (t, T, r) and DC(t, T) be replaced
by E ,, , F ., , G ,, i and DCa&, respectively, the transfer to receptor 1
Hrjk nijk ™"lV " J
(4-100)
from receptor m corresponding to Eq. 4-89 is given by
v lfc
mjk mjk
and, corresponding to Eq. 4 -90,
"mjk
110
-------
ap r osS ,-aB a
H., = ) G ,, * A2 , •
jk £, rrgk mk
is the total transfer to receptor j from all other receptors.
The quantity
ag r. a0 ag a
* A2 • a
is the corresponding term representing transfer from receptor j tap through
time T to all other receptors,
The final source term corresponding to Eq, 4 - 92 is then
^ - 4 • < * $ - L£
The local dispersion factor depends on both the zone and the
receptor, and is thus represented by DS,..
3"-
So, corresponding to Eq. 4 -93,
is the activity at time T in Zone k due to release in the time interval
At".
Summing over all release times up to population dose time T /
corresponding to Eq. 4 -94,
is the total activity at time T in Zone k.
If the population dose rate transfer coefficients are represented
by A31. and A32 , , the resulting local dose rates are given by
MlP = RTBfc -"A31., (4-105)
and the resulting nonspecific dose rates corresponding to Eq. 4 - 96 are
^ {4-106}
ic
Tliese last two equations represent the final output of AMRAW-A.
Ill
-------
Page Intentionally Blank
112
-------
CHAPTER 5
DESCRIPTION OF AMRAW-A COMPUTER CODE
The AMR&W Code is written in Fortran IV language. The two parts of
the codes are: 1} AMR&W-A which contains the Source Tens, the Release
Model, and the Environmental Model, and 2} AMBAW-B which contains the
Economics Model. They are being run separately but may be joined if
desired. There is an advantage to running the first part independently
to determine sensitivity of environmental concentrations and dose rates
to variations in input. Similarly, there is an advantage to running the
economic model independently to study the response to varied economic
parameters. User's manuals are Volume IV for AMBAW-& and Volume VI for
AMRAW-B. This chapter provides a brief description of &MR&W-A; similarly,
Chapter 6 in Volume V describes AMBAW-B,
The present dimensioning of &MKAW-A is as follows;
1) Radionuclides; 25.
2) Environmental receptors: 4, designated by programming as Air,
Land Surface, Surface Water, and Ground Water.
3) Release Model events: 9 events or event combinations under
each of the 4 environmental receptors. Each may be input with
up to 4 conponent factors. Each of these factors may be flagged
far type of function {constant, step, ramp, exponential, or
delta) and specified by three appropriate function parameters.
4) Environmental pathways: 2 main pathways (modes) are programmed
for each environmental receptor. Dimensioning provides for up
to 6 subpaths for each receptor (each mode under a given receptor
is divided into the same number of subpaths).
*>
5) Geographic zones: 8.
6) Human organs: 8, Typically, one of these is total body, but
there is no restriction.
7) Time increments: 50.
113
-------
With this dimensioning, the code runs with 256 k bytes of core storage,
10 cylinders (1459 k bytes) of disc storage, and requires 21 minutes
of CHJ time in the UNM IBM 360/67 coraputer. The range of subscripts for
variables is specified by input data and may be any "value within the
above dimensioning with the exception of environmental receptors which
are fixed within the code at four. Dimensioning may be increased if
necessary, limited only by available core storage or other system re-
quirements. Also, some exchanges of dimensioning can be used for spe-
cial cases without increasing storage requirements. For example, 9
Release Model events, each with 4 component factors represent 36 storage
combinations (-9x4), If release is described by an involved function
representing dynamic repository simulation (see Section 4.C.l.d), AMRRW can
be dimensioned as one release event with up to 36 component factors if
needed. The number of geographic zones, presently dimensioned at 8 is
limited to 9 because of programming for the variable "NPRINT" which
controls output options.
Large output matrices for local and nonspecific dose rates are
written onto disc to conserve core space, Complete output is then writ-
ten onto magnetic tape for retention but ouput may be diverted directly
to printer by job control statements if preferred. Printed output is
subsequently obtained from the tape as needed. If AMH&W-B is to be
coupled to AMRftW-A for a combined run, &MRAW-B may access the disc for
dose rate input data. The operation demonstrated at UNM is separate
running of AMRAW-B. For this purpose, the dose rate portion of the
AMRAW-A output is obtained from tape,
AMRAW-A has provisions for running more than one case, per submis-
sion. This can ber 13 more than one set of conditions for a waste
management phase such as terminal storage, or 2) aiore than one phase,
such as repository operations and terminal storage. A full set of input
data is read in for each case.
There are three subroutines in AMR&W-A which evaluate transfer co-
efficients between sequential sections of the systems model (Fig. 4-2).
Subroutine FAULT handles the Release Model {see Section 4.C.I) and provides
the transfer coefficients used to accumulate releases to four preliminary
input receptors from all release events considered. This subroutine uses
114
-------
function RI£ACH when an event involves leaching into ground water. Sub-
routine TRINP handles transport from the preliminary input receptors to
the environmental input receptors (see Section 4.D.I}, providing trans-
fer coefficients which account for physical and environmental decay and
ground water transport delays. Hhis subroutine uses function CRATIO for
the ground water transport calculations. Ose of the transfer coeffi-
cients from TRIM? by the main program leads to net environmental concen-
trations for input to pathway analysis. Subroutine TKMftN handles
evaluation of transfer coefficients between environmental concentrations
and population dose rates (see Section 4.D.2) for the various pathways,
A directory of fiMSAW-A output tables is given, in Table 5-1. Output
is divided into six sections, separated by divider pages, to output
control parameter, HPEINT (see Vol. IV)r controls which of the 10 types
of tables are output and whether for all zones and organs or for only
selected zones and/or organs. If all tables are output as currently
implemented, 627 tables are obtained. If dimensioning for zones is
increased from the present 8 to the program limit of 9, 68 additional
tables could be generated. If in addition, Section 6 tables are re-
quested for all 50 times, 810 more tables would result, for a possible
total of 1505 tables. Clearly, discretion is called for when specifying
requested output, particularly for the Section 6 group. In practice, an
adequate sampling of Section 6 dose stunraary tables is obtained with 2
zones and 5 times, yielding only 20 tables from this section. In Table
5-1, the complete title for each type of table is stated, including the
variable name called for and the units for the tabulated values. Each
table as printed is identified with the appropriate radionuclide identi-
fication, zone number, and organ name as appropriate.
115
-------
Table 5-1. Directory of AMRAW-A Output Tables
Description
SECTION 1. Data Input
1, Output listing of AMKRW input.
SgCTION 2. Release to Environment
1. Release Fractions by Each Cutset, RELOOT
2. Release Increments to Preliminary Environmental
Input Receptors, R1J, from All Release
Events , Ci
3, Concentrations at Environment Input Receptor,
R2T0T. Units: JP = 1 pCi-y/cm3, JF « 2 pCi/csa2 ,
JF - 3 and 4
3. Local to Individual
1, Average Annual Local Dose to Individual, MAM1L,
mren/y .
SECTION 4 , _ Monspecif ic_ _ jPpseu_ tj3__Pppulatiant
1. Average Annual Nonspecific Dose to Population,
HAN IN, manre»/y .
cr of Table Combinations
Total
Nuclides
{20
25
25
25
25
25
Zones
pages)
Organs
Environ.
Receptors
(8 in each
table)
(8 in each
table)
(4 in each
table)
25
25
200
200
25
-------
Table 5-1. Directory of Output Tables (continued)
Total
SECTION 5. Total Dose j>yReceptors
I. Average Annual Local Dose to Individual,
MAM2DF for JF = 1 to 4, for Total,
mretn/y, Total for All Kuclides.
2. Average Annual Nonspecific Dose to Population,
MAN2KF for JF = 1 to 4, for Total,
manrem/y, Total for All Nuclides-
SECTIOM 6. Dose Summary Tables
1. Average Annual Local Dose to Individual,
H MAN1L, in Zone , mrem/y.
2. Average Annual Nonspecific Dose to Population,
MANHT, manrem/y.
Total Number of Tables
Mote:
a. All output tables, except Section 6 are for 50
time steps, 0 to 10° years.
b. Individual zones may be specified.
c. Section 6 may call for a table for each of all
times beginning with 100 y or skip some times;
5 tables result if call for every ninth time.
Nuclides
(25 in each
table)
{25 in each
table)
Zones
8
b
up to 8
up to 8
Organs
8
8
(8 in each
table)
(8 in each
table)
Environ ,
Receptors
(4 in each
table)
{4 in each
table)
C5
C5
64
8
40
40
627
-------
Page Intentionally Blank
-------
CHAPTER 6
APPLICATION OF MODEL
The computer code that implements the Radioactive Waste Management
Systems Model is totally dependent upon externally generated input data.
One function subprogram calculates nuelide-dependent leach rates as a
function of leaching duration when called upon by the Release Model.
Bnother function subprogram calculates the nuclids-dependent concentra-
tion ratios for points of usage versus the point of release as a func-
tion of ground water transport time intervals, Both of these subprograms
depend upon input data for values of all parameters used. All other
calculations in AMRAW are arithmetic operations which collect appropriate
numerical components from the input data for the calculations, accumulate
totals from contributing increments, and route results to the appropriate
output tables. The nature of the input data dictates; 1) the waste
management phase studied, 2} the inventory ace-omulation of radionuelides
and their buildup and decay, 3) release scenarios, whether probabilistic,
discrete events, statistical occurrence or dynamic repository simulation,
4} transport to environmental receptors via air dispersion to each geo-
graphic zone, ground water transport and by other transport mechanisms,
5) nuclide concentrations in food associated with depositions, 6) agri-
cultural production and exposed populations, and 7} dose commitment rates
associated with calculated intakes and exposures. The flexibility in
AMRAW implementation permits use of various existing and accepted codes,
reviewed and published data compilations, and estimates by experts in
various fields, for preparation of input data,
Chapter 4 provides a step-by-step discussion of data needs in the gen-
eric sense. Volume II, Part 1, presents a base case which illustrates data
acquisition for terminal storage at a specific repository site in bedded
salt. Other cases illustrate sensitivity analysis showing the effects
on calculated results of variations in selected input parameters, and
consequence analysis showing consequences following discrete release events
and the effect of the time of occurrence. Part 2 of Vol. II demonstrates
other applications of the model. These include a case demonstrating pre-
liminary application to the repository operations phase, discussion of
119
-------
application to ground surface storage, m case demonstrating a preliminary
application to another geologic setting {repository in shale) , and a
discussion of model feasibility for application to other radioactive
and nonradioactive hazardous materials.
Volume III describes the aMR&W-B part of AMR&W and demonstrates
implementation for the base case dose rates obtained with AMRAW-& arid
for several consequence analysis cases. Volume IV is the &MR&W user's
manual which provides specific information on input data formats and
sequence. Part 1 of Vol. IV is for AMBAW-A and Part 2 is for &MR&W-B.
120
-------
APPENDIX A
CONCENTRATION DISTRIBUTIONS IN
GROUND WATER TRANSPORT
1. Line Sourc_e Equivalent of Plane Source. The solution of the
radionuclide transfer equation (Eq. 4-79), from Duguid [AHS ], for
the instantaneous release from a rectangular plane source of width f,
parallel to the y-z plane and centered at the origin is
C S51
(A-l)
where M" is the (or Curies used here) per unit area of the plane
source, obtained by dividing the released quantity of a particular radio-
nuclide by the product of the width f and the aquifer thickness z .
a
Other parameters are as defined in Chapter 4.
It is now desired to obtain the equivalent solution for the instan-
taneous release from a line source located at the origin and parallel
to the z-axis. The line source equation compresses the plane source
into a width which approaches zero, providing for simpler calculations,
The form of the error function is
. , M" .
4 (WE t}"5
3C
(x
- k_v t) "
2 p
. k3Vpt
erf H
: (••
^ .
u 2
erf u = -r- I e dn (A-2)
2 f
u = — I
^J
erf u = " (erf u) = — ~ e dr.
2
e"U {A-3}
Consider the error function factor in the exponent of Eq. A-l, and use
Taylor's series to approximate the error functions. It is implicitly
assumed that width f/2 becomes small when going to the line source.
121
-------
compared with distances y from the plume centerline.
erf
2/E t
y
. erf
2/E t
y
= erf
erf.
-erf
erf
2E t 4VE
y / y
erf
2/E t \2/E t
y • \ y /
exp -
E t
y
(A-4)
Substituting from Eq. A-4 into Eq. ft-1, simplifying, and also substituting
M' = M" £ (release per unit of aquifer thickness), obtains
c =
M'
exp -
4-rr/E E t
x y
(x -
2 p
_
3
2 1
4E t
y
(A-5)
Using the following substitutions from Chapter 4;
3 R,
A.
R,
4a
C4 = ¥T
E =
x
— a v
R, Vp
rV
4 3 p
122
-------
Eq. A-5 becomes
kl
exp —
v t *
P
'(x-k^t)2
kjv t
3 p
2
k,v t
4 P
(A-6)
which is Eq. 4-84 in Chapter 4 and is equivalent to an equation by
Duguid [ANSj for the line source. As shown later, with input of an
effective value of y (parameter YY) , Eg. A-6 as calculated in AMR&W pro-
vides the average concentration within the equivalent plume width (param-
eter YW, the width within which C > .001 C ).
max
Figure A-l shows computer generated plots of concentration versus
y at a distance of x - 10 km for the plane source (f = 3000 mi , Eq. A-l
and the line source Eq. A-6 for a 1 Ci instantaneous release in an aqui-
fer of thickness z — 50 m. Other values of parameters used are from
a
the application in Volume II: a = 50 m, a = 6 m, and v = 1.46 m/y.
Lt T p
The plots shown represent the distributions at the time of peak passage
at distance x; any consistent pair of time t and retardation factor R.,
applies. The areas under the two curves are equal, indicating equiva-
lency of the two source concepts.
Figure A-2 presents isometric views of 3-dinension computer plots of
the concentration distributions in peaks at the time of arrival of the
maximums at a distance of 10 km, for a plane source (length 3 km) and the
equivalent line source. The computer plots are normalized to the same
maximum ordinate value; actually, the line source peak is approximately
3.4 times as high as for the plane source (as in Fig. A-l) such that the
volumes within the solid surfaces are equal. It should be noted that the
leading face, as a peak approaches, is steeper than trailing force. The
integrated volumes
/"*/*"
Volume - z j § C{x, y) dy dx , Ci, {A-7)
aJ J
G O
123
-------
1 K 10 V
NJ
c
O
4J
m
u
c
O
O
-3.0
Line Source
Plane Source (3 km width)
3.0
Distance y from center line, km
Figure A-l. Transverse distribution of concentration
of peaks at distance of 10 km for plane
and line sources.
-------
Source
(a) Plane source,
leading face
(b) Plants soyrce
traiI ing face
Ln
.«-
Source
ic) Una sourca,
leading face
(d) Line source,
trai1!ng fact
Figure A~2. Concentration distribution 10 km from the source for
plane and line sources with instantaneous release.
-------
calculated by computer show that an instantaneous release of 1 Ci is
properly accounted for fay Bgs. A-l and A-6 for a plane source and a
line source, respectively. This proving step has showi that porosity e,
contained in the denominator of the original Duguid equations, should be
omitted as is done here.
Figure A- 3 illustrates the spreading out of a peak, both longitu-
dinally and transversely, as travel distance increases. Again, the
computer plots are normalized to the same maximum ordinate value? actually
the maximum concentration decreases with distance such that the volumes
within the surfaces (see Eg. A-7) are constant,
2. Calculation of :Sffe ctiye Plume Width _ an_d JPr an .s verse Distance
to ^Average Cgncentratipri, The effective plume width YW and the trans-
verse distance corresponding to the average concentration YY are input
to AMRAW for each travel distance involved in calculations . The deri-
vation of equations used for obtaining the input data values is pre-
sented here. Consider Eq. A-6, and simplify it for the time of arrival
of the centerline peak concentration. The time of peak arrival at dis-
tance x is
v
p
, V x R_
Then (x - knv t) => x - r— * -*- - = 0, and the first term in the ex
2 p Kg Vp
ponential drops out. The denominator of the second term becomes
k,v t - 4 — - • v • - = 4a x
4 p R p v T
The coefficient becomes
kl
V t
p 31
M/Za
T{aLaT)% XRd
R P v
d P
M/z
S.
4,(aLaT,'^
Equation A-6 for peak distribution at x becomes
126
-------
VS^
-f-
Concentration
line source, at
of 10 and 20 km
\
Zk
-------
M/z
\4a x
T
2 2
A exp -(By)
(A-8)
M/2
where A
(A-9a)
2 1
B *** f-TT-V-r,-
(A-9b)
The transverse distance y = — y (Figure A-4) for decrease in concsntra-
^ Wf
tion to 0.1% of the centerline peak valtie is obtained from
= 0.001 - exp
"
Then,
0.001
2,63
The effective plume width (YW for AMK&W input) becomes
The average concentration across the pl»uine width is
C =
fhy"
J '
C dy
1
~—
2
— vr
2 Yw
It can be shown that
„
By
C dy = erf
= erf 2.63
and 0.9998 < erf 2.63 < 1.0000. Therefore, the integrals are equal to
3 significant figures.
128
-------
A j exp - B2y2 dy
2B
(K)
Substituting for B from Eg, A- 10,
= °-337
At what value of y does Eq* A-8 yield 5" directly? Prom A-8,
0.337 a = A exp - (B y2}
2 Jin 0.337
~
- j-,.:,.04-
y ~ B * (A-13)
This is the traverse distance corresponding to the average concentration,
input as YY to AMR&W.
To illustrate evaluation of AMBAW input parameters, again consider
values of parameters from the application in Volume II: a = 6 m. For
a travel distance of x = 10 km (10,000 m), from Eq. A-9b,
B - 1—._ - i „ = 2.04 x 10~3
2 (ax)'5
Then, from Eq. A-10
5.26 5.26
2.04 x 10~3
and from Eq. A-13,
2.04 x 10
129
510..
-------
It may be noted that YW an<3 TfY depend only upon a and x; as sucb, AMRAW
could calculate YW and ¥¥ but these values are included as input data
(for x values appropriate to each zone) for greater flexibility,
In summary, substituting for 8 from Eq. A-9b, the effective plume
width, from Eq. A-10/ is
= 10.
(A-14)
and the transverse distance corresponding to the average concentration/
from Eq. A-137 is
- 2.08(aTx)
CA-15)
y = YW
'w
Figure A-4. Effective plume dimensions.
130
-------
B
RADIONUCLIDE CONCENTRATIONS IN TERRESTRIAL FOODS
The transfer coefficient used in AMR&W for environment-to-man
pathways (see Section 4.D.2) includes a component factor, BJOP&C, which
relates radiomiclide concentration in food to a unit concentration in a
corresponding environmental input receptor. In AMRAW, the calculations
for terrestrial {land surface receptor) pathways are based upon the con-
cept of integrated food concentration following an acute deposition.
There is a numerical equivalence between: 1} the ratio of the equili-
brium concentration in food, uci/g, to a unit continuous surface depo-
Ml'
2
2
sition rate, MCi/cra -d, and 2) the ratio of the integrated concentration
in the food, uCi-d/g, to a unit acute surface deposition, yCi/on
A systems analysis methodology developed at the Oak Ridge National
Laboratory by Booth et al. [Bh71] has a three-fold purpose of: 1) pre-
dicting intakes by man, 2} estimating dose commitments, and 3} identi-
fying "critical" exposure pathways resulting from radioactivity releases
to a terrestrial environment. An important part of this methodology is
a generalized dynamic model simulating selected terrestrial pathways
which assumes that fallout is the only source compartment and that
man is the ultimate receptor compartment of interest. The model is
implemented by the computer code TERMOD (Ki76]. A similar code, FOOD,
was developed at Battelle Pacific Northwest Laboratory by Baker et al,
[Ba761.
Discussion is presented here to support the observation that integrc
of concentrations in terrestrial foods versus time is virtually complete
within a period of five years after an acute deposition,
1. Introduction. The mathematical compartment models depicting
terrestrial pathways, as developed by Booth and co-workers [Bh?l] is
shown in Pig. B-l. The objective of this model is to obtain predictions
of radionuclide intakes by man through consumption of milk, beef, and
plant parts contaminated as a result of fallout. Pig. B-l indicates a
2
fallout rate, pCi/m -d, but it is shown later that the system equations
may also be solved for an initial one-tiroe deposition, in units of pCi/
2
m .
131
-------
FALLOUT SOURCE
• - day!
ABOVE
SURFACE
FOOD CROP
E
1 e. m
- r.
e,s •
SOIL SURFACE
BELOW THE
FOOD CROP
Si/rCi/m2}
SUBSURFACE
SOiL POOL FOR
THE FOOD CROP
P<
49
PASTURE GRASS
{ MILK AND MEA
PRODUCTION }
GE»iCi/m2)
-.1 I
'9.' _?
* rr,9
* 1
• b PASTURE
SOIL
Rf^Ci/m2)
I
T» A
q.c
INPUT TO MAN 1 t^Ci/cioy)
Figure B-l, Compartment diagram of the terrestrial
food pathways by which radioactivity can
be transferred to man [Bh713.
Considering the above-surface food crop (ASF) first, a fraction S
A
of the fallout deposits on the food and a fraction S {where S + Sn =
1,0) deposits on the soil surface below the food crop. The radioactivity
enters the ASP crop by deposition and is retained either by external
adhesion to, or foliar absorption into, the crop's edible parts. This
crop is assumed to be continuously harvested during and after fallout,
with biomass removal balanced by crop growth. Transfer rate coefficients,
T, are shown between the various compartments in Fig, B-l, Washoff from
ASF to the soil surface below is represented by t . The half-time for
e t s
this is generally taken as 14 days (taken as 30 days for desert graaing
land in Vol. II), corresponding to T = 0.693/14 = 0.05 « d~ . The
e fs
other removal of ASF radioactivity is by harvesting the crops/ represented
132
-------
by T , and transfer directly to man. Contamination on the soil sur-
e ,m
face moves down into the subsurface soil pool (root zone) at the rate
T , and from there, moves below the root zone into the soil sink at
s,p
the rate T ,. This model does not consider root uptake by ASF but
p,d * J
simulates this instead by the link T between, the soil pool and nan,
p,m
Root uptake can be shown to represent at most only a few percent of
ASF concentrations.
Next, consider meat and milk production. A fraction S of the fall-
*5
out deposits on pasture grass (or rangeland vegetation as appropriate),
Washoff to pasture soil surface is per T and root uptake in per r
* g,r ^ * r,g
again radionuclieJes in the pasture soil migrate to the soil sink at
rate T ,. Meanwhile, transfer to meat and milk via consumption of
pasture grass is by t for meat {beef) and T for milk. The .trans-
grb g,c
fer rates from meat and milk to man are T, and T , respectively.
b,m c,m
The milk compartment variable C(t) is the concentration of radioactivity
in milk produced by a cow grazing on the contaminated pasture. In the
Booth model, radioactivity is transferred from the grass directly to the
milki this simulation is used mainly because the milk of grazing cows
can be in transient equilibrium with the forage radioactivity after
about two days. The beef compartment variable B(t) is the radioactivity
in the meat or muscle of cattle grazing on the contaminated pasture,
Radioactivity is directly transferred from the grass to the meat as in the
milk compartment; removal is via radiodecay, biological elimination, and
slaughter of the cattle. Transfer to uncontaminated feed lots terminates
intake of radionuclides. The parameters d through d in Fig, B-l are
dietary correction factors which account for cleaning and trimming of
food. The gradual accumulation in the soil sink effectively removes
radionuclid-es from food pathways and limits the duration of impact fol-
lowing deposition.
AMRAW applies this model only for determining the concentrations in
ASF, meat and milk, in relation to deposition. Intake rates of these
foods and corresponding dose commitment rates are handled in AMRAW,
2< Formulationof the System Equations. Referring to Fig,B-l,
the conservation equation describing the rate of change of contamination
2
of above-surface food crops, E(yCi/m }, [Bh71] is
133
-------
rlF
dt-slFtt) -V2 ^
where I"{t) = deposition as function of time,
X = X 4- ~--— — -f- T effective removal constant, d
a R ft e,s '
A = radiodecay constant, d f
H
2
T - crop harvest rate, m /d,
e,ro
3 2
a = soil surface area producing food crops for one person, 10 m , aid
~i
T = fractional transfer rate, foliage to soil surface, d *".
6 tS
Other parameters have been discussed previously. It should be noted here
that this model expresses ASP contamination in terms of crop area? appli-
2
cation in AMBAW requires conversion to pCi/f (typically using 100 g/m
for the conversion). The equation for soil surface below the food crop,
S(lJCi/m2) is
S2Ftt)' vC±/m (B-2)
2
where X — X^ •+• T , effective removal constant, d
s R s,p '
t = fractional transfer rate, soil surface to soil pool, d
*™1
T = fractional transfer rate, crops to soil surface, d
e,s
Subsurface soil pool concentration, P, is yCi associated with one person's
food supply, typically 1000 m . This changes as
dP
^ = ATs,PS ~ V (B-3S
where X =AT+T +T ,, effective removal constant, d ,
p R p,m p,d
T = fractional transfer rate, soil pool to roan, d ,
p,m
T „ = fractional transfer rate, soil pool to soil sink, d , and
Pf«
T = fractional transfer rate, soil surface to soil pool, d
s ,p
134
-------
2
Moving to the pasture pathways, pasture grass contamination,. G, UCi/m ,
responds as
f -S3F(t) - \,G+TR (B-4)
where X » A_ -<• T +V/AD, effective removal constant r d ,
g R g»r c7 g g' '
T = fractional transfer rate, grass to soil, d ,
9'r
V /A D- = fractional grass consumption rate, d (related to T , and
o' g g s * g,b
i , Pig, 8-1} , and
g, c
T » fractional root uptake rate , soil to grass , d
2
Pasture soil contamination, R, pci/m , changes as
= T G - * R (B-5)
dt g , x x
_ i
where A=A+T +T ,, effective removal constant, d , and
r R r,g r,d
-"1
T = fractional transfer rate, pasture soil to soil sink, d
r ,ct
2
Soil sink lumps sinks for crops and pasture areas in D, pCi/m as
f~ = T ,R + -£~- P - A_D,
dt rfd A R
Contamination in milk, C, yCi/A, varies as
« T G - A C (B-6)
dt g , c c
where X = A + t .„, , effective removal constant, d ,
c R rnxlk
*•- 1
T . , = transfer rate from udder, d , and
milk
2
T = transfer rate, grass to milk, m /£-d,
g,c
Contamination in beef, B, pCi/Kg varies as
f - T,bG ' XbB CB-?)
.35
-------
__1
where A = A + T , effective removal constant, d ,
t, , = fractional rate of removal of beef nerd, d , and
beef
T = transfer rate, grass to n?eat, m /kg-d,
g,b
All the above equations represent the change with tints of the radio-
i
activity in each compartment. Subsequent expressions for intake to man
are omitted here; AMBAW provides this step.
3. Equilibrium Solutionsfor Constant Deposition Rate. If the
2
deposition source, F(t}, is set equal to a constant value, P, yci/m -d,
and the rates of change of compartment values set equal to zero
(e.g. dE/dt = 0), the equilibrium values are obtained;
E = S,F/X (B-8)
•L St
S = (S_F + T E)/A (B-9)
2 e ,s S
P = AT S/X (B-10)
s,p p
G = (S P + T R)/X (B-ll)
"5 X f *s y
R - T G/A (B-12)
D =
C = T G/A (B-14)
g,c c
B » T ^G/^. (B-15)
g,b b
4, Transient Solutions ...for Unit Initial Deposition. The substitution
F(t} = P <5{t) , where 5 (t) is the Kronecker delta function, represents
a pulse or acute deposition, may be applied immediately before t = 0 such
that F(o) = P . Then,. the solution of Eq. B-l is [Kr67]
-A t
E(t) = S.P e . (B-16)
i o
136
-------
For the soil surface below the food, the solution of Eg. B-2 is, noting
that S = S0F at t = 0,
2 o
S-F T
-X t -A t
-At
2o
2 o
(B-17)
The initial condition for the subsurface soil pool is P = 0 at t =
0. Then, using Eq, B-3, the solution of Eq. B~17 is {Kr6?}
P(t)
S-.F T T A
I o e,s s,p
(X -X ) (A -X ) (A -X )
s p as pa
-A t
-At
-X t
(A -A )e + (X -X )e
as pa
(A -X )e
s p
A r -At -A t]
p - s I JB-18)
Subsequent solutions of B (t), C(t) and G{t) yield [Kr67]
B(t) = -TT-
S.,F T
3 o g,b
X t
-At
where X
X +• X + f(A -fX }2 - 4(X X -T T }
g r L g r _ g r r,g gfr -»
2
A + X - f(X +X ) - 4(X X -T T }
9 r L g r _ g r r,g g>r
At
(B-19)
(B-20)
(B-21)
C(t) = S
3 o g,c
-X t
(X -A )(X -A ){A -A )
c 1 12 2 c
-At
X t
(B-22)
and
G(t} = S3FQ
£A -A MA -X } (X -A.)e
c 2 2 r c 1
\ -X.)(X.-X )(X -X )e
c 1 1 r 2 c
where A and X are defined in Eqs. B-20 and B-21r respectively. As
(B-23)
137
-------
noted earlier, the term A in Eq. B-18 is the soil surface area required
2
to furnish food crops for one man (taken as 1000 m ),
As an example, consider 1-129. The long half-life for this isotope .
C1.7 x 10 y) illustrates the dominance of the other transfer coefficients
over the physical decay constant, Subsituting values for parameters used
by Booth et al. [Bo71, 101763 for average U. S. conditions into Eq. B-16
B-19 and B-22 obtains the following food response equations, respe-
2
tively, following deposition of F = 1
Ett)
0.1 e
-(5.2 x 10~2)t
(B-24)
B(t) - 2.30 1(2.06 X
10~3)t
~(2.08 x
(1.42 x
(B-25)
C].
(B-26)
These are plotted in Fig. B-2, along with the corresponding curves for
soil surface, subsurface pool, and pasture grass. The above-surface food
concentration is a maximum initially and decays primarily by washoff.
Milk concentration quickly builds up to a maximum at 3 days and meat
reaches a maximum at approximately 80 days. The curves in Pig. B-2
have differing scale factors. To place the peaks in perspective, Table B-l
summarizes the peak values in the units determined by the compartment
model, and converted to common units of pCi/g.
Table B-l. Peak Concentrations in Foods
Following Unit Deposition of 1-129
Above-Surface Food
Milk
Meat
0.1 yCi/m
-2
3 x 1D
-4
4 x 10 yCi/kg
1 x 10
3 x 10
4 x 10
-3
-5
-7
138
-------
Hi Ik, C
U)
yj
Pasture G rags , G
x 10
Above-Surface Food, E
uC!/in2 x 1 O2
Figure B-2 .
Subsurface Pool, P
pCi x 10-2
Soil Su rface, S
PC i/m2 x 0, 5
Meat, fi
PC i/kg x 10
100
Time, days
150
Linear plot of 1-129 concentrations in response to
unit initial deposition of 1
-------
It may be noted that above-surface food dominates the peak -rallies, but
as shown in Fig. B-2, concentrations in meat have longer residence times.
Fig. B-3 is a semi-log plot of food concentrations showing that they
drop virtually to zero within 5 years. Shorter half-lived radionuelides
have greater decay constants, A , and increase the effective removal
K.
constants. Fig. 4-16 shows food concentrations versus tine for Sr-90.
5« Integrated_Concentration in Food. Integrating above-surface
food concentration from Eq. B-16 over time,
~0 CO
/-A t
e a dt = S, F /X . (B-27)
•>• o / a
0 0
Comparing with the equilibrium value of S for a continuous deposition
rate, P, it is seen that the total time integrated concentration in
above-surface food (area under curve in Fig. B-2 or Fig, B-3) following
a unit initial deposition is numerically the same as the equilibrium
concentration with a continuous deposition o£ one unit per unit time.
The same is true for milk and meat but the integration is complex and
is not given here. Overall, the analysis shows that the time constants
for transfer downward from foliage through soil horizons to the soil sink
dominate the significance of physical half-life such that complete inte-
gration is practically attained in less than five years. AMRAW is cur-
rently implemented with time increments no shorter than 5 y and most
are 10 y or greater. Thus, it is concluded that the deposition accumu-
lations onto land surface during one time increment and treated as an
acute deposition for input to the following time increment results in
integrated food concentrations which have virtually complete integration
within that following increment.
140
-------
30 -
20 -
c
o
flj
C
V
o
c
c
10 L.
Above-Sur face
Food, E
uC i/m x
200
10
- 2
- 1
100
T i me, days
I ,000
10,000
Figure B-3,
Response of concentration of 1-129 in food to
unit initial deposition of 1 yCi/m2.
-------
GLOSSARY
damages
diatveme
distribution
coefficient
the value of adverse or unwanted effects measured
in economic units, usually dollars. Total damages
are a summation over causes and time; marginal damages
are total damages divided by a reference production
quantity,
a mobile core such as salt which moves upward
injecting into the more brittle overlying rock.
a volcanic vent or pipe, typically less than 1000 m
in diameter, drilled through enclosing rocks by the
explosive energy of gas-charged magmas (mobile,
possibly molten r rock material) ,
a sorption parameter relating amount of material
soirbed on solid material and amount remaining in
solution.
dose
health effect
leash Incident
local dose
"committed dose equivalent" is sometimes referred to
here as simply "dose," Dose equivalent is the pro-
duct of the absorbed dose from radioactivity and the
quality factor, loosely called biological dose,
expressed in units of rem or millirem (inrem) .
Committed dose is the sum of future dose accrual
(generally over 50 yj resulting from a radioactivity
intake. Dose expressed in roan-rests is the sum of dose
to individuals in a given population.
the rate at which dose (committed dose equivalent)
accrues following an intake or during .exposure to an
external source. Where an intake rate is also
involved, reference is made here to "dose committment
rate" (committed dose equivalent rate} .
an unwanted health effect such as leukemia, a cancer,
or serious genetic effect , equatable to a death for
damage estimation purposes,
a combination of events that introduces circulating
ground water to the waste inventory and starts dis-
solving waste components. Time delays for the leach
process and migration via ground water flow retard
the environmental effects,
committed dose equivalent to individuals located in a
given geographic zone, in mrem.
142
-------
nonspecific dose
nualide
offset fault-ing
probabilistic
radionualide
resuspension
risk
soTption
volcanicj
voloanism
explosion
committed dose equivalent to an undefined population
from consumption of largely exported agricultural
products, in man-rent.
a nuclear species characterized by the number of
neutrons and protons in the nucleus. Dsed here at
times in lieu of the more descriptive term: radio~
nuclide.
movement producing relative displacement of adjacent
rock masses along a fracture and resulting in a
separation or gap.
based on probability, which is the number of times
something will probably occur in & given amount of
time. The probabilistic mode refers to operations
with probabilities included in the calculations.
a nuclide which is unstable or radioactive.
a breach of containment which allows radioactive
material to migrate through the geosphere. A release
may or may not be directly to the biosphere.
the process of material deposited onto land surface
being picked up by wind action and resuspended,
The product of probability of occurrence of an event
and the consequences of an occurrence. As used in
economics, risk refers to the chance of damage or
loss.
an overall term referring to retention of a species
on a solid by any of several processes such as
absorption, adsorption, and ion exchange.
adjective and noun, respectively, pertaining to
natural processes resulting in the formation of
volcanoes or lava flows.
a violent explosive form of volcano ejecting material
into the atmosphere.
volaanogenic
transport
non-explosive carrying of material by any of three
mechanisms: magma transport, volatile transport,
or hydrotherma1 transport.
143
-------
VOLUME 1
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