United States
Environmental Protection
Agency
Office of
Radiation Programs
Washington DC 20460
EPA-5 20/3-80-006
December 1982
Radiation
£EPA
Population Risks
from Disposal of
High-Level Radioactive
Wastes in Geologic
Repositories
Draft Report
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EPA 520/3-80-006
POPULATION RISKS FROM
DISPOSAL OF HIGH-LEVEL RADIOACTIVE WASTES IN
GEOLOGIC REPOSITORIES
C. Bruce Smith
Daniel J. Egan, Or.
W. Alexander Williams
James M. Grunlke
Cheng-Yeng Hung
Barry L. Serini
Draft Report
December 1982
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Radiation Programs
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FOREWORD
The Agency has recently published environmental standards addressing
disposal of high-level radioactive wastes (40 CFR Part 191) for public
review and comment (47 FR 58196). An important part of this effort is the
evaluation of how effective mined geologic repositories are for isolating
these wastes from the environment for many thousands of years. EPA's
assessments indicate that carefully designed repositories at good sites
can keep long-term risks below those that would exist if (on a generic
basis) the uranium ore used to create the wastes had not been mined to
begin with. Accordingly, the Agency has proposed environmental standards
tnat would restrict projected releases from high-level waste disposal
systems—for 10,000 years after disposal—to levels that should keep
the risks to future generations less than the risks they would have been
exposed to from the unmined ore if these wastes had not been created.
This technical report presents these assessments of long-term
repository performance. It describes the models that the Agency developed
specifically for this project, reviews the various assumptions made, and
identifies the data used in these models. In general, a relatively simple
analytical methodology was formulated that should tend to overestimate the
long-term risks from geologic repositories.
Because much of this methodology is new, and because these risk
assessments are a key part of our rulemaking, the Agency is publishing
this as a draft report. During the public comment period on 40 CFR 191,
a Subcommittee of the Agency's Science Advisory Board will conduct an
independent technical review of our risk assessments (48 FR 509). All
meetings of this Subcommittee will be announced in the Federal Register
and will oe open to the public.
In addition, I encourage users of this report to submit any comments
or suggestions they might have. Such comments would be most helpful
if received by May 2, 1983, and they should be sent to: Central Docket
Section (A-130); Environmental Protection Agency; Attn: Docket No. R-82-3;
Washington, D.C. 20460. For additional information, please contact
Dan Egan at (703) 557-8610; Office of Radiation Programs (ANR-460);
Environmental Protection Agency; Washington, D.C. 20460.
Glen L. Sjoblom
Director
Office of Radiation Programs
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CONTENTS
Chapter 1: Introduction
Chapter 2: Disposal Systems
2.1 Engineered Controls
2.1.1 Waste Form
2.1.2 Waste Canisters
2.2 Geologic Media
2.2.1
2.2.2
2.2.3
2.2.4
2.2.5
Bedded Salt
Domed Salt
Granite
Basalt
Shale
2.3 Repository Construction
Chapter 3: Groundwater Transport
3.1 Basic Model
3.1.1 Host Formation Model
3.1.2 Aquifer Model
3.2 Gradients: Host Rock
3.3 Hydraulic Conductivity: Host Rock
Chapter 4: Groundwater Geochemistry
4.1 Retardation Factors
4.2 Solubility Limits
4.3 Geochemical Factors
4.3.1
4.3.2
4.3.3
4.3.4
4.3.5
4.3.6
4.3.7
4.3.8
4.3.9
4.3.10
4.3.11
Americium
Carbon
Cesium
Iodine
Neptunium
Plutonium
Strontium
Technetium
Tin
Uranium
Zirconium
Page
.1
7
8
8
15
17
18
19
21
23
25
29
31
31
37
38
41
46
49
50
56
58
58
64
64
65
65
66
67
68
68
70
71
m
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CONTENTS
Chapter 5: Release Mechanisms and Probabilities: 73
5.1 General Release Models 73
5.1.1 Direct Impact: Releases to Air and Land Surface 74
5.1.2 Direct Impact: Release to an Aquifer 75
5.1.3 Repository Disruptions: Releases to Land Surface 76
5.1.4 Repository Disruptions: Releases to an Aquifer 78
5.2 Specific Release Mechanisms 80
5.2.1 Normal Groundwater Flow 81
5.2.2 Human Intrusion (Drilling) 94
5.2.3 Faulting 108
5.2.4 Breccia Pipes 117
5*2.5 Volcanoes 121
5.2.6 Meteorites 126
Chapter 6: Environmental Pathways 131
6.1 Releases to a River 132
6.2 Releases to the Oceans 136
6.3 Releases to Land Surface 138
6.4 Releases to Atmosphere 139
6.5 Health Effects Calculations 144
Cnapter 7: Results 147
7.1 Releases from Low Probability Events 148
7.2 Releases from High Probability Events (Human Intrusion) 150
7.3 Releases from Normal Groundwater Flow 151
7.4 Results for Reference Repositories 152
7.5 Effects of Different Assumptions J.65
7.5.1 Different Waste Form Release Rates and
Canister Lifetimes 166
7.5.2 Solubility Limits 171
7.5.3 Different Retardation Factors 175
7.5.4 Summary of the Effects of Geochemical Factors 181
7.5.5 Different Integration Periods 183
7.5.6 Higher Probabilities 185
IV
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CONTENTS
Page
Appendix A: Repository Radionuclide Inventory 187
Appendix B: Radionuclide Transport in Groundwater 203
Appendix C: Derivations of Equations 209
C.I Solution to Equation 5-3a 211
C.2 Solution to Equation 5-5 212
C.3 Solution to Equation 5-7 213
C.4 Solution to Equation 5-18 215
C.5 Solution to Equation 5-5 with V*(t) from Equation 5-20 216
C.6 Solution to Equation 5-28 217
Appendix D: More Conservative Probability Estimates 219
D.I Human Intrusion (Drilling) 221
D.2 Faulting 221
D.3 Breccia Pipe 223
D.4 Volcanoes 224
D.5 Meteorites 224
Appendix E: FORTRAN Listing of Computer Program (REPRISK) 225
Appendix F: Input Guide for REPRISK 291
Appendix G: Sample Input and Output for REPRISK 315
References 323
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B-l Relative Error due to Omission of Diffusion Effect
TABLES
2-1 Characteristics of Radioactive Waste (Spent Fuel) 10
2-2 Various Waste Forms 11
2-3 Glass Leach Rate Constants 13
2-4 Reference Repository Parameters 16
3-1 Aquifer Characteristics 40
3-2 Equivalent Gradient and Viscosity Coefficient
for Aquifer Interconnection 43
3-3 Equivalent Gradient and Viscosity Coefficient
due to Thermal Buoyancy 45
3-4 Example Intrinsic Properties for Typical Repository
and Associated Lithologies 48
4-1 Soluoility Limits and Retardation Factors 51
6-1 Health Effects per Curie Released for Different Release Modes 145
7-1 Cnaracteristies of Low-Probability Events
(Faults, Breccia Pipes, Volcanoes, Meteorites) 153
7-2 Characteristics of Normal Groundwater Flow 154
7-3 Characteristics of High-Probability Events
(Human Intrusion by Drilling) 155
7-4 Expected Health Effects over 10,000 Years: Reference Cases 159
7-5 Expected Healtn Effects over 10,000 Years by Radionuclide
Reference Cases 160
7-6 Expected Health Effects over 10,000 Years:
No Radionuclide Solubility Limits 172
7-7 Expected Health Effects over 10,000 Years:
No Geochemical Retardation 176
7-8 Expected Health Effects over 10,000 Years:
Denham Retardation Factors 176
7-9 Expected Health Effects over 10,000 Years:
Effects of Different Geochemical Factors 182
7-10 Expected Health Effects over 10,000 Years:
Higher Event Probabilities 186
208
D-l More Conservative ("Second Estimate") Frequencies of
Occurrence for Various Events 222
G-l REPRISK Input Cards fpr Sample Proolem 317
G-2 REPRISK Output for Sample Problem 319
VI
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FIGURES
Page
2-1 Reference Repository in Bedded Salt 20
2-2 Reference Repository in Domed Salt 22
2-3 Reference Repository in Granite 24
2-4 Reference Repository in Basalt 26
2-5 Reference Repository in Shale 28
3-1 Schematic of Groundwater Model 32
6-1 Schematic of a Release to Rivers 133
6-2 Schematic of the Ocean Pathway 137
6-3 Schematic of the Land Surface Release 140
6-4 Schematic of the Release to Air 143
7-1 Complementary Cumulative Distribution Functions
.(Bedded Salt and Granite) 156
7-2 Complementary Cumulative Distribution Functions
(Basalt and Shale) 157
7-3 Expected Health Effects over 10,000 Years for
Reference Repositories in Different Geologic Media 161
7-4 Consequences and Risks for Different Events
(Bedded Salt and Granite) 162
7-5 Consequences and RisKs for Different Events
(Basalt and Shale) 163
7-6 Expected Health Effects over 10,000 Years vs.
Different Waste Form Leach Rates 167
• 7-7 Expected Health Effects over 10,000 Years vs.
Different Canister Lifetimes 168
7-8 Expected Health Effects over 10,000 Years vs.
Different Waste Form Leach Rates:
Granite Repository—Various Canister Lifetimes 169
7-9 Expected Health Effects over 10,000 Years vs.
Different Canister Lifetimes:
Granite Repository—Various Waste Form Leach Rates 170
7-10 Expected Health Effects over 10,000 Years vs.
Different Waste Form Leach Rates:
Bedded Salt Repository—Effects of Solubility Limits 173
7-11 Expected Health Effects over 10,000 Years vs.
Different Canister Lifetimes:
Bedded Salt Repository—Effects of Solubility Limits 174
7-12 Consequences and Risks for Different Events
(Effects of Retardation Factors) 178
7-13 Expected Health Effects over 10,000 Years vs.
Different Waste Form Leach Rates:
Granite Repository—Effects of Retardation Factors 179
VII
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FIGURES
Page
7-14 Expected Health Effects over 10,000 Years vs.
Different Canister Lifetimes:
Granite Repository—Effects of Retardation Factors 180
7-15 Average Healtn Effects per Year over Integration Period
Relative to Average over 10,000 Years 184
A-l Radioactivity in Hign-Level Waste from Different LWR
Fuel Cycle Options (100,000 MTHM) 190
A-2 Decay Heat from High-level Waste from Different LWR
Fuel Cycle Options (100,000 MTHM) 191
A-3 Total Radioactivity in Reference Repository 193
A-4 Significant Fission Products in Reference Repository 196
A-5 Significant Actinides and Daughters in Reference Repository 200
vm
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Chapter 1 - INTRODUCTION
The Environmental Protection Agency is developing—and has recently
proposed for public review and comment (47 FR 58196)—generally applicable
environmental standards for the management and disposal of high-level
radioactive waste. An important part of this process is to evaluate
now proposed disposal methods can limit the long-term dangers from these
wastes. This report describes our estimates of the population risks
associated with disposal of the wastes in mined geologic repositories.
There is a wide variety of potential disposal methods for high-level
wastes (IRG 79). However, most of the research to date has focused on
emplacement in geologic formations using conventional mining techniques.
As a result, this method could be implemented more rapidly than any other,
and more information is available to assess its potential environmental
effects. Therefore, the analyses described in this report consider only
geologic disposal. A report by the MITRE Corporation reviews other
disposal methods (AL 79a).
High-level wastes may be potential environmental hazards for a long
time. Accordingly, these analyses address environmental effects which may
happen over many thousands of years. We consider unplanned releases which
may occur from a geologic repository. Such releases are of particular
concern since institutional controls may not be reliable over a long
time. For example, human intrusion into the repository may not be
prevented, and unplanned releases may not be cleaned up.
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It is important that these analyses be summarized a
as possible; therefore, estimates of potential excess cancer deaths have
been associated with projected releases of radioactivity. However, the
limitations of this part of the analysis must be emphasized. Population
distributions, food chains, and technological capabilities will probably
change dramatically over thousands of years. Unlike geologic processes,
they can be realistically predicted only for short times. Accordingly,
very general models of releases resulting from manmade events and models
of environmental pathways, populations, and living habits have been
developed (SMJ 82). Rather than attempt to predict future changes in
population distributions, cancer cure rates, etc., the models use present
values for these parameters.
The analyses described in this report consider only risks to
populations, as opposed to risks to individuals. As a result, many
simplifications were possible in the analytical models. Most importantly,
total quantities of radioactivity released are of concern, rather than
concentrations of radioactivity released. This assumption is reasonable
since we are concerned with the total doses received by man and not the
maximum dose to any individual. Because of these simplifications,
individual doses cannot be determined from the information in this
document. However, a companion report (GO 82) describes analyses that
assess individual doses from several types of release.
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We developed a generic reference model of a repository system to
assess the population risks from geologic disposal. This model includes
the amount of radioactive wastes, the waste form, the waste canisters, the
repository design, the surrounding geologic media, the geochemical and
hydrological properties of these media and environmental pathways.
Various host rocks were considered, including bedded salt, domed salt,
granite, basalt, and shale. This reference model was then used to
calculate the consequences of releases from the repository to the
environment for a wide variety of circumstances. The consequences are
then placed in their proper perspective by combining them with appropriate
probabilities of occurrence.
Relatively simple mathematical representations of each part of the
repository system were used. However, there are several components, which
can interact in many ways. Many combinations of parameters were studied
to determine the effects of various assumptions. To perform this large
number of computations, a computer program called REPRISK was developed.
A FORTRAN listing of this program, instructions on its use, and a sample
input and output are provided in Appendices E, F, and 6. The mathematical
equations and the parameters used to represent the various parts of the
repository system are discussed in Chapters 2 through 6 of this report.
The reference repositories and waste characteristics are described in
Cnapter 2. Each component of the repositories is discussed, and the
parameters used to describe eacn component are identified. Chapter 3
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explains the mathematical equations used to calculate movement of
radionuclides through groundwater pathways. Chapter 4 discusses the
geochemical interactions of these radionuclides with the groundwater
system; such interactions are a very important part of the overall
analysis. Chapter 5 summarizes the mathematical equations used to
describe the mechanisms, both expected and accidental, that may release
radionuclides from the repository to the surrounding environment. These
release calculations are based on the analyses contained in the report
prepared for EPA by Arthur D. Little, Inc. (ADL 79). Chapter 6 provides
an overview of the equations used to calculate the movement of released
radionuclides through environmental pathways and the associated population
health impacts; these models are more fully explained by Smith, et al.
(SMJ 82). The combination of all of these models of various parts of the
repository provides estimates of the population risks associated with
generic reference repository system designs. These estimates are examined
in Chapter 7, along with sensitivity studies which examine the effects of
different assumptions about the various parts of the disposal system.
The objective of these analyses is to provide enough information to
judge the adequacy of geologic disposal in limiting the release of the
waste to the environment. The important characteristics of repository
systems have been identified as variables to study their effects on the
overall risks. These variables are used in relatively unsophisticated
models which are intended to overestimate, rather than underestimate, the
risks. Because of the generality and simplicity of this approach, these
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analyses cannot be used to judge the risks from a specific disposal system
at a specific site. The detailed data and particular circumstances
associated with that specific site must be considered. (For example, in
our analyses, basalt repositories always show higher risks than granite
repositories; however, a basalt repository at a specific site may have
lower risks than repositories at many potential granite locations.)
However, we do believe that the analyses described in this report provide
reasonable upper bounds of the risks from geologic repositories—given the
specific assumptions for each analysis. Accordingly, the Agency has used
these analyses as an important tool in selecting the long-term containment
requirements in its proposed standards for disposal of high-level wastes
(EPA 82).
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Chapter 2 - DISPOSAL SYSTEMS
We have represented a high level waste disposal respository as three
interrelated subsystems which isolate the waste from the environment: the
engineered controls, the surrounding geologic media, and the groundwater
flow system. The first subsystem—the controls engineered to contain the
waste—includes the waste matrix and the waste canisters. Other engineered
controls that would help isolate the waste from the environment—but which
are not included in these analyses—include material packed around the
canisters and backfill in the repository to inhibit ground water movement.
The second suosystem is the natural structure of the geologic media.
This report describes five types of geologic disposal media: bedded salt,
domed salt, granite, shale, and basalt. The geologic roedia; subsystem
includes the host rock, the overlying and underlying geologic materials,
the repository and the shafts and seals which penetrate the host rock.
The original properties of the host rock media are very important; however,
the alterations to the rock that occur during and after repository
operation are also critical to evaluating the degree of risk associated
with waste disposal. It is also important to evaluate aspects of
repository construction and excavation, such as the number and size of
shafts and boreholes as well as the repository backfill material.
The tnird subsystem, the groundwater flow system, includes the
overlying and underlying aquifers and their hydrologic and geochemical
characteristics. This subsystem is discussed in Chapter 3.
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2.1 Engineered Controls
2.1.1 Waste Form
We considered two types of waste: solidified high-level waste which
results from reprocessing spent fuel to recover uranium and/or plutonium,
and spent fuel itself. The engineering controls for spent fuel disposal
could be limited to containment of the fuel in an outer steel canister
purged and backfilled with dry nitrogen (ADL 79b), or additional
procedures could be used, such as casting metal into the spent fuel
canister. The high-level liquid waste resulting from spent fuel
reprocessing would be solidified in a stable matrix, such as glass.
The most important single characteristic of either of these waste forms is
the rate at which they release radionuclides into groundwater in the
repository. For certain radionuclides, this release rate may be limited
by their solubility in groundwater. Solubility limits are discussed in
detail in Chapter 4. To simplify our analysis of releases from the waste
package, we selected a reference waste form which incorporates the most
important characteristics of both spent fuel and reprocessed waste.
We also simplified our analysis by considering only a few of the
radionuclides which would be buried in a repository. The modified
inventory is based on a detailed computer analysis with the ORIGEN
computer program (BE 73) that was conducted by ADL (ADL 79a). This
analysis revealed that many of the hundreds of radionuclides which were
evaluated could be omitted from further consideration. The criteria for
including a radionuclide in our analysis is either the large quantity of
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radioactivity, large dosimetric significance, long half-life, and/or short
retention times by the geologic media. The inventory of radionuclides we
analyzed is presented in Table 2-1. Further discussion of the repository
inventory is included in Appendix A. We used the radionuclide mixture
contained in spent fuel to characterize the waste since it has a higher
inventory of many important radionuclides and represents a more
concentrated heat source.
To develop a reference waste form release rate (which we sometimes
call a "leach rate"), ADL reviewed the effectiveness of various waste
forms (ADL 79b). The scope of this study, which considers high-level
liquid wastes, cladding hulls and fuel handling residues, and spent fuel
elements is illustrated in Table 2-2. We considered only high-level waste
and spent fuel in this report since the other waste categories involve
much less radioactivity.
To develop a reliable reprocessed waste form, solidification of the
waste liquid could be performed by calcination followed by glassification
(ADL 79b). Calcination occurs when the liquid waste is roasted at high
temperatures to produce a granular powder that is stable and less mobile
than liquid wastes, but is still highly leachable. Calcines are relatively
soluble and have high surface-area-to-mass ratios. Since full dissolution
of calcined waste would be expected to occur in less than one year, the
calcined waste should be converted to glass to limit dissolution. Calcined
waste is glassified by melting the waste together with glassmaking frits
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Table 2-1
Characteristics of Radioactive Waste
Radionuclide
Am-241
Am-243
C- 14
Cs-137
1-129
Np-237
Pu-238
Pu-239
Pu-240
Pu-242
Sr- 90
Tc- 99
Sn-126
Zr- 93
(Spent Fuel)
Initial Quantity in
Repository (ADL 79a) (curies)
1.7 E8
1.7 E6
2.8 E4
8.6 E9
3.8 E3
3.3 E4
2.2 E8
3.3 E7
4.9 E7
1.7 E5
6.0 E9
1.4 Eb
5.6 E4
1.9 E5
Half Life
(years)
458
7,650
5,730
30
1.6 E7
2.14 E6
89
24,400
6,260
3.8 E5
29
2.1 E5
1.0 E5
9.5 E5
10
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Table 2-2
Various Waste Forms*
Source of
Waste
Converted
Waste Form
Assumed Mode
of Disposal
Canister Material
Notes
High Level calcine
Liquid Waste
deep geologic burial
Spent Fuel
boroslHcate deep geologic burial
glass
none deep geologic burial
Cladding Hulls* none
deep geologic burial
Krypton-85 none storage at reprocessing
plant
Iodlne-129 none deep geologic burial
Carbon-14 none deep geologic burial
Tritium release
(a) carbon steel
(b) titanium
stainless steel
(a) carbon steel
(b) titanium
carbon steel
steel (pressure
cylinders
carbon steel
carbon steel
spray calcination process
spray calcination process
In-can melt process
dry nitrogen backfill
dry nitrogen backfill
compacted to 1/3 original
volume
stored for -100 years for
decay
as silver zeolite and
mercuric iodate
as calcium carbonate
*For this study fuel bundle hardware is assumed to be separated from cladding hulls and treated as low-level
waste.
+Based on Information from the ADL report (ADL 79b, AOL 79c).
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to form a relatively homogeneous mixture of waste products in glass. Many
years of laboratory work have shown that glass leaching is usually a very
slow process. The theoretical models and physical data, however, are
often conflicting, imprecise, and incomplete. Studies of the effects of
factors such as temperature, flow, pH, and salinity on various types of
glass are currently under investigation (ME 81). The extrapolation of the
short-term laboratory tests to very long time periods is hindered,
however, by the limited amount of long-term leaching data available.
The adequacy of short-term leach rate data to represent long-term
processes needs to be evaluated. Several different sources of leach data
for glass have been reviewed by ADL (ADL 79b) and are summarized in
Table 2-3.
Since the data are so sparse, it appears prudent to assume a
conservative (i.e., high) value for glass leach rates. A value of
—ft 9
10 g/cm per day has been chosen as the reference value for this
report. This value is larger, by at least a factor of seven and as much
as a factor of 100, than any reported leach rates measured one-year after
initiation of leeching (ADL 79b,c). We assume no change in the leach rate
with time—resulting in a constant fractional radionuclide release rate
for our analyses. We believe our conservative approach should compensate
for any uncertainties concerning long-term deterioration of the waste
package, such as devitrification.
12
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Source:
Table 2-3
p
Glass Leach Rate Constants (gm glass/cm -day)
Leach Period - Days
20
115
300
700
2900
Mendel
(A)
Based on Cs
anu on Sr
Ross
(B)
10'
-6
Based on Soxnlet Test:
(Time not indicated)
Based on Cs
First Test
(Glass 1)
Second Test
(Glass 2)
Field Test
(Glass 2)
io-°
io-5
io~5
4x10
~8
-5
10'
-7
10
-6
10
-7
10
4xlO"7 2xlO~7 1.5xlO~7
10'
,-8
7x10'
,-8
4xlO~10 SxlO"11
(A) Reference (ME 77a) Devitrification of these same glasses increased the
leach rate by a factor of 10 to 20.
(B) Reference (RO 77) Soxnlet test is batch "flowing" water at approximately
90°C. Devitrification increased leach rate by up to 6 times the rate
measured by the Soxnlet test.
Reference (ME 77o).
13
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To determine the total release rate of radioactive material, glass
leach rates (g/cm2 per day) must be combined with surface-to-mass ratios
(cm2/g) to give fractional releases per day. ADL assumed an initial
surface-to-mass ratio of about 0.4 cm2/g for glass. This value is
consistent with test data on actual canisters considering normal cooling
transients and additional breakage from normal handling. The resulting
initial release rates range from roughly 0.01 percent per year down to
0.0001 percent per year, depending upon the assumed glass leach rate value.
Tne leacn rate for spent fuel can vary widely depending upon
temperature, groundwater chemistry, and oxygen content. The range
reported in the ADL report (ADL 79b) spans five orders of magnitude, from
/- p p
1x10 g/cm per day to 0.1 g/cm per day. Considerably more effort
is required to increase our knowledge of spent fuel leach rates. We assume
the radionuclide release rate for the spent fuel matrix is 10~^ yr
(0.01 percent per year). This value is based on the conservative value
chosen for glass since it is expected that the eventual spent fuel matrix
will have to be at least as resistant to leaching as a low leach rate
material which is presently available, such as glass. To determine the
importance of tne release rate in disposing of radioactive waste, several
other release rates were analyzed—including a low release rate for glass
of 10" yr~ and a high release rate of 10~2 yr"1, which is more
representative of calcines.
14
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2.1.2 Waste Canisters
The waste matrix discussed in the previous section will be enclosed
in a canister. Canister lifetimes can range from as little as several
years to more than 1000 years, depending upon canister material and
repository characteristics (ADL 79b). The manufacture of high-integrity
canisters with expected lifetimes up to 1000 years appears to be feasible—
either by using thicker sections of conventional materials, such as carbon
steel or stainless steels or, in salt media, through the use of a material
with a low corrosion rate, such as titanium. In this report, we briefly
discuss carbon steel, stainless steel, Inconel, and titanium canisters;
a more complete review is contained in ADL's report (ADL 79b). The number
and spacing of canisters to be stored in the reference repository are
listed in Table 2-4.
The importance of the resistance of the canister to corrosion in the
geologic disposal medium depends on the degree of containment desired. To
be conservative, we nave assumed that in a salt repository the canister
will be in a hot, moist, salt-saturated environment. We have assumed the
environment of nonsalt media to be less corrosive but still hot and
moist. Carbon steel and stainless steel have very poor corrosion
resistance in hot brine. Although Inconel has outstanding resistance to
corrosion in hot flowing seawater, it is quite vulnerable to pitting and
serious localized attack in quiescent seawater. Tne corrosion rates of
mild steel range from 0.08 to 1.6 mm yr; rates for Inconel alloys range
from 0.0008 to 0.134 mm yr; and stainless steel corrosion rates range from
0.0001 to 0.97 mm yr (ADL 79b). Titanium and its alloys are outstanding
15
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Table 2-4
Reference Repository Parameters
Depth of Repository 460 m
Dimensions of Repository width 2 km
length 4 km
height 5 m
Number of Canisters 35,000
Numoer of Waste Drifts 350
Canisters per Waste Drift 100
Lengtn of Waste Drift 500 m
Canister Spacing 5 m
Total mined volume 10
16
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in their resistance to corrosion by seawater under all conditions of
temperature and velocity. Titanium corrosion rates in hot salt water are
on the order of 0.002-0.02 mm per year—tne lower rate applies to titanium
alloys, and represents a service life of 1000-10,000 years for a
25 millimeter thick canister (ADL 79b).
Since we do not know what the final design characteristics or
capabilities of the canister will be, we have taken a conservative
approach. We assumed a canister life of 100 years for salt media, and a
500-year canister life for less corrosive host rocks. To simplify our
analysis, we have also assumed tnat all the canisters fail simultaneously
and completely at the end of their assumed life. To determine the
sensitivity of our analysis results to canister life expectancy , we also
analyzed canister lives of 1000 years and 5000 years.
2.2 Geologic Media
Based on the efforts being conducted by the Department of Energy, ADL
concentrated its study on the following five geologic host media (ADL 79b).
1) bedded Salt; stratified, plastic
2) domed Salt; intrusive, plastic
3) granite; intrusive, fractured
4) basalt; stratified, fractured
5) shale; stratified, fractured
Other rock types have been considered for repositories, such as welded
volcanic tuffs, desert alluvium, anhydrite, and seabed sediments (ADL 79d)
Nevertheless, the media included in the ADL report span a wide range of
17
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geologic structure and rock properties, and we believe an analysis based on
them is representative of the performance capabilities of geologic
repositories in general.
The host media are generally overlain with several hundred meters of
earth, usually silt, shale, or sand, and bounded above and possibly below by
aquifers. The host rock is either stratified (such as bedded salt, shale,
or basalt) with an aquifer above and below, or is an intrusive (such as
granite or domed salt) with only an aquifer above the repository. The host
rock characteristically is either plastic and tends to move under earth
pressures, or structurally very rigid but susceptible to fracturing. The
host rocks that are plastic (bedded salt, domed salt, some shales) are
almost impermeable to water and, if fissures in the rock occur, the rock
tends to reseal itself. The host rocks that are structurally rigid
(granite, basalt, most shales) have low permeabilities, but can be
fractured, especially as a result of faulting or thermal change, and they
do not reseal themselves. All of these host rocks are good heat conductors,
with salt being the best dissipator of heat.
2.2.1 Bedded Salt
More research has gone into analyzing bedded salt as a suitable waste
repository medium than for any other lithology. One of the more attractive
features of bedded salt is its common occurrence in stable formations at
depths considered for repositories (200 meters to 1000 meters). It
possesses the following properties: (1) it is very soluble, which is not a
18
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good characteristic for a waste repository; (2) it is plastic under
pressure, thus tending to creep into voids and cracks and seal itself to
the flow of water; and (3) it is the best thermal conductor of the five
media.
Salt is frequently mined and is often associated with other minerals,
oil or gas. However, because bedded massive salt deposits are numerous in
the United States, sites can probably be found which have minimal economic
value and a range of other desirable characteristics. ADL developed a
generic bedded salt repository which is schematically represented in
Figure 2-1 (ADL 79d). The reference repository is 460 meters deep, in the
middle of a homogeneous bed of salt 100 meters thick, with overlying and
underlying aquifers. The salt is bounded by layers of shale which are
50 meters thick.
2.2.2 Domed Salt
Some salt formations have been forced up through overlying rocks from
original beds several thousands of meters deep. These domes or stacks of
salt are composed of fairly homogeneous halite and are generally devoid of
the interbeds or similar features found in bedded salt. Typically, a salt
dome will be roughly a kilometer in diameter and capped with a blanket of
less soluble evaporite.
19
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Surface
Surface
Deposits
380
mnr Shale innr^rtnnnnrzru^nrinnnn^r^nri
410 Meters
Salt
.*— Repository
:_—_- Shale
460 Meters
510 Meters
560 Meters
590 Meters
FIGURE 2-1: REFERENCE REPOSITORY IN BEDDED SALT
20
-------
Because the dome was injected through the overlying strata, the rock
surrounding the dome is often shattered and disrupted with prevalent joints
and fractures. The salt itself may come very near to, or even reach, the
surface, but the source of the salt column may extend to a depth of
10 kilometers. The geometry of a dome prevents an aquifer from being
directly below the repository. However, the fracturing of the surrounding
rock causes the salt to be in contact with groundwater in adjacent
aquifers. These and other differences between bedded and domed salt
deposits require separate analyses for each. As with bedded salt deposits,
domes are frequently associated with oil, gas, and various mineral
resources. In addition, salt domes are often mined for their relatively
pure salt or used as storage caverns.
Figure 2-2 is a schematic illustration of the reference domed salt
repository described by ADL (ADL 79d). The repository is 460 meters below
the earth's surface in the middle of a homogeneous salt dome. The overlying
aquifer is assumed to be identical to the one for bedded salt at a depth of
200 meters. The lower aquifer surrounds the dome at 560 meters.
2.2.3 Granite
Granite, which is a monolithic crystalline rock, is another potential
host medium. It is an assemblage of minerals forming a rigid and
essentially insoluble rock. It is relatively strong and does not flow
plastically; thus, cracks can remain open to migrating fluids, although
some cracks may become filled with clay or other materials. In addition,
21
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Surface
Surface
Deposits
Country « V
Rock ' X
Aquifer
200 meters
230 meters
460 meters
560 meters
590 meters
FIGURE 2-2: REFERENCE REPOSITORY IN DOMED SALT
22
-------
water passing through granite is generally less corrosive than the brines
associated with salt. Because it is intrusive and not underlain by
stratified deposits, the granite repository would not generally have an
underlying aquifer. This affects the analysis of water flow through the
repository.
Many areas of the country have granite or similar rocks at depths
suitable for a repository. Occasionally, vein minerals, pegmatites, or
quarry stone make granite economically important, but the vast expanse of
crystalline rocks suggests that many potential site locations exist.
Figure 2-3 is a schematic illustration of the reference granite
repository described by ADL (ADL 79d). The reference granite repository is
460 meters below tne earth's surface. The overlying aquifer is assumed to
be identical to the one for bedded salt, but at a depth of 200 meters.
2.2.4 Basalt
Basalt is another igneous rock that is being considered as a
repository medium. It shares with granite many properties common to
igneous rocks. It is strong, rigid, highly resistant to dissolution, and
has a complex mineralogy.
The extensive flow basalts currently being investigated are unlike
other igneous rocks in a number of important ways. These basalts have
formed as a series of layers over a long period of time and there are
sedimentary interbeds and other permeable zones that can serve as aquifers
23
-------
. Surface
Deposits
> <.
1- r" J
,rj-, *'-•*-
r, fc •» , •• > * A*"*1- J 1 I- '
VTtr-»t>v'l.*>
"1''l,A,A«trVTT j
1-J-»1J-W>^j'--'-,
* *• *• •> »*^AL.
-.-:---. .'-/..^^.v.v,:.//,^'.',--"•''«:".
•c. v.'.:: •. •:•;, v,'.-..-. v. -;-:- \v.-: • •' >:• vV
vAvw-7v*v*,.>v,.Vs,.,v -M->uVi . .«. t.' v ' ' r >.
IT — •* -I' >>'^-»'**~~.?
VA VWTVO v» i. v r v^-iv^tj
iJ<.•l1t>rA»•'v«v'•l.^"
Surface
200 Meters
230 Meters
460 Meters
FIGURE 2-3: REFERENCE REPOSITORY IN GRANITE
24
-------
contained within them. These aquifers could exist both above and below
any oasalt flow in which the repository would be located. Basalt
characteristically breaks into slender columns as it cools, producing
vertical joints. However, weathering products of the rock often fill these
joints. Basalt is rarely associated with other mineral resources, and its
most common economic use is as fill material. The principal flow basalts
that are being investigated for possible repository siting are located in
southeastern Washington.
Figure 2-4 is a schematic representation of a reference basalt
repository (ADL 79d). The reference repository is 460 meters below the
earth's surface with 100 meters of basalt above and below the repository.
The basalt is bounded by overlying and underlying aquifers at 330 meters
and 560 meters, respectively. The two aquifers are identical to those for
the reference bedded salt repository.
2.2.5 Shale
Argillites, siltstones, and shales are the most common and extensive
sedimentary rocks. These clay-rich rocks are found in thick deposits, and
they are often nearly impermeable. Some shales exhibit a plastic behavior
similar to salt, and they have the added advantage that they are essentially
insoluble. The hydrologic and geochemical properties of shales vary
considerably.
25
-------
-Surface
Surface
Deposits
iv^ Aquifer
-., > \ ;-7
•r330 meters
460 meters
FIGURE 2-4: REFERENCE REPOSITORY IN BASALT
26
-------
Clay minerals have a number of properties that may be important to
waste containment. Several clays can absorb water into their structures,
swelling in the process and sealing pore spaces and potential water
passageways. Similarly, clays can absorb chemicals, including
radionuclides, and severely retard their movement. Many clay minerals,
however, can also be dehydrated by heating. This process could change both
their chemical and mechanical properties, thereby affecting their ability
to contain wastes.
Argillaceous (clay-containing) deposits have a variety of economic
uses. Their abundance, however, suggests that many potential sites could
exist where economic and social impacts would be minimal. We assume the
reference shale repository is highly indurated, which would aid the
stability of a mine while pernaps increasing the potential for fluid flow
through fractures. While some shales are nearly impermeable to the flow of
water, the hard shale in the model is assumed to have hydrologic properties
similar to that of basalt.
Figure 2-5 is a schematic representation of a reference shale
repository. The schematic is identical to the one for bedded salt except
that a shale layer replaces the salt layer.
27
-------
Surface
Surface
Deposits
i.j»',...im.j..i,mni«. 330 meters
iilss:i«i£l&3!<e
460 meters
fAquifer feipl^pij^^^ ^
'////////
Basement
Complex
FIGURE 2-5: REFERENCE REPOSITORY IN SHALE
28
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2.3 Repository Construction
The ADL report discusses many aspects of repository construction and
the design of the mined tunnels, boreholes, shafts, etc. (ADL 79b).
However, the only construction characteristics considered in this analysis
are the repository backfill and the borehole and shaft seals.
During repository excavation, all of the mined material may be brought
to the surface, stored during emplacement of the wastes, and then used as
backfill for the tunnels. Alternatively, if a working mine volume has been
created, mined material from a tunnel under construction may be used
immediately as backfill for a tunnel already loaded with waste. In either
case, based on a mined fraction of 25 percent and a repository height of
5 meters (ADL 79d), the volume of backfill would be IxlO7 m3. Since
the backfill cannot be packed very tightly, we assume the porosity of the
backfill is 20 percent. Thus, the porosity volume would be 2x10 m .
After backfilling the repository, if any water is available the backfill
can become recharged with water. This recharge water can be supplied
through the surrounding bulk rock and/or by the migration of water through
permeable borehole and shaft seals. In salt repositories the undisturbed
salt is essentially impermeable to the flow of water. Thus, the recharge
of the backfill would only occur through the shafts and boreholes.
29
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During the operational stage several vertical shafts and many
boreholes will be required for ventilation, exploration, and transportation
of personnel and materials between the mine and the surface. Sealing the
repository to isolate the radioactive waste requires that these shafts and
boreholes be filled to prevent them from serving as conduits for fluid flow
and radionuclide migration. The sealing materials will probably have
chemical and mechanical characteristics very similar to those of the
surrounding rock. The seal may consist of several layers of completely
distinct types of materials to provide redundant barriers to intrusion.
Nevertheless, it is reasonable to expect that—over a long period of time—
the combination of processes such as settling, leaching, expansion and
contraction due to fluctuations in water content or temperature, earth
movements, weathering, and fatigue may lead to some degradation in the
integrity of the seal. We represented this degradation with a generic
model that characterizes the shaft seal integrity by a spatially uniform
hydraulic conductivity K. One hydraulic conductivity value (Kn) is
assumed for the time of seal placement, and another value (K,) is
projected for the time 10,000 years later, we then assume that K increases
linearly from KQ to KI over this period (ADL 79d).
30
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Chapter 3 - GROUNDWATER TRANSPORT
There are several models which have been developed to describe the
complicated movement of radionuclides from a repository to an aquifer and
then through the aquifer to a river or other body of surface water
(ADL 79c). These models often require extensive data and generally
calculate the concentration of radionuclides at specific locations and for
specific times. However, our analysis of population risks, which requires
only the calculation of total releases to the environment, can use simpler
models. One of our principal considerations is the time required for
radionuclides to travel from the repository to the environment.
This chapter describes our simplified model and compares it with more
sophisticated models. We discuss the specific parameters we used—
especially those describing the reference aquifer, the hydraulic
gradients, and the hydraulic conductivity and porosity of the host rock.
3.1 Basic Model
Tne transport of radionuclides from a deep geological repository
through the groundwater pathway to the biosphere depends on the
hydrological and geocnemical properties of the aquifers overlying and
underlying the repository and the path from the repository to these
aquifers. A schematic of the groundwater model we used is shown in
Figure 3-1. We made the following assumptions in developing our reference
groundwater model:
31
-------
Co
ro
Ground Surface
Surface Stream
Groundwater Flow Velocity in Aquifer
Groundwater Flow Velocity in Aquiclude
Repository Aquiclude
Radioactive Waste Repository
FIGURE 3-1: SCHEMATIC OF GROUNDWATER MODEL
-------
1. The waste will be disposed in geological formations with very low
hydraulic conductivities. For this analysis these formations can
be lumped together and considered to be a single host formation.
2. Generally, aquifers lie above and beneath the host formation.
For intrusive geologic media such as granite and domed salt there
is no aquifer below the host rock. However, domed salt
formations are assumed to have a "lower" aquifer surrounding the
dome below the level of the respository. There is no lower
aquifer for granite.
3. The upper and lower aquifers are confined by relatively low
permeability layers of rock and they deliver a steady groundwater
flow over the entire time of interest.
4. The hydrologic and geohydrologic characteristics of the upper and
lower aquifers are identical except for the potentiometric head.
The hydraulic gradient between the aquifers caused by the
potentiometric head difference is assumed to be constant. The
potentiometric head in the lower aquifer is assumed to be greater
than the head in the upper aquifer, and flow is from the lower to
the upper aquifer.
5. A buoyant force is assumed to result from a temperature
difference and is designated as a thermal buoyancy gradient.
This is dissussed further in Section 3.2.
33
-------
Based on these assumptions, tne radionuclides being released from the
repository into the groundwater will be transported upward through the
host formation to tne upper aquifer. The radionuclides are then slowly
transported horizontally through the upper aquifer to a body of water on
the earth's surface, such as a lake or river, where they become available
to people.
For simplicity, we chose two one-dimensional ground water transport
models to describe transport through the host material and the aquifer.
One represents vertical transport through the host rock and depends on the
area, hydraulic conductivity, and gradient of boreholes, shafts, or
fractured host rocks; the other represents horizontal transport through
the aquifer and depends on the properties of the aquifer. The basic
assumptions used to describe the one-dimensional transport of a
radionuclide through a homogeneous medium are:
1. Tne flow in the geological formation is laminar and one-
dimensional. The restriction that Darcy's law is valid only under
conditions of laminar flow, and that it requires modification when
turbulent flow prevails, should not affect analyses for a suitable
repository site. Even though turbulent flow conditions may exist
on a microscopic basis as groundwater moves through geologic
media, the macroscopic flow in generally low permeability regimes
(such as should exist in the geologic media surrounding any
reasonable site for a repository) may be adequately described by
the laws governing laminar flow (Darcy's Law).
34
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2. The driving forces which transport the groundwater and
radionuclides tnrough the host rock are a combination of the
buoyant force resulting from the thermal gradient plus the
hydraulic gradient which exists between the upper and lower
aquifer.
3. Equilibrium between the sorbed and dissolved radionuclides within
the groundwater system is maintained at all times. That is, the
rate of reaction for the sorption process is much faster than
that of the radionuclide migration and radionuclide decay.
4. Hydrodynamic dispersion remains constant and is independent of
the concentration gradient. Furthermore, we decided that
dispersion may be neglected in this risk assessment. Details of
the evaluation leading to this judgment are presented in
Appendix B.
The equation which describes one-dimensional transport of a single
radionuclide in a homogeneous medium is:
aC Da2C
2
3t .Rsx Rsx
+ xC = 0 (3-1)
wnere C is the concentration of the radionuclide as a function of distance
x and time t, D is the coefficient of hydrodynamic dispersion, v is the
interstitial velocity of the groundwater, x is the radioactivity decay
constant, and K is a retardation factor which is a function of the
physical and geochemical interaction of radionuclides with the geologic
media. The coefficient of hydrodynamic dispersion, D, refers to the
35
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spreading and mixing whicn is caused in part by the bulk movement of
groundwater and molecular diffusion. For many field situations the mixing
caused by the bulk movement of groundwater is most important, but in low
velocity systems, such as are expected near a repository, molecular
diffusion is the dominant process affecting hydrodynamic dispersion. In
the absence of hydrodynamic dispersion the physical and geochemical
interactions of radionuclides with the geologic media can significantly
affect the rate of radionuclide transport. For example, if the
retardation factor, R, equals 10, the radionuclide is transported slower
than the groundwater by a factor of 10.
If the dispersion effects are small and can be ignored, then
equation 3-1 cah- be written:
This equation can be rewritten to describe the rate of total radionuclide
activity being transported by introducing:
Q = CAnv
(3-3)
in which Q is the rate of total activity being transported through distance
x at time t, n is the porosity of the geological medium, v is the
interstitial velocity, which is assumed to be constant along the flow
path, and A is the cross-sectional area of the flow path. Substituting
equation 3-3 in equation 3-2 results in:
.ay. va(j
at + Rax + ^ - ° (3-4)
36
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Equation 3-4 is the basic differential equation for the groundwater
transport model and can be solved either numerically or analytically when
the interstitial velocity is known and the boundary and initial conditions
are defined.
3.1.1 Host Formation Model
Tne repository may be exposed to natural or man-caused disruptions
that result in abrupt or gradual changes in the hydraulic conductivity of
a portion of the host formation. Should these disruptions ever occur, we
have assumed that the hydraulic gradient across the host formation would
be upward. The groundwater interstitial velocity appearing in
equation 3-4 can be described as:
v = Ki/n (3-5)
where K is the hydraulic conductivity, n is the effective porosity, and
i is the hydraulic gradient across the host formation. The hydraulic
gradient in this equation represents the combined effects of the aquifer
interconnections (assumed to create an upward gradient) and the
temperature effects, as stated previously.
Since the heat generated from the waste will vary with time, the
fluid properties, such as viscosity and density will change with time—
as will the interstitial velocity. Tne relatively slow rate of change of
velocity, however, allows a quasi-steady state solution to equation 3-4 by
assuming that the velocity is constant over time. The resulting
analytical solution is:
37
-------
6 = Oft - t - R.X../V..J EXP (-x R.X../V,) U[t - t - R-X-./V,! (3-6)
waq ^L e 1 1' 1J 1 1 1' ell' 1J
where t Is the time tne release occurred, x is the vertical distance
between upper aquifer and the waste repository, the subscript 1 denotes the
host formation, and Q „ is the rate of release to the aquifer. The
aq
U term is a step function. The amount of radioactivity which would reach
the aquifer is the same as the amount leaving the repository, corrected
for radioactive decay during transit. For the host media and barrier
seals, R-, is conservatively assumed to be 1 for all the radionuclides.
Because the distance from the repository to the aquifer is a small
fraction of the distance to the environment, the analysis results are not
sensitive to values of R-,.
3.1.2 Aquifer Model
The most important aspect of the aquifer is the radioactive decay
which occurs during transit from the host rock to the environment. We
make tne assumption that tne hydraulic gradient and hydraulic conductivity
of the upper aquifer remain unchanged regardless of any disturbance of the
repository. We derive the aquifer transport model from our basic
differential equation 3-4. The analytical solution for equation 3-4,
using equation 3-6 as a boundary condition, is:
Q- QLt-te-tdJ EXP[-xtdJ U[t-te-tdJ (3-7)
*d " ldl + *d2 = R1X1/V1 + R2X2/V2
38
-------
The subscript 2 denotes the aquifer, and the other variables have been
defined previously. The rate of radionuclide release into the surface
water from the aquifer therefore can be estimated by using equation 3-7-
For modeling aquifer flow we assume there is no difference between
the aquifers of the five types of geologic repositories. Table 3-1
presents the reference aquifer cnaracteristics and their range of values.
These values are taken from the ADL report (ADL 79c) and are
representative, for example, of sandstone formations with low-to-moderate
hydraulic conductivity.
Transport of radionuclides to the environment is dependent on the
ability of the overlying and underlying aquifers to transmit water.
Groundwater moves from points of higher head to points of lower head, and
the flow rate is directly proportional to the hydraulic gradient. The
relationship between the hydraulic gradient and the groundwater flow rate
is expressed by Darcy's Law:
Vaq ' aquifer
3
where: V = aquifer volumetric flow rate, m /yr
aq
K = hydraulic conductivity of the aquifer, m/yr
i = hydraulic gradient of the aquifer
o
A = cross-sectional area of the aquifer, m
Using the parameters in Table 3-1, the limiting aquifer flow rate is
3
calculated to be 37,800 m /yr, and the interstitial velocity is
calculated (equation 3-5) to be 2.1 m/yr.
39
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Table 3-1
Aquifer Characteristics
Distance from reposi-
tory to overlying
aquifer (meters)
bedded salt, basalt
granite, domed salt
Reference
values
100
230
Range
of values
Distance along aquifer
to man's environment
(meters)
1600
Hydraulic conductivity
in aquifer pathway
(meters/year)
31.5
.31-31.5
Gradient in aquifer
pathway
.01
.01-0.1
Effective porosity
in aquifer pathway
.15
.15
Cross-sectional area of
aquifer overlying the
repository (square meters)
(normally the thickness of
the aquifer times the widest
dimension of the repository
floor area)
1.2E5
Thickness of aquifer (meters)
30
15-45
40
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Tne travel time in our reference aquifer from the host rock to the
environment can be calculated using equation 3-9:
td2- (R2xn)/(Ki)aquifer (3-9)
wnere K and i are the hydraulic conductivity and gradient of the aquifer,
x is the distance to tne environment from the repository, and n is the
porosity of tne aquifer. Using the appropriate parameter values from
Table 3-1, the aquifer travel time for R equal to 1 is calculated to be
aoout 762 years. If tne retardation factor were higher by a factor of 10,
tne travel time would oe 7620 years.
3.2 Gradients: Host Rock
The driving forces for transporting water from a repository to an
overlying aquifer are the combination of the hydraulic gradient between
tne overlying and underlying aquifers and an additional gradient caused by
tnermally induced buoyancy. For salt repositories, the lithostatic
pressure from the overburden can also force groundwater in the repository
up through shaft seals to the overlying aquifer. The pertinent aspects of
these forces and their appropriate application are briefly described in
tnis section—and are discussed further in Chapter 5 for specific releases.
We assume the hydraulic gradient between the aquifers is upward to
provide a worst-case analysis. If a downward gradient did exist, it would
represent a more favoraDle condition—since any flow would then be to
strata at greater deptns. ADL (ADL 79d) estimated the upward gradient
41
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oetween aquifers to be between 0.01 and 0.5. We have assumed that 0.1
would be a conservative gradient for our evaluation.
The heat generated by the decay of radioactive waste in a repository
affects the viscosity and density of any water present. These changes in
water properties affect the volumetric flow of groundwater from the
repository to the overlying aquifer. To calculate the volumetric flow,
equation 3-8 can be modified by replacing the gradient term with the
product of a viscosity correction factor, c(u), and the sum of the
original hydraulic gradient and a thermally induced buoyancy gradient.
ADL provided values of the viscosity coefficients y, of the water as
a function of temperature and time since sealing of the repository
(ADL 79d). These values are presented in Table 3-2. The viscosity
correction factor, c(u), is dimensionless and is the ratio of the viscosity
of water at 20°C to its viscosity at the temperature of interest. The
viscosity of water at 20°C is 0.01 poise, thus c(u) can be represented as
the inverse of the viscosity at the specified temperature multiplied by
0.01. The right hand column of Table 3-2 is an analytic approximation to
the time-gradient viscosity data points. The change in water density
caused by the heat generated by the decay of radioactive waste results in
a buoyant effect that creates an upward force from the repository to the
upper aquifer (ADL 79d)—resulting in corrective movement of water. The
equivalent gradient resulting from this buoyancy effect depends on the
time dependent temperature of the repository. The average density of the
water column extending from the repository to the aquifer was estimated to
42
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Table 3-2
Equivalent Gradient and Viscosity Coefficient
for Aquifer Interconnection*
time, temperature viscosity,
years (at 350m), °C y, poise
c(y) iac(u)**
100
200
300
400
500
1000
2000
3000
4000
5000
10000
120
111
106
102
99
90
72
61
54
48
30
.0023
.0026
.0027
.0029
.0029
.0033
.0039
.0047
.0050
.0056
.0082
4.35
3.85
3.70
3.45
3.45
3.03
2.56
2.13
2.00
1.79
1.22
.43
.38
.37
.34
.34
.30
.26
.21
.20
.18
.12
.38
.37
.36
.36
.35
.32
.27
.23
.20
.18
.12
*The reference granite repository does not have an underlying aquifer;
therefore, ia is zero for that case.
assumed gradient and calculated viscosities are ta«en from the
ADL report (ADL 79d).
**
c = 2.88
Y = 2.b x 10
,-4
43
-------
be approximately tne same as the water density at a depth of 350 m for all
times after about 100 years. ADL has estimated this thermally induced
equivalent gradient as a function of temperature and time (ADL 79d) and it
is presented in Table 3-3. The right hand column represents an analytic
approximation to the time, thermal ouoyancy gradient and viscosity
coefficient data. The equation for this approximation for the thermal
buoyancy term is:
ibc(w) = ae ~at+ be ~3t (3-10)
where: i = thermal buoyancy gradient
c(u) = viscosity correction factor
a = 0.132
b = 0.102
a = 1.6 x 10~3
6 = 3.1 x 10~4
and the equation for the aquifer interconnection gradient is:
iac(u) = ia ce~yt + 1.0 (3-11)
where: i^ = aquifer interconnection gradient
c(p) = viscosity correction factor
c = 2.83
Y = 2.6 x 10~4
To include the viscosity and density effects on the volumetric flow of
water from the repository to the overlying aquifer, equation 3-8 can be
rewritten as:
Vaq = K i* A (3_12)
where: i* = i& c(y) + ib c(u)
44
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Table 3-3
Equivalent Gradient and Viscosity Coefficient due to Thermal Buoyancy
time,
years
100
200
300
400
500
1000
2000
3000
4000
5000
10000
* a =
b =
a =
temperature
(at 350m), °c
120
111
106
102
99
90
72
61
54
48
30
0.132
0.102
1.6 X 10~3
thermal
buoyancy
gradient"*"
.057
.050
.046
.042
.041
.035
.023
.020
.014
.011
.004
viscosity"1",
u, poise
.0023
.0026
.0027
.0029
.0029
.0033
.0039
.0047
.0050
.0056
.0082
«
4.35
3.85
3.70
3.45
3.45
3.03
2.56
2.13
2.00
1.79
1.22
,„„,
.25
.19
.17
.14
.14
.11
.06
.04
.03
.02
.005
*
ae-W1
.21
.19
.17
.16
.15
.10
.06
.04
.03
.02
.005
e = 3.1 x io~4
+ The calculated viscosities are taken from the ADL report (ADL 79d)
45
-------
Lithostatic pressure is applied by the overburden to each of the five
repositories. The only significant potential release of radioactivity to
tne overlying aquifer resulting from the effects of litnostatic pressure
occurs in the salt repositories. When subjected to loads for extended time
periods, salt undergoes gradual plastic deformation subsequent to the
initial elastic and plastic response. This gradual deformation is known as
salt creep. The ADL report (ADL 79d) analyzed the significance of salt
creep and estimated that the effect of salt creep would be to reseal the
reference salt repository in about 200 years. Chapter 5 of this report
discusses the relationship of the lithostatic pressure and shaft seal
leakage for salt repositories.
3.3 Hydraulic conductivity: Host Rock
The hydraulic conductivity used in equation 3-5 for the host rock can
either be (1) the primary hydraulic conductivity of a porous rock medium;
or (2) tne secondary hydraulic conductivity of the rock if flow is
predominantly through fractures, fissures, or other types of small
discontinuities. The magnitude of the primary hydraulic conductivity is
mostly dependent upon the grain size, the degree of crystallization and/or
cementation, and compaction of the rock mass. Primary hydraulic
conductivity reflects intact, unfractured or unbroken rocks. Secondary
hydraulic conductivity reflects disturbed zones (fractures, faults, joints,
solution channels, etc.) where the extent of disturbance—and not the rock
itself—controls the movement of water. Since the primary hydraulic
conductivity of the proposed host rock is likely to be small, secondary
46
-------
hydraulic conductivity is likely to be of greater concern when considering
potential groundwater flow through strata surrounding a repository.
Secondary hydraulic conductivity must usually be determined in field
experiments from well-planned borings drilled to intersect the predominant
disturbed zones in the rock. Representative values of bulk rock hydraulic
conductivity for various host rock are presented in Table 3-4.
47
-------
TaDle 3-4
Example Intrinsic Properties for Typical Repository
and Associated Lithologies*
Dense Unweathered
Parameter Salt Shale Basalt Granite
Porosity (percent) <1 10 1-40 .05-3
Hydraulic conductivity (cm/sec)
Ranges + 10~5-<10-9 10-5-10~9 10-6-<10-10
Selected Values + 10~9 1(T9 lO'10
* (ADL 79c)
+ Essentially impermeable for the purposes of this study
48
-------
Chapter 4 - GROUNDWATER GEOCHEMISTRY
Isolation of radioactive waste from the environment also depends
on the solubility of the waste in the repository groundwater and on the
retardation of radionuclide transport in the surrounding aquifers.
Radionuclides with low solubility in groundwater will have restricted
entry into the flow system. Consequently, their discharge rates into the
biosphere will be low. we believe determining local solubility limits
should be an important part of site evaluation and selection.
After moving vertically from the repository to the overlying aquifer,
groundwater moves horizontally through the aquifer before reaching the
environment. Some of the dissolved radionuclides may react chemically
with the aquifer rock mass, and their rate of transport will be retarded.
This general process is commonly represented by a retardation factor. For
example, a radionuclide with a retardation factor of 2 would take twice as
long to reach the environment as the water does.
Solubility limits and retardation factors are site and species
dependent. Thus, for a generic assessment of radionuclide transport,
we had to establish several important criteria for estimating reasonable
values for solubility limits and retardation factors. First, we assumed
that careful site selection procedures could result in a repository with
favorable geochemistry: that is, a reducing and slightly basic (a pH
greater than 7) environment. Such conditions, found in a wide range of
49
-------
geological environments in the continental United States, favor both
retention of waste by rock in the aquifer and low solubility of many
radionuclides in the repository groundwater. However, because there is
considerate uncertainty associated with these parameters, we have made
conservative estimates of the geochemical factors for our reference
repositories. We expect that actual repository sites will have lower
groundwater solubility limits and higher retardation factors for the
important radionuclides in the repository. Table 4-1 presents the
reference retardation factors and solubility limits used in our principal
analyses.
In addition, we made separate analyses: (1) assuming no constraint
on radionuclide solubility; (2) using retardation factors equal to one;
and (3) assuming both of these situations at the same time. We also
evaluated radionuclide transport using the much higher retardation factors
derived from a report by Denham, et al. (DE 73). These higher factors
also appear in Table 4-1.
4.1 Retardation Factors
The physical and chemical processes which most affect radionuclide
retardation in an aquifer are ion exchange, adsorption, polymerization,
colloid formation, and the chemistry and solubility of the radionuclide
(AM 78). These properties characterize the potential for chemical and
physical interactions between the minerals in the geologic media and the
radionuclides in the groundwater. The interactions generally vary with
50
-------
Table 4-1
Solubility Limits and Retardation Factors
Radionuclide Half-Life Retardation Factors Solubility Limits
(years) Reference Denham (DE 73) (ppm) Ci/m
Am-241
Am-243
C- 14
Cs-137
Cs-135
1-129
Np-237
Pu-238
Pu-239
Pu-240
Pu-242
Sr- 90
Tc- 99
Sn-126
U-238
U-234
Zr- 93
458
7370
5730
30.2
3 million
17 million
2.1 million
86.4
24,400
6,600
387,000
28
212,000
100,000
4.5 billion
250,000
1.5 million
100
100
1
1
1
1
100
100
100
100
100
1
1
10
100
100
100
10,000
10,000
10
1,000
1,000
1
100
10,000
10,000
10,000
10,000
100
1
1,100
14,300
14,300
10,000
50
50
na
na
na
na
.001
.001
.001
.001
.001
na
.001
1
.001
.001
.001
160
10
na
na
na
na
7.2xlO~7
1.7xlO~2
6x1 0~5
2.2x10^
4xlO~6
na
2xlO~5
3x1 0~2
na
na
2xlO"6
na - Solubility limit not used or not known.
51
-------
the groundwater mineral content, pH, Eh, complexing materials, organic
content, and radionuclide concentrations. The low levels of radionuclide
concentration normally do not alter the geochemical properties of a
geologic formation. Therefore, field and laboratory tests for geochemical
factors using nonradioactive elements can be used for some of the
geochemical analyses described in this report.
The characteristics of each separate geochemical interaction are
extremely difficult to describe, and the technology for quantifying each
process is not available at this time. To quantify the rock-water
geochemical interactions, the nature of the rock surface must be specified
precisely with respect to its mineral and chemical composition and the
surface area per unit of mass. The measurements must be carried out under
conditions similar to those expected in the natural environment. The
current method of evaluating the complex physiochemical reactions is to
characterize their combined effect rather than to deal with each
individual process. The effect of the combined processes is commonly
called sorption and is expressed by means of distribution coefficients
(AM 78). The distribution coefficient represents the partitioning of a
substance between solution in groundwater and attachment to the rock
matrix. Use of the distribution coefficient is appropriate when the
reactions that cause partitioning are fast and reversible. Distribution
coefficients for porous and fractured media are given by:
52
-------
K _ Mass of solute on the solid phase per unit mass of solid phase _ m x
d ~ Concentration of solute in solution f. x M.
i> W
(4-1)
and:
f x Lv
K _ Mass of solute on the solid phase per unit area of solid phase _ _m
a ~ Concentration of solute in solution f_ x F,
S a
(4-2)
where K^ and K are the distribution coefficients for porous and
Cl a
fractured media respectively, fm is the fraction of total activity
adsorbed on tne media, or solid phase, f is the fraction of total
activity in the aqueous solution, MW is the mass of the solid phase,
Lv is the volume of solution in equilibrium with the solid phase, and Fa
is the total surface area of the fracture.
It is more convenient to discuss radionuclide transport using the
term retardation factor, which—for a particular element—is defined as
the ratio of the water velocity to the element migration velocity. The
retardation factor, R, is related to the distribution coefficient by:
R . 1 + -^ (4-3)
n
for porous media, and by:
R = 1 + K Rf (4-4)
a T
for fractured media, when n is the pore fraction, pg is the bulk density
of the rock mass, and Rf is the ratio of the total surface area to the
volume of the fractured medium.
53
-------
Ames and Rai (AM 78) note that "... there is a general lack of
systematic evaluation of various factors that determine element-solid
matrix interactions and no information at present is available to
determine the magnitude of the various factors affecting the environmental
transport of radionuclides." Differences in the concentrations and types
of minerals, particle size, weathering, and trace-element composition will
affect the distribution coefficients for different radionuclides. A
particularly serious problem in the analysis of radionuclide transport is
that few investigators have controlled the oxidation potential of an
experimental system (BO 79). Another problem is that few experimenters
have measured or estimated the retention of radionuclides in the same
geologic system for a variety of radionuclides. Thus, it is difficult to
\
select a comprehensive and consistent set of geochemical characteristics
of the reference aquifers in which the radionuclides migrate.
Denham, et al. (DE 73), provide a consistent set of retardation
factors for all the radionuclides we considered in our analyses. However,
Denham's factors are for a site specific (Hanford), near-surface soil
under oxidizing conditions and have limited application to our analyses.
We selected reference retardation factors after surveying the available
data, particularly that summarized by Ames and Rai (Am 78). Our selection
reflects our expectation that reducing conditions will exist in the
groundwater at a selected site, and they also reflect our intent to make
conservative analyses because of the limited information available (i.e.,
we picked retardation factors that are probably considerably lower than
54
-------
those that can reasonably be achieved by careful site selection). The
considerations that led to our choice of reference values for each
radionuclide are discussed below.
In our risk assessments, only those radionuclides with a retardation
factor less than 15 will reach the environment during the time of
interest. For most radionuclides under consideration, use of either
our reference retardation factors or the ones contained in the Denham
report will not affect the result of our analyses. Of the remaining
radionuclides, the two most important are carbon-14 and tin-126. Our
reference retardation factor for C-14 is 1 as opposed to a reported value
of 10 (Denham 73). Since we are not sure at this time of the chemical
form of C-14 in the waste, we believe our more conservative approach is
warranted. Very little work has been done in evaluating the retardation
factor for tin, and additional experimental work is needed. Our
retardation factor of 10 is more conservative than the value of 1100
reported by Denham. We do not believe a retardation factor for tin lower
than 10 is required, since we expect tin to exist as both a cation and an
anion and will not be as mobile as elements that exist only as anions.
55
-------
4.2 Solubility Limits
Tne solubilities of radioactive elements in groundwater are affected
by groundwater temperature, pH, Eh, chemical and radiolytic processes. In
particular, the solubility of some elements (Zr, Sn, Th, U Np, Pu, Am, and
Tc) will be extremely low in a reducing environment with a neutral to basic
pH (AM 78, BO 79, EDA 78, BO 75, PO 66). This is the type of groundwater
geochemistry tnat we believe should be favored in siting a repository.
However, relatively few studies of radionuclide behavior in groundwater
have considered reducing environments. The work of Bondietti and Francis
(BO 79) is a notable exception, and we have used results from their study.
In deriving solubility limits for the various radionuclides, we also used
thermodynainic data from the literature (e.g., AM 78, PO 66, RA 78).
Several factors which might increase solubility limits have not been
adequately evaluated for reducing environments and are not considered in
the report. For example, cnemical and radiolytic processes could increase
the solubility of elements above those levels predicted by classical
thermodynamics. Elevated groundwater temperatures can also increase or
decrease the solubility of some elements. In this report we have not
considered the effects of elevated temperatures on radionuclide solubility
limits. Neither have we considered the possiblity that some low
solubility waste forms might chemically react with other chemicals present
in the waste. We have not considered the possibility of these
interactions in establishing our solubility limits because the stability
of some complexes of nuclear waste elements are not known.
56
-------
Tne ideal method of calculating radionuclide solubility is to develop
simultaneous equations of all the known equilibria of the radioactive
element for a site-specific groundwater and disposal geology. Runnel Is,
et al. (RU 80), have done this for 213 solid and 197 aqueous uranium
species. However, their approach has two drawbacks for our analysis:
(1) the thermodynamic data for many aqueous species are not known for the
transuranic elements we consider most important, and (2) a description of
the groundwater chemistry for this type of evaluation requires precise,
site-specific concentrations of aqueous species. This type of detailed
information is beyond the scope of our generic analysis.
Our approach was to examine the available thermodynamic and
solubility data for the important radioactive elements, and select
conservative solubility limits (i.e., our reference solubility limits are
probably higher than what can reasonably be expected at carefully selected
sites). Even so, for most of the solubility-limited radionuclides in
Table 4-1, the reference limits are so small that the contribution of
these radionuclides to the overall risks is negligible. Even if the
solubility limits were an order of magnitude larger, their contribution
would still be negligible. An important exception, however, is americium.
A large part of the projected risks are attributable to concentrations of
americium isotopes. The concentrations of americium in groundwater are
usually only limited by solubility constraints in the salt repository
backfill, where there is very little water. Thus, determining site
specific solubility limits of americium for a salt repository would be a
very important step in evaluating the projected risks.
57
-------
4.3 Geochemical Factors
In the rest of this chapter, we review the information we analyzed to
select reference retardation factors and solubility limits for each of the
important radionuclides. The solubility limit of americium is one of the
more important factors in our risk assessment, and we describe in consid-
erable detail the calculations that we used to select this reference limit.
4.3.1 Americium
4.3.1.1 Solubility
Tne solubility limit of the americium isotopes is sensitive to the
geochemistry of the repository groundwater. To select our reference
solubility limit we estimated the solubility of americium in pure water
(i.e., zero ionic strength), then we estimated the limit in groundwater
with hydroxide, sulfate, chloride, and nitrate complexes. Our analyses
indicated that the most conservative approach would be to select the
solubility limits for americium hydroxide complexes, since they appear to
represent the highest concentration of all species present in solution
(i.e., Am+3, Am+3Cl, Am+3OH).
Americium has two radioactive isotopes of concern, Am-241 and
Am-243. Americium is expected to exist in the +3 valence state.
According to Rai and Serne (RA 78) the behavior of this ion in pure water
is described by the following equilibria equations:
Am(OH)3sol ±; Am+3 + 30HT K0 = 2.7 x 1CT20 (4-5)
and:
Amaq li; AmOHaq + H+ KI = 1.2 x 10~6 (4.5)
58
-------
KQ and K^ are the equilibria constants that describe the thermodynamic
relationship of the reactants and products when they have reached
equilibrium. The equilibrium constant in equation 4-5 is defined as:
{4.7)
[Am(OH)3]
where the brackets denote the reacting activity of the species in question.
Since the activity of a solid (e.g., Am(OH)3) at repository
conditions is approximately unity, equation 4-7 may be simplified to:
[Am+3] [OH-]3 = K* [Am(OH)3J = 2.7 X 1CT20 (4-8)
If there is no formation of Am(OH)2+ or Am(OH)+, then the balance
of the masses of the Am ion and the hydroxide ion produce three
equivalents of OH~ for each equivalent of Am species that are in
solution. Thus, as a first approximation:
[Am+3] (3[Am+3J)3 = 2.7 x 10~20 (4-9)
and solving equation 4-9:
27 [Atn+3]4 = 2.7 x ICT20 (4-10)
gives:
[Am+3J = 5.7 x ID'6 m (4-11)
59
-------
The limiting concentration of Am , using the above assumptions,
is 5.7 x 10 molar, or approximately 1.4 x 10 grams per liter for
either Am-241 or Am-243 in pure water of ionic strength zero where the
activity coefficient is equal to one and no (OH") complexes exist.
According to Rai and Serne (RA 78) and Ames and Rai (AM 78),
groundwater may contain hydroxide, nitrate, chloride and sulfate ions.
Am may form complexes with any of these species. These complexes
may be important depending on the concentration of these ions and the
formation constants for these complexes. To determine the concentration
+o
of the AmOH complex in solution due to the dissociation of Am(OH)o5
the equilibria for equations 4-5 and 4-6 must be expressed. The
equilibrium expression for equation 4-5 has already been shown as
equation 4-7. Equilibria for equation 4-6 can be expressed as:
if the activity coefficient is equal to 1 and the ionic strength is zero.
We need to know the equilibrium constant for the following equation:
[Am(OH)3Jsolid <=-> AmOHaq + 20H~ (4-13)
which can be explicitly stated as:
-*
60
-------
Multiplication of each side of equation 4-7 by equation 4-12 will
yield expression 4-15:
3] CQH-J3 ^3 [H+3 = 2Q _6
LAm(OHj3]sol
This may be simplified to:
When the ionization constant for water is included:
LH+J LUH-J = 1U-14 (4-17)
equation 4-16 may be further simplified to:
[AmQH+2] W2 1Q"14 . 3.2 x 10-26 (4-18)
[Am(OH)3Jso1
so that:
LAmOH+2][QH-2] = ^ = 3>2 x 10_i2 (4_19a)
[Am(OH)3]sol
[Am(OH)3J is defined as 1, thus:
K2 = LAmOH+2][OH-J2 = 3.2 X ID"12 (4-1 9b)
Solving this equation for [AmOH+2] is similar to the solution shown
+ n +2
previously for Am . This equilibrium concentration of AmOH is
equal to 9.3 x 10~5 molar or 2.3 x 10~2 grams of americium per liter
of water, and a concentration of OH~ equal to 1.9 x 10 molar.
61
-------
+2
Since the dissolution of Am(OH)3 to ArnOH produces a more basic
solution than the dissolution of Am(OH)3 to Am+3, these two reactions
are competing for a common ion, OH~. If the acidity of the dissolved
solution is calculated using equation 4-17, and OH~ equals 1.9 x 1CT4
molar, the concentration of H+ is 5.3 x 10" molar. Using this H+
concentration, equation 4-12 can be solved for the concentration of
+ •1 _Q
Am . This solution gives a concentration of 4.1 x 10 molar for
Am , which is much lower than the earlier estimated concentration of
Am. It is clear that the high stability of AmOH results in a
+3 +3
lower concentration of Am . This Am species is important because
it can form complexes with chloride, nitrate, and other anions. A low
concentration of Am will give low concentrations of its complexes.
Rai and Serne (RA 78) indicate that nitrate, chloride, and sulfate
may also contribute to complexing. We will discuss the chloride complex
since this is the more common of the three complexes for the groundwater
of interest. For chloride calculations a 10 molar solution of NaCl is
used, although this concentration slightly exceeds the solubility of
Nad. For the reaction:
Am+3 + Cl~ <-- AmCl+2, (4-20)
62
-------
Rai and Serne (RA 78) indicate:
-1.5X101-K3 (4-21)
[Am ] [C1-]
Since we assume the chloride concentration is 10 molar, the ratio of
+2
the complex AmCl to the uncomplexed ion will be:
. 160
+3 _9
For the Am concentration of 4.1 x 10 molar, the concentration
of the complex AmCl is 6.2 x 10 molar or 1.5 x 10 grams/liter.
The concentration of the hydroxyl complex is over 100 times higher than
the concentration of the chloride complex. Thus, supported by the work of
Ames and Rai (AM 78) and Rai and Serne (RA 78), we estimate that the most
significant species in the dissolution of Am(OH)3 is the monohydroxo
+?
(AmOH) complex. Since we calculated the concentration of this complex
_2
to be 2.3 x 10 grams/liter, we chose a conservative limiting
_2
solubility of 5.0 x 10 grams/liter for this study. This allows for
some reasonable uncertainties in the equilibrium constants as well as for
those complexes for which no equilibrium constants have been measured.
This limiting solubility is equivalent to 160 curies/m for Am-241 and
10 curies/m3 for Am-243. Recent work by Rai and Strickert (RA 80) and
Ogard, et al. (OG 80) and Rai, et al. (RA 81) suggest that americium is
much less soluble than these concentrations. Tne most recent work by
Rai, et al. (RA 81) suggests that americium solubility limits are 100 to
100,000 times lower than the values used in our analyses. These workers
have not, however, identified the species responsible for this lower
solubility.
63
-------
4.3.1.2 Retardation Factors
In tneir recent review of the literature on radionuclide interactions
with soils and rocks, Ames and Rai (AM 78) observe that the Kd for
americium ranges from 0 to 50,000 milliliters per gram. We have selected
a reference retardation factor for americium of 100 for this report. Many
of the low K , values—and, consequently, retardation factors—summarized
by Aines and Rai (AM 78) are for solutions with high concentrations of
organic compounds. We think that repositories can be found where the
groundwater does not have a high concentration of organic compounds.
Therefore, we believe a retardation factor of 100 is clearly achievable.
4.3.2 Carbon
Carbon exists in spent fuel as C-14, an activation product whose
chemical form is unknown. For this reason we have assumed there is no
limiting solubility for C-14 and that any C-14 that migrates does so with
a retardation factor of one.
4.3.3 Cesium
Ames and Rai (AM 78) indicate cesium is highly soluble, therefore we
have not used a solubility limit. They also report measured Kd values
ranging from 0 to almost 100,000 for different rocks and minerals.
Because of the wide variation in the reported values, the reference case
retardation factor is one.
64
-------
4.3.4 Iodine
According to Ames and Rai (AM 78), 1-129 usually exists as iodide,
which is very soluble. For this reason no limiting solubility has been
used. Since iodide is anionic, we can expect little or no retention in
soil. Thus we have chosen a retardation factor of one, which is the same
retardation factor reported by Denham, et al. (DE 73).
4.3.5 Neptunium
Neptunium-237 is produced in a reactor primarily by activation of
uranium. Np-237 will exist in either a +4 or +5 valence state in most
natural conditions (PO 66, BO 79, AM 78). In a neutral or basic
environment with reducing conditions, the +4 valence state will
predominate (BO 79, PO 66).
4.3.5.1 Solubility
In a reducing environment, the expected chemical state of Np-237 is
tetravalent. Bondietti and Francis (BO 79) placed a 16 nM (3.8 parts per
billion) solution of Np-237 in contact with a number of different rock
types and measured a substantial loss of Np from their solution. They
identify this behavior as a reduction of Np02 to the relatively
insoluble NpO,., species. This reduction is confirmed by Ames and Rai
(AM 78). Tney indicate that the +4 species of Np is very insoluble.
Hence, we use a solubility limit of one part per billion in water for
neptunium, whicn is equivalent to a solubility limit of 7.2 x 10"
curies/m .
65
-------
4.3.5.2 Retardation Factors
A wide range of retardation factors has been reported for neptunium
(AM 78, BO 79). However, Bondietti and Francis are the only investigators
who have examined the geochemical relationship between neptunium and the
oxidation potential of the host rock. We have selected a retardation
factor of 100, which is the same factor reported by Denham, et al. (DE 73).
Some measurements have shown that the retardation factor of neptunium can
be lower than 100, out these measurements were made under geochemical
environments that were not representative of good repository conditions.
4.3.6 Plutonium
Plutonium exists in spent fuel as a mixture of plutonium-238, -239,
-240, -241, and -242. Chemically, plutonium exists in the +3, +4, +5, and
+6 valence states. A number of papers review the stability and migration
of plutonium and its compounds (AM 78, RA 77, RA 78, PO 66).
4.3.6.1 Solubility
All of the reviews indicate that plutonium is very insoluble in a
basic reducing environment. We use a solubility limit of one part per
billion for plutonium, even though concentrations shown in the reports
cited are sometimes much lower. We believe the plutonium will be present
as a tetravalent solid. This solubility limit corresponds to limits for
plutonium-238, -239, -240, and -242 of 1.7 x 10~2, 6 x 10~5, 2 x 10"4
and 4 x 10" curies/m , respectively.
66
-------
4.3.6.2 Retardation Factors
Ames and Rai (AM 78) indicate an extremely wide range of retardation
factors for Pu. Most of the low Kd values summarized by Ames and Rai
are for solutions with hign organic content. We use a retardation factor
of 100, which is substantially below that measured by most workers and is
much less tnan the 10,000 reported by Denham, et al. (DE 73).
4.3.7 Strontium
Strontium-90 is a fission product which exists as a +2 cation in
rock, and its salts are moderately soluble (AM 78). For this reason we
have used no solubility limit in this report. A wide range of retardation
factors has been reported for Sr-90. In this report we use a retardation
factor of one, which clearly underestimates the extent of retention we
expect for migrating strontium (AM 78).
4.3.8 Technetium
Technetium-99 is a fission product that exists in many chemical
states from +7 to -1. The most stable valence states are the +7 and +4
(PO 66, AM 78, BO 79). The +7 form is highly soluble and mobile, and
the +4 form is virtually insoluble and immobile. Under the reducing
geocnemical environment that is favorable for repository siting, we
believe the less soluble and mobile +4 form will be the most common.
67
-------
4.3.8.1 Solubility
Using the solubility data of Pourbaix (PO 66) and Bondietti and
Francis (BO 79), we predict a low concentration of Tc in reducing
groundwater. Bondietti and Francis observed a substantial loss
(over 95 percent) of Tc from a 0.11 pM (11 ppb) solution after contact
with reducing rocks. Based on tnis experiment and associated stability
information, we have chosen a solubility limit of one part per billion,
_t -3
wnich is equivalent to 2 x 10 curies/m .
4.3.8.2 Retardation Factor
A retardation factor of one has been selected for Tc-99. The review
of Ames and Rai (AM 78) and work of Bondietti and Francis (BO 79) makes it
clear that Tc-99 is mobile under some circumstances, even when it is at
low concentrations. Since the measurements are ambiguous, the conserva-
tive approach is to assume the lowest reasonable retardation factor, which
in this case is one. It is also likely that any technetium in solution
would be the mobile +7 form rather than the insoluble, immobile +4 oxide.
4.3.9 Tin
Tin-126 has received little attention as a nuclear fission product.
Neither the reviews of Ames and Rai (AM 78), or Rai and Seme (RA 78)
discuss this isotope at all, and it appears that little or no work has
been done concerning it.
68
-------
4.3.9.1 Solubility
Pourbaix (PO 66) reports that, excluding complexation, SnO is the
most soluble form of tin. The other form is Sn02> which is less soluble
and would exist in oxidizing environments rather than in reducing
environments. According to Pourbaix (PO 66):
log (Sn+2) = 1.07 - 2pH (4-23)
and:
log (HSnO^) = -14.81 + pH. (4-24)
For a pH = 7 these equations can be solved to be:
(Sn+2) = ~10-13 (4-25)
and:
-7
(HSn02) = ~10 (4-26)
Sillen and Martell (SI 64) report strong chloride complexes with
Sn+2. These complexes should be less than the HSn02 ion concentration
unless the equilibrium constants summarized by Sillen and Martell are
substantially in error. They report no simple complexes of HSnO^. To
maintain a conservative solubility limit for tin, we selected a limit of
one part per million, or 3 x 10~2 curies/m^. This concentration may
overestimate the solubility of tin by a considerable margin.
69
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4.3.9.2 Retardation Factor
Tin should exist predominantly as an anion, even though it can exist
as a cation. Tin should be relatively mobile compared to the actinides,
which are cationic. However since it can exist as a cation, we have
selected a retardation factor of 10 instead of 1. Clearly, further
experimental work is needed to determine the retardation factor.
4.3.10 Uranium
Although tnis report does not consider the health impact of uranium
in spent fuel, it is possible that the solubility of uranium could limit
the rate at which most nuclides are leached into repository groundwater.
While some waste nuclides would not be trapped in the U02 matrix
(I or Cs, for example), other nuclides (Np, Pu or Am, for example) would
subsitute for uranium in the uranium dioxide matrix. For reprocessed
high-level waste, the uranium would be separated by a chemical process,
and the release of waste nuclides to water would not be dependent on the
solubility of uranium. Ogard, et al. (OG 80) consider the effects of
uranium solubility on leaching rates in a mildly reducing environment.
Ames and Rai (AM 78), Langmuir (LA 78), and Rai and Serne (RA 78)
discuss the solubility of uranium and its compounds. Based upon their
stability diagrams, we chose a solubility limit of one part per billion.
This concentration is at the lower end of values given by Fix (FI 55) and
Germanov and Panteleyev (GE 68) for the uraniferous waters they examined.
70
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4.3.11 Zirconium
Zirconium exists in waste in a +4 valence state. It is one of the
most insoluble and geochemically immobile elements.
4.3.11.1 Solubility
Ames and Rai (AM 78) snow the solubility of solid Zr02 and Zr(OH)4
to be very low. We have taken the solubility for zirconium to be one part
per billion. This estimate is well in excess of values shown graphically
in Figure 3-28 of Ames and Rai's work. This solubility is equivalent to
2.6 x 10~6 curies/m3.
4.3.11.2 Retardation Factor
Zirconium is strongly sorbed, and the review by Ames and Rai (AM 78)
shows both experimental and field data in complete agreement on this
point. For the reference retardation factor, we used a conservative value
of 100. The distribution coefficients summarized by Ames and Pai (AM 78)
are consistently higher than 100.
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Chapter 5 - RELEASE MECHANISMS AND PROBABILITIES
This chapter presents models to describe the release of radionuclides
to the environment from various unplanned release mechanisms and from
normal groundwater flow. Our models and assumptions are based on
information in the ADL report (ADL 79d). First, general models are
developed to describe the movement of radionuclides either released
directly to the air or land surface or released by transport in
groundwater to an aquifer. Then, the general models are expanded in order
to describe specific release mechanisms and normal groundwater flow in
various repository media. Where possible, model parameter values are
suggested for use in evaluating the impact of various release mechanisms
on the environment. Summary tables of the parameters introduced in this
chapter are also displayed with the probaoility and consequence
evaluations in Chapter 7. Techniques for solving the equations presented
in this chapter are described in Appendix C.
5.1 General Release Models
Releases of radioactivity from a repository can be the result of a
direct physical disturbance of the waste package or an indirect
disturbance caused by disruption of the repository containing the waste.
Direct disturbances can result in transport of a fraction of the waste to
the land surface or into the air, followed by release of the waste
remaining in the repository to groundwater and then to an overlying
aquifer.
73
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Mechanisms of direct waste package disturbance include the following:
Mecnanism Results in release to
Volcanoes air and land surface
Meteorites air and land surface
Drilling land surface and aquifer
Faulting aquifer
Breccia pipes aquifer
Disruption of the repository can result in indirect disturbance of
the waste package, allowing the release of radioactivity to either the
land surface or transport in groundwater to an aquifer. Repository
disruption mechanisms that might lead to the release of radioactivity
include the following:
Mechanism Results in release to
Drilling land surface and aquifer
Faulting aquifer
Breccia pipes - aquifer
5.1.1 Direct Impact: Releases to Air and Land Surface
The model equation we have used to calculate direct releases to the
land surface or into the air is:
Q = fQ0e~Xte (5-1)
where:
Q = activity of released waste, curies
f = fraction of repository inventory released
Q = initial radionuclide inventory, curies
u _1
x = radionuclide decay constant, yr
tg = time event occurred after repository sealing, years.
74
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Tne exponential term, e x e, reduces the initial radionuclide
inventory of the repository by the amount of radioactive decay of the
radionuclide since repository sealing.
5.1.2 Direct Impact: Release to an Aquifer
After disturbance of the waste package causes release of some
radioactivity, the radioactivity remaining in the waste package may be
transported to tne overlying aquifer by diffusion and convective flow.
ADL discusses the diffusion process and concludes that transport by
diffusion is usually much slower than transport by convective flow
(ADL 79d). Transport by convective flow depends on the radionuclide
release rate from the waste matrix, the solubility of the radionuclide in
water, and tne radionuclide inventory at the time of interest. If there
are no limits to radionuclide solubility, the equation for the
radionuclide release rate into the groundwater in the repository is:
Q = 0 t
-------
If the radionuclide is solubility limited, the release rate from the
waste matrix is the product of the solubility limit and the volumetric
flow of water. Equation 5-2b is the expression of this release rate:
Q = CQ V*(t) (5-2b)
where:
3
C = solubility limit, Ci/m
V*(t) = volumetric flow rate from the repository to the
overlying aquifer, m /yr.
The volumetric flow rates are different for each of the host
repositories. Equations describing V*(t) are presented in Section 5.2.1.
The total quantity of a radionuclide released from the time of the direct
disturbance to the time of interest is the integral of equation 5-2a or
5-2b over that time period.
5.1.3 Repository Disruptions: Releases to Land Surface
Events which do not directly disturb the waste package but do disrupt
the surrounding repository require more complicated equations to describe
releases to the land surface or to the overlying aquifer. The pore spaces
of a repository will become saturated with water which begins migrating
into the repository as soon as it is sealed. When the canisters fail, the
waste matrix will begin to dissolve. As the waste matrix dissolves, a
slow buildup of radioactivity occurs in the pore volume of the
repository. This radioactivity can be transported to the overlying
76
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aquifer or to the land surface if the repository is disturbed. Releases
from the pore volume can be modeled by developing an equation that
balances the inputs and outputs of radioactivity in the pore spaces.
The rate of change of tne activity in the pore volume can be
expressed as the product of the volume of pores, V, and the derivative of
the concentration of radionuclides over time, dC(t)/dt. This product is
equal to the sum of the input of radionuclides into the pores by leaching
from the waste, LfQ (t), and the output of radioactivity by radioactive
\f
decay, -xVC(t). The resultant expression for the rate of change of
activity is:
v dcoti = LfQc(t) _ xvc(t) {5_3a)
where:
Qc(t) = Q0e- e--c (5-3b)
and:
V = pore volume, m
3
C(t) = activity/volume = concentration in V, Ci/nT
Q (t) = activity in affected waste, curies
\f i
f = fraction of waste leaching into void volume V
t = lifetime of the canister shell, years.
The activity of tne waste, Q (t), remaining in the repository is
the product of the inventory of radionuclides, QQ, the rate of
radioactive decay up to the time of interest, e~x \ and the rate of
release—which only takes place from the time of canister failure, tc,
until tne time of interest t, |_e ~ c' where t> tc]—as shown by
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equation 5-3D. We have made the worst-case assumption of simultaneous
failure of all canisters, and equation 5-3a models the sum of all
canisters of waste rather than failure of an individual canister. Each
factor in equation 5-3a thus involves the sum of all canisters (i.e.,
q = inventory of the sum of the waste in all canisters). The solution
to equation 5-3a is obtained by substituting 5-3b into 5-3a and assuming
that the concentration, C(t), is zero up until the time of canister
failure (until t = t ). This yields:
C(t) = fQ^-H-e--J/V (5-4)
where:
all of the variables are as defined for equation 5-3.
The solution of equation (5-3a) is described in detail in Appendix C. If
the radionuclide is solubility limited, C(t) is replaced by the solubility
limit, C .
5.1.4 Repository Disruptions: Releases to an Aquifer
Tne differential equation describing the change in activity in the
pore volume during release to an overlying aquifer is identical to
equation 5-3a — with the addition of a term to account for the removal of
radioactivity from the repository by ground water flow, V*(t) C(t). The
resulting equation is:
V ^ii . LfQc(t) _ xvc(t) - V*(t)C(t) (5-5)
where:
V*(t) = volumetric flow rate, m3/yr.
All the remaining variables are as defined for equation 5-3a.
78
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This equation is solved using an integrating factor in a manner
similar to that used to solve equation 5-3a [see Appendix C (C.2)]. The
general form of the solution is:
C(t )y(t )
6
e
where:
t = time of interest, years
te = initial time of release, years
tc = lifetime of canister, years
p(s) = EXP[JS OV*(s)/V] dsj
q(s) = (LfQ0/V) EXP(-xs-Ls+Ltc)
C(te) = concentration at the initial time of release
(see equation 5-4 for t=te).
Equations describing V*(t) for the various materials of the surrounding
repository are presented in section 5.2.1. A solution to equation 5-5
using V*(t) as defined by equation 5-20 is presented in Appendix C.
Some release events nave very large calculated groundwater flow rates
from the repository to the overlying aquifer. If these calculated flow
rates are faster than tne rate of recharge of groundwater to the
repository, we assume the flow rates are limited by the rate of flow of
water from the underlying aquifer. In these cases, V*(t) in equation 5-5
is a constant, V . By substituting V for V*(t) in equation 5-5,
aq aq
the rate of change of activity can be expressed:
VdC(t) = LfQ.(t) - xVC(t) - VaQC(t) (5-7)
u M
79
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The solution is an integral of tne form of equation 5-6 evaluated from the
time of tne event to the time of interest. The solution is presented in
Appendix C (C.3). If the radionuclide is solubility limited, C(t) is
3
replaced with the solubility limit, CQ, expressed in Ci/m .
The product of the concentration and volumetric flow rate in
equations 5-4 and 5-5 is the rate of radionuclide released to the aquifer
over time. The total release to the aquifer is the integral of this
product from the time of the event to the time of interest, t-:
r'1
Q = J C(t) V*(t) dt (5-8)
5.2 Specific Release Mechanisms
This section is arranged according to the following release
mechanisms: normal groundwater flow, human intrusion (drilling),
faulting, breccia pipe formation, meteorites, and volcanoes. Mathematical
equations are used to calculate concentrations of radionuclides at the
time of release and within pathways following release. Parameters are
introduced for solution of the equations for repositories in various rock
types. A complete discussion of the initiating events and their effects
on a repository is contained in Volume D of ADL's report (ADL 79d).
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Tne release pathways for each release mecnanisrn are listed below:
Mechanism Pathway
Normal Groundwater Flow surface water via aquifer
Human Intrusion land surface and
surface water via aquifer
Faulting surface water via aquifer
Breccia pipes surface water via aquifer
Meteorites air and land surface
Volcanoes air and land surface
5.2.1 Normal Groundwater Flow
5.2.1.1 Salt Repositories
Release oy normal groundwater flow at a salt repository is governed
by the interaction of two processes. Water may be recharging the voids in
the repository oackfill while lithostatic pressure is simultaneously
reducing the volume of the voids. If the volume reduction exceeds the
initial volume of unsaturated voids, contaminated water may be squeezed
out of the oackfill and into the overlying aquifer. Equations for water
flow, rate of repository closure, and maximum and minimum pore volume
(developed in chapter 3) are used to estimate the potential volume of
contaminated water. Equations for radionuclide concentration are then
applied in order to descrioe possible releases of radionuclides.
The litnostatic pressure of the overburden causes the salt to deform
plastically, tnereby reducing the void volume and fully sealing the
repository within a few hundred to a thousand years. After the repository
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seals itself, the salt is essentially impermeable to water flow and
further releases of radioactivity are not expected. Before closure is
complete, however, degradation of the shafts (section 2.3) can allow some
water to flow down into the unsaturated backfill. Recharge water that
fills the voids of the backfill may be squeezed back up these shafts owing
to the litnostatic pressure acting to seal the repository. Determining
the volume of this water is important in estimating the degree of
contamination by normal groundwater flow out of a salt repository.
The volumetric flow of water from an overlying aquifer through the
permeable shaft can be calculated using Darcy's Law (equation 3-9),
V*(t) = KiAc(u). The parameters substituted in this equation are:
V*(t) = time dependent flow rate of water from the overlying
aquifer into the pores of the repository backfill,
m /yr.
K = KQ + K t linearly increasing hydraulic conductivity
of tne shaft seals (section 2.3) m/yr
i = hydraulic gradient between the overlying aquifer and the
repository.
o
A = area of the shafts, m .
c(y) = viscosity correction factor (section 3.2)
Substitution for K results in:
V*(t) = (K + K*t) c(P) i A (5-9)
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The coefficient of hydraulic conductivity of the shafts (K + K t)
was developed by ADL (ADL 79d) assuming an initial shaft seal hydraulic
conductivity, KQ, of 3.2 x 10~3m/yr. Since better information is not
available, the shaft seals are assumed to degrade linearly over 10,000
years (t.^) to increased hydraulic conductivity values (K,) of 0.32 m/yr
for main shafts and 3.2 m/yr for the miscellaneous boreholes. These
values are representative of the range of hydraulic conductivity for sand
or silt. Our estimate of K1 is:
resulting in:
K1 = (Kx - K )/tx = 3.17 x 10 5
K = (3.2 x 10~3 + 3.17 x 10~5t) m/yr.
In order to calculate tne hydraulic gradient between the overlying
aquifer and the repository, we assume that there is no resistance to
vertical flow within tne aquifer and that all head loss occurs between the
repository and the bottom of the aquifer. The hydraulic head at the top
of tne aquifer (130 meters above the repository in the bedded salt
example) is then essentially equal to that at the bottom of the aquifer
(100 meters above the repository). The head difference between the
repository and the bottom of the aquifer (130m) is divided by the path
lengtn (100m) for a nydraulic gradient of 130/100 = 1.3. For a domed salt
repository, the respective parameters yield a hydraulic gradient of
260/230 =1.1.
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The area of the main shafts (4 shafts 5m x 5m each) is calculated to
be 100 m2 (ADL 79d). Each borehole is assumed to have a cross-sectional
area of 0.1 m2. There are assumed to be 50 boreholes from the upper
aquifer to the repository in both bedded salt and domed salt. In addition,
the bedded salt repository is assumed to have 10 boreholes extending to the
lower aquifer for a total of 60 boreholes. The total shaft area is thus:
Bedded salt: A = 100m2 + .Im2(60) = 106m2.
Domed salt: A = 100m2 + .Im2(50) = 105m2.
The viscosity correction factor, c(p), for our analyses is 5 and is
based on a water viscosity, y, of 0.002 poise at a temperature of 125"C.
Substituting all of these parameters into equation 5-9 yields a flow
rate of water through shaft seals into bedded salt and domed salt
repositories of:
Bedded salt repository: V*(t) = 2.2 + 0.021t (5-10)
Domed salt repository: V*(t) = 1.8 + O.OlSt (5-11)
Tne total volume of water which can flow into each repository through all of
these pathways is the integral of each of these equations over the time it
takes for the decreasing pore volume of the repository backfill to equal the
volume of the water that has leaked in to fill the pores (saturation time).
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An expression has been developed to describe the maximum volume of
recharge water—but, in order to evaluate this integral, the time at which
the volume of water equals the pore volume (saturation time) must be
evaluated. This is done by setting the expression for the volume of water
equal to the expression for the remaining volume of the voids and solving
them simultaneously. The initial volume of the voids, V , is 2x10 m3
(section 2.3). The sealing of the repository by salt creep is anticipated
to collapse pore spaces in the backfill down to a minimum void volume,
o
Vmin' of 20>0°° m—or down to tne amount of water that has entered
o
through the shaft and borehole seals if the amount is less than 20,000 rrr
by the time of repository closure, T , . If more than 20,000 m of
water has entered by the time of closure, the amount in excess of
20,000 m is assumed to be squeezed back up the shafts, as described in
the following paragraphs. T , , the time required for reduction of the
void volume, is assumed to be 200 years (ADL 79d). The expression for pore
volume, V , at time t is thus:
Vv = Vm1n + (V0 - Vmin) (Tclos - t)/Tclos (5-12)
where:
V = volume of the voids at time t, m
3
V = initial volume of the voids, m
V - = minimum volume of the voids, m
mm
T , = time of closure, years.
Using the example for bedded salt, the integral of the flow rate in
equation 5-10 is set equal to the void volume of 5-12:
(V0 - VminMTclos - t)/Tclos = 2.2 + O.OZlt (5-13a)
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Substituting V = 2 x 106 m3, V . = 2 x 104 m3, and T = 200 years
0 iii i n L» i uo
and integrating yields:
(2 x 104) + (2 x 106 - 2 x 104)(200 - t)/200 = 2.2t + 0.0105t2 (5-13b)
The solution for t in this expression is always negative. This means that
the volume of water leaking into the repository does not equal or exceed
the minimum pore volume within the 200 year assumed closure time. This
can be verified by calculating the water volume after 200 years by
substituting 200 for t in the right-hand side of equation 5-13b. This
substitution yields a water inflow volume of 878 m after 200 years.
Since the volume of water in the voids does not exceed V . no water
would be squeezed back out of the backfill in this example. The estimate
for the amount of water that leaks into a salt repository by T-,
(878 m in this case) is used in section 5.2.2.1 to calculate the amount
of contaminated water that might be brought to the land surface by
inadvertant human intrusion.
If different parameters were selected for a more conservative
analysis—or for a different case such that the hydraulic conductivity, K,
for the shafts and boreholes was larger or the closure time, T -i , was
assumed to be longer (ADL 79d, second estimate), then more than 20,000 m
of water could flow into the backfill in less time than the closure period.
The repository closure time would be longer than the saturation time.
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The remaining void volume would be less than the water inflow volume and
tne excess water (wnicn may be contaminated) could be squeezed back up the
shafts and boreholes. The volume of water remaining in the repository
after the lithostatic pressure begins to squeeze water up the shafts and
boreholes can be calculated using the following equation:
r t
V(t) = Vrch - J V*(s) ds (5-14a)
Trch
where:
V(t) = the time dependent saturated repository volume, m
V = the volume of water when the backfill of the
I Lr I I n
repository is initially saturated, m
Trcn = the time when recharging is complete, years.
and the rate of water flowing back up the boreholes is:
V*(t) = K(t) i A c(y) (5-14b)
with:
K(t) = K + K*t (equation 5-9)
A = area of the shafts
i = hydraulic gradient caused by the change in lithostatic
pressure (described below)
c(y) = viscosity correction factor
To evaluate equation 5-14a and 5-14b, we used the same coefficient of
hydraulic conductivity, K, and the same shaft area that were used to
evaluate equations 5-10 (bedded salt) and 5-11 (domed salt). The effective
nydraulic gradient generated by salt creep may be estimated as follows.
The pressure exerted by the salt on the pore water is roughly equal to
(arid certainly bounded by) lithostatic pressure, which—assuming a rock
density twice that of water—can be approximated by twice the hydrostatic
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pressure of a column of water extending to the surface. For bedded salt
with a repository whose depth is 460 meters, this corresponds to a
pressure head of 920 meters of water. The saturated permeable shafts
cover a distance of 100 meters from the repository to the bottom of the
aquifer, at which point the hydrostatic pressure is approximately 30 meters
of water. Therefore, a net head difference of 920-100-30 = 790 meters of
water acts over a path length of 100 meters, corresponding to a maximum
hydraulic gradient of i = 790/100 = 7.9. Because this number overestimates
the driving force, it is slightly conservative and appropriate for the
approach of this report. The value is conservative because full
lithostatic pressure on the pore water will never quite be achieved as
long as there is a flow path from the repository. The volume of water
which flows into the repository, V ., and the time required for
saturation, T ,, can be calculated using equation 5-13a.
The rate of volumetric change of the repository after resaturation
cannot be greater than the closure rate before resaturation. The flow
rate of water calculated from equation 5-14D must be checked with the
volume reduction calculated by equation 5-12. If the water flow rate
predicted by 5-14b is faster than the volume reduction rate, then the
slower rate must logically be assumed. To make this comparison of the two
methods, we will rewrite equation 5-12 into terms that correspond to the
terms in equation 5-14a and 5-14b.
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Equation 5-12 can be simplified slightly by expanding terms,
resulting in:
- Vo +
-------
Substituting C(t)V(t) for Q(t) yields:
V(t) lLL + c(t) dVtl m LQ(t) _ xc(t)v(t) _ V*(t)C(t) (5-17)
Suostituting -V*(t) for d(V(t) )/dt— from the relationships between
equations 5-14a and b, and between 5-1 5 a and b— and factoring V(t) yields:
= LQc(t)/V(t) - xC(t) (5-18)
Equation 5-18 is of tne form [p(s)y + y1 = q(s)J and can solved in the
same manner as equations 5-3a and 5-5. The solution is of the form of
equation 5-6 witn:
u(t) = ext
q(t) = L qc(t)/v*(t)
C(te) -
T saturation time
Using equation 5-4, the concentration of radioactivity at saturation time
can be evaluated as:
= Qo e rch [1 - e'rcrf] /V (5-19)
where:
Vrch = the volurne °f water at initial saturation time.
Tnis solution is described in Appendix C (C.4). The rate of release
of radionuclides is the product of the radionuclide concentration and the
volumetric flow of water. The cumulative radionuclide release is the
integral of this product (equation 5-8) evaluated, for this case, from
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time of initial saturation, T n, to the time of repository closure,
T i . If the radionuclide is solubility limited, C(t) is replaced by
the solubility limit, C . A summary of tne parameters used to evaluate
releases from salt repositories caused by resaturation of repository
backfill and the effects of salt creep are summarized in Table 7-2.
5.2.1.2 Granite, Shale. Basalt Repositories
Groundwater flow through the host rock of a repository can be altered
by the effects of the heat produced during radioactive decay. Temperature
changes will cause stress changes in the host rock that may alter the
hydraulic properties of that rock through such processes as: rock
expansion, compaction of fill, slippage and movement along fractures, and
mineral alteration. In the immediate vicinity of the waste, temperatures
as high as 100-200 degrees centigrade are predicted (ADL 79d). The
temperature rise may actually cause a decrease in rock permeability,
thereby restricting flow; however, the subsequent temperature decrease may
result in increased permeability and increased water flow.
To analyze the effects of temperature change on the volumetric flow
of water through the host rock, we used another application of Darcy's law:
V*(t) = KAi(t)c(y) (5-20)
where all the parameters are as defined for equation 5-9. The hydraulic
gradient, i(t), and the viscosity correction factor, c(y), both change
over time because of the alteration processes caused by the temperature
changes. The changes in these two parameters were calculated independently
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by ADL (ADL 79d) for eacn repository host rock. The general equation
descrioing changes in hydraulic gradient and viscosity over time is:
i(tjc(y) = ae -at + be ~Bt + iflce ~yt + ifl (5-21)
The parameters a, b, c, a, e and Y and ifl vary with rock type when this
expression is used to evaluate equation 5-20.
The effects of waste heat on the host rock matrix may alter its fluid
transmitting properties such that the hydraulic conductivity is increased
by a factor of 10. If so, representative values of hydraulic conductivity
—4 -3
would be 3 x 10 m/yr for granite and 3 x 10 m/yr for basalt and
shale. The cross-sectional area (A in equation 5-20) of the repository is
2
8km . The values used as input for the flow through bulk rock
calculations are summarized in Table 7-2.
The build-up of the radionuclide concentration in the repository
groundwater, C(t), is estimated by solving equation 5-5 using the
volumetric flow V*(t) described by equation 5-20. The solution is
presented in Appendix C (C.5). In this case, f=l, and the solution has
the genera! form of equation 5-6, with the following parameters:
q(t) =7Qc(t)
p(t) = x + K A i(t) c(y) / V
C(tc) = 0 at tne time of failure of the canisters
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If the calculated volumetric flow rate of water V*(t) exceeds the
limiting aquifer flow, V , then equation 5-5 is solved using V in
aq aq
place of V*(t). This is the same as solving equation 5-7 with f=l:
V - = Lgc(t) * xVC(t) - V*q C{t) (5~22)
Tne radionuclide concentration, C(t), is determined by solving this
equation in the same manner as equation 5-7 is solved in Appendix C (C.3).
Tne integral is solved from time = t to the time of interest, which
\*,
yields the following expression for C(t):
-U+V/V)t (L t )
LQ e aq e -(L-V /V)t -(L-V /V)t
C(t) = -2 n f-r [ e aq - e aq C J (5-23)
vaq
If tne radionuclide is solubility limited, the concentration, C(t), in the
repository voids is assumed to equal tne solubility limit, C .
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To calculate releases from the repositories, the product of the
concentration and volumetric flow rate is integrated from the time of
canister failure, t , until the time of interest, t^ The following
equations illustrate this integral:
No aquifer flow limit or solubilitiy limit:
t.
Q = [ ^ V(t) C(t)dt (5-24)
*cj
Aquifer flow limit, no solubility limit:
Q = Vaq J i C(t)dt (5-25)
tc
Solubility limit, no aquifer flow limit:
t.
Q = CQ J V(t)dt (5-26)
Limits on both aquifer flow and solubility:
Q " Vaq Co ('i - tc) <
Some of these integrals cannot be solved analytically and must be
evaluated numerically.
5.2.2 Human Intrusion (Drilling)
Future drilling at a repository site might either directly impact
waste or disturb the host rock surrounding the waste. The worst result
would be a direct deposition of radioactive material on the land surface
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overlying the repository. Analysis of a quantitative model for human
intrusion indicates the most important aspects would be the frequency of
drilling, the quantity of material transported to the surface, and the
assumptions made about remedial actions taken after a release.
We have assumed that institutional controls will prevent any human
intrusion for the first 100 years, after which time we assume the site
will revert to prevailing land use patterns. Based on these assumptions
ADL estimated the frequency of future drilling. Table 7-3 details the
annual probabilities of drilling into each type of repository. The
drilling activities we have considered for each repository type are:
1. oil and gas exploration
2. water exploration
3. geothermal resources evaluation
4. brine injection or disposal of other wastes
5. mineral exploration
6. scientific investigation
7. fluid storage
Past drilling rates into potential repository formations provide
useful information for estimating possible future drilling. However,
present drilling appears to be well documented only for the petroleum
industry. ADL estimates oil and gas drillings in 1976 and 1977 in the
United States average approximately 0.04 holes drilled per year per
possible repository site. Since the development of the petroleum industry
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is fairly recent, long term predictions based on present drilling rates
may not oe very accurate. Significant change could occur in the future
for the following reasons:
1. Scarcity of oil, gas, water, or certain minerals may encourage
more extensive exploration or make their use obsolete, so that
exploration for them ceases.
2. New recovery methods or drilling techniques may make deposits or
formations attractive wnicn were previously not worth exploiting.
3. New resource recognition may initiate entirely distinct drilling
programs.
Thus, any structured mathematical estimate of drilling frequency into a
potential repository site is not very meaningful. The ADL report uses the
following simple rationale for estimating the frequency of drilling into a
bedded salt repository:
1. Persons in the future may drill to explore potentially economical
deposits of petroleum and minerals.
2. In the course of their exploration, they will discover that the
site has no valuable resources. Subsequently, however, this fact
and the site location will be forgotton—or economic or social
conditions will change—and exploratory drilling will occur
again. ADL assumes the period of time to "forget" is 50 years,
thereby assuming a frequency of 2 exploratory drillings per
century.
Based on these premises, the estimated drilling frequency for the other
generic repository types is compared with the frequency for bedded salt
and is presented in Table 7-3.
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We estimate the probability of impacting a canister during drilling
by comparing the total area of the intersection of the drill hole and
canister to the respository area. Assuming 35,000 canisters with an area
O p
of intersection of 0.2m (ADL 79d) and a repository area of 8 km, the
probability of hitting a canister per drilling event is equal to product
of the number of canisters and canister area divided by the area of the
repository—or about 0.001.
The drilling frequencies assumed for shale are based on tne same
criteria as those for bedded salt. The drilling frequencies for basalt
are based on tne same types of exploration as bedded salt; however, ADL
expects at least a factor of 2 decrease in the frequency of exploratory
drilling in basalt compared to bedded salt based on a comparison of
present drilling activity for basalt and bedded salt formations. Present
drilling practices at domed salt formations indicate that the majority of
the drilling is around the edges of the dome where petroleum or minerals
are more likely to be found. ADL conservatively assumes the drilling
frequencies will be the same at domed salt and bedded salt repositories.
Presently, there is little reason to drill into or through a granite
repository, although drilling to explore for geothermal resources is a
possibility. The drilling frequency for granite is conservatively
selected to b,e about a factor of 10 lower than the frequencies at any of
the other reference repositories.
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Drilling into a repository may lead to the release of radionuclides
by several mecnanisms, the principal ones being:
1. Direct impact on waste and transport of a fraction of it to the
land surface.
2. Transport of radionuclide contaminated water from the repository
to the surface.
3. Transport of nuclides witn ground water to the upper aquifer
through the backfilled but permeable borehole pathways.
The extent of releases depends on the degree to which the drillers
recognize the repository ana its associated hazards when they encounter
it. If the drill bit passes directly into a waste drift backfilled with
porous and unconsolidated material, an anomaly will probably be indicated
by any of several signs, among them:
1. Rapid downward movement of the drill stem,
2. Loss of drill fluid,
3. Drill stem wandering and chatter,
4. Down-hole temperature changes caused by increased cooling of the
drill by water in the repository. (This would only be detected
in the case of constant thermal monitoring, as presently
practiced in some geothermal exploration work).
The drillers might interpret these anomalies as an extensive shear zone
or, if they have some idea that there is a repository in the area, they
might identify it as such. If they did identify the unconsolidated zone
as part of the repository, they would presumably exercise caution.
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They could take samples of rock and water, employ down-hole logging and
geophysical techniques, and grout or case the hole to seal off the
repository during subsequent use of the drill hole. Or they might simply
seal the hole and abandon that site.
Even if they fail to recognize the presence of a waste repository, it
is likely the hole would be cased through the backfilled level—at least
during the active life of the well. If, however, the drill were to pass
through a rock pillar rather than a mined opening, recognition of the
repository would be much less likely.
Despite the foregoing discussion, we have not assumed recognition of
the repository by future drillers in our assessment. Our approach is
based on three considerations:
1. The mined portion of the repository occupies only 25 percent of
the total cross-sectional area.
2. The earlier assumption about loss of control and knowledge of the
repository site makes it possible that anomalies encountered when
drilling into a repository would simply be interpreted as a zone
of incompetent rock.
3. Ignoring considerations about recognition of the site as a waste
repository leads to a simple and conservative model.
If a drill bit hits the waste, some fraction of the contents of a
canister will be transported to the surface. Based on an ADL analysis,
tne expected fraction of the canister intersected by a drill is
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approximately 0.15. ADL assumed the drill would pass right through the
portion of the canister it intersects, which implies that this fraction
also corresponds to the expected volumetric fraction of the contents that
is raised to the surface. The quantity of radionuclides transported to
the surface can be calculated using equation 5-1, with f= 0.15/35000 and
t equal to the time the drilling event occurred:
Q = f Q0e ~Xte (5-1)
Following impact of waste by a drill, the borehole may be sealed.
The characteristics of borehole seals have been discussed previously. If
the Dorehole interconnects the upper and lower aquifer, a pathway for
groundwater flow is created. The release of radionuclides through this
plugged borehole is described by equations 5-2a and 5-2b. The V*(t) term
for volumetric flow in equation 5-2b can be described by Darcy's law for
porous media and is discussed later for equation 5-28.
For drilling events that penetrate the repository but do not directly
impact waste, the analysis is separated into two cases: repositories in
salt and repositories in granite, shale, or basalt.
5.2.2.1 Salt Repositories
As discussed previously for expected releases, water can seep
gradually into the backfilled repository through the somewhat permeable
shaft and borehole seals. Since we assume a minimum volume of 20,000 m3
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o
remains in the repository, as much as 20,000 m of water can leak into
the backfill and remain there. In addition, fluid inclusions in the
seemingly intact rock may migrate toward the waste canisters because of
thermal gradients, thereby increasing the water content of the backfill
close to the canisters. Water in the inclusions of the backfill may
contribute to the dilution of radionuclides leaching into the void
volume. Because a recent analysis indicates very little dilution can be
attributed to fluid inclusions (NRC 80), we have ignored the included
water.
Integrating the volumetric flow of water into the repository
(equation 5-10 for bedded salt) over the repository closure time
(200 years) yields 878 m3 of water in the backfill. Using equation 5-11
3
for dome salt, the estimate is 736 in of water. These estimates are
slightly different than those calculated by ADL because ADL did not assume
a minimum repository volume, V . . The estimate for the volume of fluid
released by a drilling event is based on the low porosity and low fluid
availability at salt sites—and corresponds to the fluid surrounding two
cansiters. Since we assume 35,000 canisters in the reference
repositories, the volume of fluid released during drilling at a salt
repository is estimated to be approximately 0.05m for bedded salt and
0.04m3 for domed salt.
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Prior to a drilling event, the concentration of radioactivity in a
urine pocket can be calculated using equation 5-4:
C(t) = f Qoe~xt[l-e~L(t"tc)]/V (5-4)
In equation 5-4, f is the fraction of canisters contributing to the
buildup of radioactivity in the brine pocket and V is the volume of water
released during drilling. When a brine pocket is intercepted during
drilling, we have assumed tnat the pressure in the pocket is high enough
to eject the entire liquid contents into the drilling fluid, which is then
carried directly to the land surface. The concentration calculated is
multiplied oy V to obtain the total quantity of radionuclides released to
the land surface. If the radionuclide is solubility limited, the
solubility limit, C , is multiplied by the volume V to calculate the
total quantity released.
Following tne release of a brine pocket to the land surface, the
drilled borehole may or may not be sealed. In either case the hydraulic
conductivity of the borehole shaft seal will not be zero. Recharge of the
pocket is possible if the original drilling also intercepted the lower
aquifer. If water is available, the empty pocket can be recharged and the
remaining waste can leach radioactivity back into the pocket. Subsequently
contaminated water can be transported up the borehole shaft to the
overlying aquifer.
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The equation describing the buildup and release of radioactivity to
the aquifer from the brine pocket is calculated using equation 5-5:
= LfQ(t) - xVC(t) - V*(t)C(t) for t > t (5-5)
U C
where:
Qc(t) = QQe -Ate -L(t-tc) t > ^
V*(t) = K(t) i(t) A c(y)
o
A = area of borehole = 0.1 m
K(t) = K+ K'(t-te), linearly increasing hydraulic
conductivity for a borehole plug constructed at
the event time te (m/yr).
[Note: if the hole is not plugged or is plugged
inadequately, K will not be small and K1 will
be 0. ADL conservatively assumed that the
borehole will be filled in the same manner as an
undetected borehole might be filled (ADL 79d).
The hydraulic conductivity is then modeled to be
uniform over time and to have an estimated value
of 31.5 m/yr,]
i(t) = hydraulic gradient from interconnection of the
upper and lower aquifer and the gradient
resulting from thermal bouyancy effects.
c(u) = viscosity correction factor
These substitutions give the equation:
Lf Qe-xVL(t~tc)-xVC(t) - K(t)i(t)c(n)AC(t) (5-28)
If the analytical expression for the product of the hydraulic gradient and
the viscosity correction factor:
c(M) = ae~at + be~3t + ci
a
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is substituted into equation 5-28, the solution to that equation can be
written in tne form of equation 5-6:
C(t )y(t )
(5-6)
where the parameters are defined as follows:
q(t) = L f Q0 e^ e-^c)
p(t) = x + V(t)/V
rt fi *
J p(s)ds xt J V (s)/V ds
u(t) = e = e e
V*(t) = A [K + K'(t-te)] (ae~at + be~et + iace~Yt + i&) (5-29)
and — because any radionuclides in solution when the drill penetrates the
brine pocket are carried directly to the surface with the drilling fluid —
the pocket is initially empty with regard to releases to the aquifer:
c(te) = o
The solution to equation 5-28 for the specific example of K1 = 0 is
presented in Appendix C (C.6). The total quantity of radionuclide released
to the aquifer is the integral of the product of V*(t) (equation 5-29) and
the concentration C(t) (the solution to equation 5-28). If the
radionuclide is solubility limited, C , the limiting concentration is
used in place of C(t). If the volumetric flow is limited by the flow of
the aquifer, then V is used in place of V*(t) [see Appendix C (C.6)].
The parameters used to evaluate these equations for predictions of the
amount of radionuclide released by drilling in salt repositories are
summarized on Table 7-3.
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5.2.2.2 Granite, Shale, Basalt Repositories
These rock types are considered to be hard rocks, and they do not
exhibit the plastic flow or sealing phenomena of the salt media. Some
types of shale may be plastic, but the type of shale considered in these
analyses has characteristics similar to hard rock. Prior to any
excavation, these hard rock formations are saturated with water.
Excavation disturbs the saturation because water flows from the
surrounding rock into the resultant cavity. During the operational phase
of a repository, this water will be pumped out. After backfilling and
closing the repository, water flowing down the filled shafts and/or
through the rock walls will gradually fill the pores of the backfill until
resaturation is completed. ADL estimates the longest time until the hard
rock repositories reach resaturation is less than 200 years (ADL 79d).
Some of ADL's other estimates indicate resaturation may take less than
10 years after sealing the repository.
The pore volume of the repository backfill can be calculated from the
following equation:
V = Ar h M n (5-30a)
where:
Ar = area of the repository = 2 kmx4km = 8km2
h = height of the repository = 5m
M = mined fraction = 0.25
n = porosity of the backfill = 0.2
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fi o
The repository backfill pore volume V equals 2x10 m . Once the
canisters fail, radioactivity can leach into this saturated volume. Since
the hard rocks do not flow plastically, the lithostatic pressure of the
overburden will not close any of the repository pores. The pores are
assumed, therefore, to remain interconnected and to act as a large mixing
volume. Prior to any drilling event, the concentration of a radionuclide
can be described by equation 5-4, with V equal to the pore volume in
equation 5-30a and f equal to one:
-xt -L(t-t )
C(t) = QQe [1-e c J/ArhMn (5-30b)
Drilling into a hard rock repository might transfer some contaminated
backfill into the drill hole and up to the land surface. The backfill
material is anticipated to be cohesive so that it will not easily wash
into the drill hole (ADL 79d). Contaminated water might more easily wash
into the drill hole and be transferred to the land surface. The quantity
of water, Vb, predicted to be transferred to the land surface is
200 rrr—the volume of water contained in a 20 meter-long section of the
waste drift centered at the drill hole (ADL 79d). The quantity of
radionuclide transported to the land surface can be estimated by
multiplying the concentration, C(t), from equation 5-30b and V. , the
volume of water transported to the land surface, yielding:
v -xt -L(t-t )
Q=^Q0e L"1 - e ] (5-31)
V
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If the radionuclide is solubility limited, then the quantity of
radionuclide released is simply:
Q = Vb CQ (5-32)
where C is the solubility limit.
Following a release to the land surface, the drilled borehole may or
may not be sealed. In either case, the hydraulic conductivity of the
borehole plug will not be zero. Contaminated water could flow through the
pores in the plugged borehole to the overlying aquifer. Since the borehole
pathway can release only a small fraction of the total volume of water, we
have assumed that the concentration of radionuclides in the borehole pores
will equal the total concentration described by equation 5-30b. This
assumption is conservative and will result in a slightly larger calculated
release than would actually occur. The quantity of radionuclide released
to the aquifer to the time t. uses the form of equation 5-8—with f=l,
the concentration C(t) described by equation 5-30b, and the volumetric
flow V*(t) described by equation 5-29—to yield:
li
f fln p-xt ,',t t v -at -et -Yt
Q = / _o!_U-e c;J[K + K'(t-t )](ae +be +ice +i)dt (5-33)
J ~17 e a a
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For the granite repository, which does not have an underlying
aquifer, and for drill holes that do not reach the underlying aquifer for
shale and basalt, i =0 in equation 5-33. If the hydraulic conductivity
a
is not changing (see discussion for equation 5-28), then K1 = 0 and
equation 5-33 simplifies to:
/
j
J dt (5-34)
a
And if the concentration of the radionuclide is solubility limited, the
solubility limit, CQ, replaces the concentration function C(t) such that
equation 5-34 becomes:
Q = AC K f (ac^+be'^+i ce~Yt+i J dt (5-35)
0 . J a a
re
The parameters used to evaluate these equations for water released by
drilling into repositories in granite, basalt and shale are summarized on
Table 7-3.
5.2.3 Faulting
The discussion of faulting in this section is based primarily on the
results of the ADL report, which indicate that — while detailed onsite data
snould be used for specific sites — repositories should generally be in
geologically stable regions where renewed or new faulting is unlikely.
Nevertheless, old faults are common in almost any location and may be
expected at or near any repository site. We assume the presence of a
certain number of faults on the site, and on the basis of their age and
density, we estimate:
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1. The probability of renewed movement along the old faults.
2. The prooability of the occurrence of new faults.
The model assumes a constant probability based on the age of the most
recent fault activity. Releases from the repository as a result of fault
movement are assumed to be by grdundwater flow to the overlying aquifer.
The most important elements of this analysis are the reference fault
characteristics, the estimation of probabilities, and the release model.
5.2.3.1 Reference Fault
The reference repository is 2 km wide and 4 km long. We
conservatively assume that a fault intersects the repository parallel to
its length. The width of the fault zone is assumed to be one meter, thus
providing a 1 meter by 4000 meter pathway from the repository to the
overlying aquifer. The widths of faults vary considerably, btrt fault
zones wider than one meter are generally associated with growth during
extended periods of activity. The porosity of the fault zone is assumed to
be 0.1. The hydraulic conductivity of the fault depends on the strength
of the host rock and is discussed separately for each repository.
5.2.3.2 Hydraulic conductivity
The hydraulic conductivity of the fractured zone associated with a
fault in a salt repository can vary widely. Actually, instead of
fracturing, the salt may simply deform to relieve the stresses that would
induce fracturing in adjoining strata. Since salt is rather weak, any
fracturing would be expected to produce fairly well crushed salt.
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The Hydraulic conductivity of compacted crushed salt has been estimated at
aoout 31.5 m/year (ADL 79d). The shale overlying the bedded salt
repository may have a lower hydraulic conductivity, but for conservatism
the entire pathway from the lower aquifer to the upper aquifer is assumed
to have the same hydraulic conductivity as the pathway through the salt.
The hydraulic conductivity of a fault through domed salt is assumed
to be the same as for Dedded salt. The hydraulic conductivity of shale is
chosen to be 31.5m/yr and is based on the hydraulic conductivity for
compacted crushed shale (ADL 79d).
Due to the nigh strength of granite, the hydraulic conductivity of
the fractured zone of a granite repository site is based on the assumption
tnat the granite is brecciated and fractured rather than pulverized.
We believe a hydraulic conductivity of 3150 m/yr is a reasonable estimate
(ADL 79d), although a large range of values is possible. This value of
hydraulic conductivity corresponds to the high range for silty sand and
gravel.
The nydraulic conductivity of basalt after faulting is assumed to be
3150 m/yr based on similar assumptions to those used for faulting at a
granite site.
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5.2.3.3 Probabilities
To estimate probabilities of renewed movement of old faults we need
information on the time, N, since their most recent movement. We use the
reciprocal of this time period, 1/N, to estimate the probability of renewed
movement. If f faults are detected, then f/N, where N is the time to the
most recent movement of any such fault, is used as a conservative estimate
of the total probability of renewed movement. This assumption is made
because movement along a fault can be regarded as a stochastic process,
and intervals between movements are analogous to the time between failures
of mechanical components in classical reliability theory. For example,
suppose we know that, over the history of the fault, several time periods
nave elapsed between movements. The period N since the last movement
should also be added to this list. Since fault movement has not yet
recurred, N underestimates the true value of the time from the previous
movement to the next movement, thus providing a conservative approximation
of the probability of movement (see ADL 79d for further discussion).
Often geologists assign a zero probability for renewed movement in the
near future to certain old faults that are well dated and understood. It
is expected that old faults at the repository site would fall into this
category. We believe the estimation of a small positive probability is
consistent with present practice and somewhat conservative (ADL 79d).
In attempting to estimate the probability of new faulting at a
repository site, it is reasonable to consider only the most recent episode
of faulting because, in general, earlier processes do not describe the
present state of a site as well as recent processes. If this most recent
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episode of faulting and fault movement occurred during a period from
M to N years before the present time period, and if the fault density of
f faults per repository area was observed, then the average rate of new
faulting over the last M years is given by f/M faults per year per
repository. In a location with a long history of stability since the last
faulting episode—and where no new geologic processes offer countervailing
evidence—this average rate can be interpreted as a conservative estimate
of the new faulting probability. In fact M is often more difficult to
determine than N, and since N is less than M, the conservative larger
probability, f/N, has been adopted for modeling purposes.
The combined rate of occurrence of either type fault movement is then
given by 2f/N. With respect to the estimation of the parameter f,
insufficient data is available for a generic statistical analysis. Some
evidence for specific repository sites can be obtained by:
1. Examination of fault densities from surfaces maps.
2. Fault maps for power plant applications.
3. Seismic surveys for parts of the Delaware basin.
4. Reported fault spacing along anticlines in the Columbia Plateau.
On the basis of such data, it appears that—for most locations—it is very
unlikely to find faults of the type discussed here spaced closer than
about one to two kilometers, with 10 to 15 kilometers being more common
(ADL 79d). Hence, we adopted an estimate of 2 faults per repository for
all the reference repository models. Therefore, the selection of faulting
probabilities for the various repositories only requires N, the last known
occurrence of faulting.
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5.2.3.3.1 Bedded Salt
The estimate for N for bedded salt is 230 million years, corresponding
to the most recent faulting during the Permian age. This is generally a
valid assumption for much of the Delaware Basin, for example (ADL 79d).
_o
Thus, the probability is calculated to be 2x10 events per year.
5.2.3.3.2 Domed Salt
The estimates for the faulting probabilities of domed salt
repositories are based on data from the Gulf Interior region (ADL 79d).
The youngest faults identified for the first estimates were dated at
13 million years when the domes stabilized, yielding a probability of
3x10 events/year.
5.2.3.3.3 Shale
The estimate for shale is based on the same geologic assumptions as
_Q
those for bedded salt, giving the same probability of 2x10 events/year.
5.2.3.3.4 Granite
The ADL estimate for granite is based on the assumption of an
ancient, stable batholith or other pluton. Some faulting would generally
be expected following final emplacement or metamorphism. In western
Massachusetts, ADL identified Triassic faulting as the most recent
faulting associated with the Montague Power Plant (ADL 79d). This age
ended 180 million years ago, resulting in an estimated probability of
_o
2x10 events/year.
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5.2.3.3.5 Basalt
The ADL estimate of the probability of faulting at a basalt
repository site is based upon relatively stable areas of the Columbia
Plateau, where the uppermost basalt layers, dated at 8 million years, show
large areas free of faults. It is possible that the most recent faulting
is still older than this, but there are active tectonic forces in the
general region. An age of 8 million years yields a probability of
5x10 events per year.
5.2.3.4 Release Model for Faulting
The release model and associated assumptions for faulting should
result in a conservative estimate of the flow rates to the overlying
aquifer at a repository. The conservatism may overestimate flows by one
or more orders of magnitude (ADL 79d). If the surrounding aquifers cannot
support the flow rates calculated, then we assume that the volumetric flow
rate is equal to that of the aquifers. Faults may heal either by plastic
deformation of the surrounding rock or by the accumulation of fill material
in the fractures. To simplify our calculations, these factors are not
included in our model. To further simplify the repository model, we assume
resaturation takes place before the fault movement occurs. In addition to
the transport of radionuclides by groundwater flow through the faulted
rock, there is the possibility that continued movement of the fault may
lead to physical transport of a portion of the repository contents to the
surface. ADL estimates show this process would be extremely slow
(ADL 79dj, and we did not include it in our assessment.
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Derivation of the equations for estimating the release of
radionuclides to the aquifer requires consideration of several processes.
First, because of the possible leaching of radionuclides prior to a fault
event, we assume the water saturating the backfill of the repository will
contain a homogeneous concentration of each radionuclide throughout the
backfill. As discussed previously, some radionuclides may be solubility
limited rather than controlled by the waste form release rates. When the
fault pathway is established, some of the contaminated fluid will mix with
the fluid moving up from below so that some of the radionuclides in
solution will be released. This effect decreases with distance from the
fault. ADL assumes the zone of influence is a band extending 50 meters
from each side of the fault. Such a zone is expected to contain 5 percent
of the repositoryarea and radionuclide inventory (ADL 79d). For the salt
repositories, we agree with this assumption since there is limited
interconnection of the brine pockets in bedded salt and domed salt
repositories. However, in granite, shale, and basalt repositories we
assume good interconnection of groundwater in the backfilll and the entire
inventory of radionuclides—hence, we assume the entire repository is
affected by the fault.
The mathematical equations describing the radioactivity in the water
saturating the backfill are basically the same for all the repositories.
They are also the same as those in section 5.1—only the assumptions of
the parameters are different. The basic equation describing the
concentration of the release is equation 5-5. The buildup of radioactivity
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in the pore volume prior to fault movement can be described by
equation 5-3a. Thus, the form of the solution is the same as equation 5-6,
with C(t) described by equation 5-4. We should note that f equals 1 and
V equals 2xl06 m3 for granite, shale, and basalt. For the salt
5 3
repositories, f = 0.05 and V = 1x10 m (5 percent of the saturated
volume of the hard rock repositories, as discussed above). Generally, the
inventory of radioactivity in the pore volumes builds up until faulting
occurs. For this case, the flow rate from the repository to the aquifer
is described by equation 5-20 with the volumes, areas, and hydraulic
conductivities presented in this faulting section. The gradient and
viscosity terms are the same as those presented in equation 5-20.
Parameters used in this section are summarized in Table 7-1.
In order to estimate the release of radioactivity from any waste in
the actual path of the fault, we assume a fault damages 100 canisters—
resulting in leaching of this waste directly into the aquifer.
Equation 5-2a mathematically describes this phenomenon with f=100/35,000=
_3
2.9x10 . For the solubility limited case, equation 5-2b applies.
Since the repository in granite does not have an underlying aquifer,
the gradient is provided solely by thermal buoyancy and the recharge water
is provided by the surrounding rock; this significantly restricts the
groundwater flow rate. The repository in domed salt does not have an
underlying aquifer either. It can be reasonably assumed, though, that a
fault intersecting a salt dome will extend beyond the flank of the dome
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on one or doth sides. Consequently, a connection will be established
between tne upper aquifer and an aquifer surrounding the dome below the
level of the repository.
5.2.4 Breccia Pipes
Slow average rates of dissolution at the boundaries of the salt bed
should not lead to breaches of the repository for tens or hundreds of
millions of years. However, there are localized dissolution features that
result from much higher than the average rates of salt removal. Deep
dissolution processes at the oottom of bedded salt deposits can lead to
the development of orine-filled cavities underneath the repository
structure. These cavities, after reaching a certain critical size, can
cause the collapse of the overlying rock and the propagation of a chimney
of uroken rock up to or toward the surface. Such a chimney structure is
called a breccia pipe. This pipe provides a permeable pathway through
which groundwater can flow and leach radionuclides from the waste. We
assume fluid flows are upward, with the release of radionuclides into the
upper aquifer. We assume that further dissolution of the salt formation
around the breccia pipe at the repository horizon will not occur (based
on qualitative considerations of water availability and degree of salt
saturation), but we also assume there will be no healing of the column by
cementation and recrystallization. Breccia pipes formed by localized
dissolution are roughly circular, with diameters of a few tens of meters
to more than 0.5 kilometers, and with an average depth three times the
diameter. The upper portions are filled with broken rock called breccia,
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ranging from small granules to blocks a meter or more across. Relatively
few measurements have been performed on the breccia filling the pipes to
determine their hydrologic properties; however, existing data indicate
that very broad ranges of porosity and hydraulic conductivity are
possible. Pipes within the Carlsbad mining district in New Mexico have
shown properties ranging from those of the intact evaporite section to
those of typical gravels—with hydraulic conductivities from 3x10 m/yr
to 3100 m/yr and porosities from one to twenty percent. At the time of
formation, higher hydraulic conductivities are expected, in the range of
300 to 3xl05 m/yr.
The probability of occurrence of a breccia pipe on the repository
site is specified in terms of a constant annual rate, except for an initial
period of 500 years during which the probability is zero. An initial
period of zero probability results from the fact that it takes some time
for a critical cavity to develop, and if a pipe were already at a
significant stage of growth at the time the repository were sealed, it
would be detected by geophysical techniques (such as radar) operating from
the mine. The time required for critical cavity growth is probably much
longer than 500 years, but this conservative value has been adopted to
account for the possibility that waste heat could induce more rapid
dissolution. The probability of a breccia pipe developing at a repository
—8
is assumed to be 1x10 events/year.
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To calculate this probability, ADL reviewed the literature and aerial
photographs to estimate densities of possible breccia pipes in several
evaporite basins. They calculated the volumetric rate of salt removal by
deep dissolution and the time period during which this dissolution has
been occurring. By comparing this rate with estimates of critical cavity
size necessary for chimney initiation and propagation to an upper aquifer,
ADL estimates the rate of breccia pipe formation. These estimates are
comparable to estimates developed in other more empirical surveys—based
simply on the number of features, basin area, and time period of
dissolution processes. The resulting probability of occurrence is
1x10 yr . ADL did not adopt this rate as the reference estimate,
because they assume the avoidance of features that could lead to deep
dissolution will have high priority in the repository site selection
process. Their reference estimate is based on the assumption that the
structures underlying a potential repository formation are simple and well
mapped, and that any underlying aquifers are heavily saturated with salt,
slow moving, at relatively low potentiometric head, and well isolated from
the host salt formation in the vicinity of the repository. We believe
these conditions can be verified with sufficient certainty to reduce the
annual probability by two orders of magnitude, which leads to their
reference estimate.
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ADL chose the following parameters as representative of conditions in
a newly formed breccia pipe:
K = 10~2 cm/sec (hydraulic conductivity)
n = 0.2 (effective porosity)
/I 9
A = 3x10 m (cross-sectional area)
If a breccia pipe were to develop underneath the repository, eventually
part of the repository would either slump or fall into the chimney-like
structure. Physical damage to the waste package would be expected in this
process, since the rock itself is rather thoroughly broken. At this point,
the canisters would be subject to leaching by groundwater circulating from
and back to an aquifer below the repository. The present model does not
treat releases to the lower aquifer separately. Rather, since chimney
growth propagates rapidly, we conservativley assume that a connection is
established between upper and lower aquifers, and that water flows upward,
driven by gradients from interconnection of aquifers and thermal buoyancy.
The canisters in the breccia pipe include about 0.4 percent of the
repository inventory, based on the cross-sectional area given earlier.
These canisters are subject to direct leaching. Furthermore, any
radionuclides that had previously leached out of the waste packages would
also be washed out with the groundwater flowing through the brecciated
zone. We assume an area twice the diameter of the pipe itself is affected
by this process, so that the cumulative leached inventory is 1.6 percent
of the canisters' contents.
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The mathematical equations for estimating the release of radioactivity
to the aquifer are identical to those used for the faulting model. The
only difference is the values of the input parameters, given above and
summarized in Table 7-1.
5.2.5 Volcanoes
We do not expect anyone will purposely locate a repository site where
future volcanic activity is likely. Nevertheless, volcanic trends can
cover large distances over a period of time, and, occasionally, completely
new volcanic centers erupt, even within stable crustal plates. This
section of the report is concerned with the intersection of a repository
by a volcanic structure that vents to the surface. The release model
consists of a c&nstant annual probability of a volcano penetrating a
repository and transporting material to the air and land surface. Rates
are estimated by counting the number of vents in various areas, dividing
by their age to obtain vent formation rates, and multiplying by the
probability that such a vent would intersect a randomly cited repository
in the region of interest.
During the last ten million years, the only volcanism in the
coterminous 48 States has been in the West. Most of this activity has
paralleled the Pacific Coast, but some has followed the graben of the
Rio Grande and an arc from Albuquerque toward Las Vegas, or has extended
westward from Yellowstone Park.
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Of concern for a repository siting are the frequency and predicta-
bility of new volcanism, since there are no present plans to consider
placing repositories within the range of influence of known volcanoes.
New volcanism will usually develop close to existing volcanic features and
in regions experiencing tensional stress.
Areas of future volcanic activity can be defined only approximately,
and predicting the timing of this future activity is even more difficult.
Future estimates of the expected frequency of eruptive activity at
volcanoes or in volcanic regions are generally based on historical records
and geologic investigation, both of which vary widely in detail and
reliability from one volcanic region to another. All of the geologic
media considered in this study can be found in areas where there is no
recent volcanism.
Tnere are many site-specific factors that can enter into an
estimation of the likelihood of future volcanism at a repository
location. These include the distance to the nearest recent activity,
whether the site lies in the direction of a trend, regional stress
patterns and the way a site has evolved over geologic time (heat flow
measurements, etc.). The model used here does not incorporate geophysical
parameters, but rather utilizes a simple counting technique for roughly
estimating the order of magnitude of the likelihood of future volcanism.
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As noted earlier, all the vents in the coterminous United States that
have snown activity within the last 10 million years are in the west.
These events actually formed over a period longer than 10 million years;
however, in estimating the rate of formation, it is conservative to use
this shorter time span. ADL estimates approximately 1300 vents over a
ft ?
western area of the United States with a land area of 3x10 km .
A gross regional average rate of vent formation is thus 4x10
2 ?
vents/km /year. For a repository of area 8 km , the corresponding
rate of intersection would be eight times the above, or 3x10
intersections per year. This number is used in an example calculation to
represent the model equation of frequency equal to 8 V/AT intersections
per year where V is the number of vents formed in the area A over a period
at least as long as T. ADL chose the 10-mi11 ion-year cut off for data on
vents to conform to the US6S volcanic hazards maps.
A simple first estimate of the frequency for all media except basalt
can be derived from the assumption that, with careful site selection, it
should be possible to locate a repository so that the probability of
future volcanisrn is less than the national average. This is because there
are enough suitable bedded salt, granite, shale, and salt dome sites so
that it should not be difficult to locate a repository in an area of very
little past volcanic activity. The national average probability,
therefore, is a conservative estimate of the frequency. This value is
obtained exactly as above, except that the entire area of the conterminous
states is used, so that the frequency is (8)(1300)/(7.83xl06)(IxlO7)
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or 1x10 intersections per year. Basalt is not covered by this
reasoning because the only basalt deposits seriously considered as
repository sites are located in a single region—namely, the Pacific
Northwest. By their mere presence, basalts indicate significant past
volcanic activity. Most of the Columbia Plateau flood basalts apparently
were deposited about 14 to 17 million years ago, but some volcanic
activity continues in locations such as Mount Lassen farther to the west.
Regional stress studies suggest that there may be locations in this region
where the probability of future volcanism is low. ADL based their
calculations on the States of Washington, Oregon, and Idaho, exclusive of
the north-south volcanic trend represented by the Cascade and Klamath
Mountains. The following parameters have been estimated for this region:
A = 4xl05 km2
V = 300 vents
T = 107 years
The resulting value of the frequency from the model equation is 6x10
intersections per year.
It.should be noted that, in calculating the volcanic vent formation
rate, the choice of regions to be considered has a great effect on the
resulting numerical value. For example, application of the above procedure
to the eastern United States would yield essentially zero rates. Simple
modifications, such as eliminating from consideration the vents along the
Pacific coast volcanic mountain zone, would indeed lower the rate for the
rest of the country. Since this modification only changes the results by
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about a factor of 2, we do not believe it is important to refine them by
making further site selection assumptions. Another modification we
considered was to evaluate only intraplate silicic eruptions. While the
consequences of these eruptions are more severe than those we evaluated,
the analysis involves lower probabilities than the ones we have
calculated. Also, an analysis of potential silicic eruptions involves
detection of developing magma chambers that could lead to silicic
eruptions over the next 10,000 years.
The dominant release mode for the interruption of a repository by a
volcanic vent is the transport of radioactive material directly to the
surface. Since the size of the vent and the nature of the eruption can
vary considerably, this analysis simply estimates parameters that would
characterize an "average" new vent. The area of the vent is taken to be
A p
3xlOH nr, corresponding to the area of a circle with radius 100 m.
This cross-sectional area also characterizes the portion of the repository
that would be affected: 0.4 percent of the repository inventory.
If we were to model the "worst possible" case in terms of
consequences, then the probabilities would need to be revised downward
accordingly. Equation 5-1 can be used to predict the quantity of a
radionuclide ejected to the land surface by a volcano where f = 4xlO~ .
The parameters discussed in this section are summarized in Table 7-1.
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5.2.6 Meteorites
The impact of a large meteorite could cause a breach of the
repository, either releasing material directly into the air and onto the
land surface or by fracturing the surrounding rock, thereby permitting
greater groundwater access. Meteorites large enough to create such
oreaches are very uncommon. Furthermore, the potential hazards associated
with repository releases would appear to be negligible compared with the
possiole effects on surface installations, the environment, and the
surrounding population; therefore, the following discussion will be brief.
From observations of cratering history on the inner planets and their
satellites, and by correlation with the ages of portions of their surfaces
(e.g., by lunar rock samples), estimates have been made of meteorite
fluxes since the formation of the solar system. The ADL report (ADL 79d)
discussses this rate since the early period of the solar system, when
interplanetary debris was rapidly removed by the gravitational attraction
of the planets. The rate appears to have been roughly constant for the
last two billion years. Using data from well studied stable regions of
the earth, a cratering production rate, 0, has been determined to be given
by the following equation (ADL 79d):
Iog1() tf = -11.85-2 log1Q D (5-36)
wnere D is the crater diameter in km and 0 is the number of craters per
2
Km per year at least as large as the diameter D. It should be noted
that D = 1 is near the lower limit of applicability of the given formula,
but for present purposes—where the emphasis is on orders of magnitude—
the formula suffices.
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The geometry of craters is relevant in determining their effect on a
nuclear waste repository. There are simple bowl-like craters, as well as
ones with complex structures, including ringed ridges and peaks in the
interior and depressed sections along the boundaries. Craters up to about
4 km in diameter in crystalline rock and 2-3 km in sedimentary strata are
usually simple, while larger ones have complex structures. For a
repository about 500 m deep, as in the generic models, a crater diameter
of at least 1 km is a reasonable cutoff for defining meteorite events of
interest.
The failure model concentrates on meteorites giving rise to craters
of diameter 1-2 km because the frequency of meteorite cratering decreases
\
rapidly with increasing size, and the larger size impacts are even more
likely to cause widespread environmental effects of greater importance
than breaching a waste repository. The target area has been taken to be
24 knr, corresponding to the repository area (2 km x 4 km) and a
1-kilometer wide buffer zone around it. Failure occurs when the center of
the crater lies within this area. Using the production rate of
_1p p
0 = 1.4x10 per km per year for craters of diameters of at least
1 km, the annual failure rate is 3xlO~ events per year. This rate is
assumed to be independent of the host rock formation, since variations in
geophysical properties are not significant for the purposes of these rough
calculations.
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A meteorite Impact crater formed on tne repository site would be
expected to be smaller than the repository, since crater sizes are biased
toward the lower end of the range under consideration. A crater of 1-km
2
diameter would nave a cross-sectional area at the surface of 0.8 km .
Tne breccia zone caused by a metorite would not even reach 500 m in
depth, and the fracture zone at that depth would be very small. For a
crater with a diameter of 2 km, the Dreccia zone would intersect the
repository. Based on simple geometry, the area of intersection of the
o
repository and the breccia zone is calculated to be about 0.8 km ,
corresponding to a circle 1 km in diameter. For our purposes, this area
2
of intersection, of about 0.8 km , has been taken as a conservative
estimate of the portion of the repository directly affected by the
meteorite event. It has further been assumed that there is sufficient
fracturing or brecciation down to the repository depth for direct releases
to the surface to occur.
Because of the higher probability of meteorites at the low end of the
size scale being considered, the expected direct release to the air and
land surface is probably very small. Although there does not appear to be
an analytical or empirical model for predicting this event, we have assumed
that 1 percent of the wastes in the affected zone (i.e., 0.1 percent of
the repository inventory) would be released to the land surface. The
remaining wastes are subject to enhanced leaching by groundwater, but this
pathway has been excluded in this evaluation, since the consequences of
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the aquifer pathway are expected to be much less than those for the direct
release to land. Equation 5-1 can be used to predict the release to the
land surface with f = .001. A summary of the parameters used in
equation 5-1 for meteorites is presented in Table 7-1.
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Chapter 6 - ENVIRONMENTAL PATHWAYS
The calculation of population doses and health effects due to
radioactive releases from a repository requires that each environmental
pathway be identified. We used very general models of environmental
pathways to convert the radionuclide releases to somatic and genetic
health effects. Population distributions, food chains, and living habits
will undoubtedly change in major ways over 10,000 years. Rather than
attempt to predict these changes, we generally chose parameters similar to
today's to use in these models. A detailed discussion of the techniques
and assumptions discussed in this chapter is presented by Smith, et al.
(SMJ 82).
There are four general release modes: radionuclide releases through
an aquifer to a river (surface water), releases via a river to an ocean,
releases directly to a land surface, and releases directly to air. For
each of these release modes we calculated the dose equivalents for each
organ and radionuclide for all the releases and environmental pathways
concerned. The organs we evaluated are bone, red marrow, lung, liver,
GI-LLI, thyroid, kidney, ovaries, testes, and total body. Total body dose
equivalents were used as an approximation for doses to all soft tissues
not otherwise specified. From the dose equivalent for each organ, we
calculated the expected fatal cancer and genetic effects for each person
exposed to the radioactivity. These fatal and genetic effects are called
health effects or health impacts. We estimated only the genetic effects
which are clinically significant enough to require medical treatment.
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Total health effects involve summing all the expected fatal or genetic
effects over tne exposed population.
6.1 Releases to a River
For the river release mode, we assume the repository is breached so
that groundwater can circulate through the repository and transport
radionuclides througn an aquifer overlying the repository. These
radionuclides are eventually released to a river. The total amount of a
specific radionuclide entering the river is determined by integrating the
release rate over the time period of interest.
When the radionuclides reach the river, we assume they are immediately
diluted in the river flow. We calculated the concentration of nuclides in
the river by dividing the release rate by the river flow rate. This
concentration is used to compute the population environmental dose
commitment and tne resulting health effects for a population exposed
through the following pathways:
— drinking water
— eating fish
— eating food raised on irrigated land including vegetables, milk
and meat
— inhaling material resuspended during irrigation
— being directly exposed to radiation from nuclides deposited on
land surface
— being directly exposed to radiation from nuclides resuspended in
air
Figure 6-1 illustrates these pathways.
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FIGURE 6-1 SCHEMATIC OF A RELEASE TO RIVERS
BEEF
CO
CO
-------
We estimated the total intake of radionuclides by the population
utilizing the river and its food products. People living along the river
ingest radionuclides dissolved in the river water if the water is used for
public consumption. The annual intake by the population is calculated
from the amount of water an individual drinks (ICRP 75), the number of
individuals drinking the water, and the radionuclide concentration in the
water. We assume there is no reduction of radionuclide concentrations in
drinking water due to water treatment, sedimentation, or river use.
Fish in the river also take up radioactivity dissolved in the river
water. These fish are caught and consumed by the public. We used
estimated fish ingestion rates by the public to determine the total intake
by the population of the various nuclides in the river water.
The river water containing radionuclides from the repository is used
to irrigate farm land used to raise vegetables and fruit and to graze milk
and beef cattle. We assume all irrigation is spray irrigation, with
direct deposition of the spray onto the crops and the land surface below
the crops. Some of the radioactive material deposited on the ground moves
down into the soil and is taken into plants through the root system. This
augments the material deposited directly on the plant surfaces. We assume
some of the irrigated plants are consumed by humans as food and the rest
are consumed by milk or beef cattle. Consumption of contaminated
vegetation by milk or meat producing animals results in transfer of
radionuclides to milk and meat. Thus, the overall result of using
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contaminated river water for irrigation is that radionuclides in
vegetaoles and fruits, milk, and meat are ingested by humans. Ingestion
rates of the food products contaminated as a result of irrigation with
river water are used to estimate the total radionuclide intake by the
population.
Some of the radioactive material deposited onto soil by spray
irrigation is resuspended into the air. We estimated the resulting
integrated air concentration using a resuspension factor and then
calculated the ingestion of radionuclides by the affected population using
a representative inhalation rate for the population. The equation used to
compute the population dose requires an estimate of population density
within the assessment area.
The radioactive material deposited on the ground during irrigation
also results in external doses to persons in the area. During the period
of time that irrigation takes place, radioactive material continues to
build up on the ground until either the irrigation stops or equilibrium is
reached. The dose rate to the population receiving this external dose is
computed using external dose rate factors, population density, and a
shielding and occupancy factor to estimate the population dose for each
organ due to ground contamination.
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These radionuclide intakes and external exposures are combined with
organ specific dose commitment factors to calculate population dose
equivalent commitments for each organ. Health effect factors are then
used to convert population dose commitments to organ specific fatal and
genetic health effects. The health effects for all organs are added to
obtain total fatalities and genetic defects.
6.2 Releases to the Oceans
We assume radionuclides from a waste disposal facility are
transported to the ocean through a river system. Other assumptions are:
— Travel time in the river to the ocean is negligible
— Depletion of radionuclides in the river due to removal by
irrigation and sedimentation is not considered.
In light of these assumptions, the radioactive releases to the oceans are
the same as those releases to the river.
To calculate the radionuclide concentrations, the oceans are divided
into two vertical compartments: a 75-meter thick upper layer in which we
assume all edible seafood is grown, and a deeper lower layer. Our model
includes a slow transfer of radionuclides between these two layers.
Figure 6-2 illustrates these two layers or compartments. To be
conservative, we assume all edible seafood is in the upper layer—since we
expect radionuclide concentrations in the upper layer to always be higher
than those in tne lower layer. Radionuclides are transferred between the
two layers and removed from the ocean by radioactive decay and
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FIGURE 6-2 SCHEMATIC OF THE OCEAN PATHWAY
AQUIFER.
CO
REPOSITORY
SEDIMENTS
-------
sedimentation. Smitn, et al. (SMJ 82) have developed and solved coupled
differential equations to calculate the concentration of radionuclides in
each ocean layer as a function of time. The upper layer concentration
equation is integrated over the time period of interest to compute the
total intake of radioactivity by the public.
Tne fisn and shellfish living in the upper layers of the ocean take
up radionuclides from the ocean water. We used estimated ocean fish and
snellfisn consumption rates by the public to determine the total popula-
tion intake of the radionuclides released from the repository. This
intake is used to compute population doses and fatal and genetic health
effects in the manner similar to river release mode.
6.3 Releases to Land Surface
We assume releases of radionuclides to the land surface are to a
small area. This area is considered a point source for calculating
resuspensiori of radioactivity from the ground into the air. Several
processes interact to distribute the radionuclides between the air and
soil. Radionuclides on the land surface are either resuspended into the
air or transported into the lower soil layers and removed from the
environment. We assume resuspended radionuclides are dispersed from a
point source. The concentration of the radionuclides in the air depends
on the time after release, the distance from the release point, and the
amount of deposition on the land surface that has occurred since the
release.
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We used a dispersion equation and deposition rate to the land surface
to calculate air concentrations. The result is an air concentration and a
ground surface concentration of radionuclides as a function of distance
from the release point and the time after the release.
The radiation dose pathways to the population which we consider
important are:
— eating food raised on land contaminated with radionuclides,
including vegetables, milk, and meat
— inhaling radionuclides
— being exposed to radiation from nuclides resuspended in air
— being exposed to radiation from contaminated land surface
Figure 6-3 is a schematic of these pathways.
These population dose pathways are similar to the pathways discussed
for the river release model. The basic assumptions are the same for each
similar pathway and do not need to be reiterated. The approach is to
compute tne total population intake of or external exposure to
radionuclides and convert these intakes to population doses and then to
fatal and genetic health effects.
6.4 Releases to Atmosphere
Violent disruption of a repository can release wastes directly from
the repository to the air. We assume such a violent release disperses the
material so that the radioactivity is eventually distributed uniformly in
the troposphere in a fashion similar to fallout from nuclear weapons.
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FIGURE 6-3 SCHEMATIC OF THE LAND SURFACE RELEASE
DIRECT EXPOSURE
BREATHING
EATING CROPS
DEPOSITION I RESUSPENSION
MILK
BEEF
DIRECT
EXTERNAL
EXPOSURE
SOIL LAYER
SOIL SINK
REPOSITORY
-------
We assume radionuclides that fallout over the land surface are
distributed uniformly in a volume equal to land surface area of the earth
multiplied by the average height of the troposphere. With the material
distributed in this manner, we develop a two compartment mathematical
model to predict radionuclide movement between the air and the land
surface. The upper compartment is the tropospneric volume above the
earth, and the lower compartment is the available land layer (i.e.,
the layer of land containing the soil surface as an upper boundary and
including the root zone or plow layer of soil). This approach is very
simplistic; however, we believe a more detailed model is not needed. One
reason for not using a more detailed model is the low probability of the
events, such as volcanoes and meteorites, that release radionuclides into
the air.
Radionuclides are transported between the two compartments by
resuspension from the soil surface to air and by deposition from air to
the soil surface. The radionuclides are removed from man's environment by
radioactive decay and transport from the soil surface to the lower,
unavailable soil layers. To obtain the quantities of radionuclides in
these two compartments, we have developed and solved a system of two
coupled differential equations. Using these solutions, we obtain
time-dependent air and ground surface concentrations of radionuclides,
wnich are in turn used to compute population doses and health effects.
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Since radionuclides are present both in air and on the ground as a
result of tne release to the air-over-land, the important radiation dose
pathways to the population are:
— ingestion of food raised on land contaminated with radionuclides,
including vegetables, milk, and meat
— innalation of radionuclides
— external exposure due to air submersion
— external exposure due to ground surface deposition
Figure 6-4 is a schematic of these pathways. The assumptions used to
calculate the doses and health effects for these pathways are similar to
those discussed earlier for the other release modes.
We assume the radionuclides released to the air over the oceans are
distributed uniformly in a volume determined by multiplying the earth's
ocean area by tne average height of the troposphere. With the material
distributed in this manner, a three-compartment model is established to
descrioe radionuclide movement between the troposhpere and the two ocean
compartments. Using this model, concentrations of radionuclides can be
determined as a function of time in the air and in each of the two ocean
compartments, which were described earlier. The radionuclides in the air
compartment are transferred into the ocean by deposition similar to
fallout. A system of three differential equations, two of which are
coupled, are written and solved to obtain the water concentration of
radionuclides in the upper ocean layer. From the concentration of
radionuclides in the oceans, we calculate total fatal and genetic-effects.
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FIGURE 6-4 SCHEMATIC OF THE RELEASE TO AIR
OJ
DEPOSITION
TO
OCEANS
-------
6.5 Health Effects Calculations
Using the methodology developed by Smith, et al. (SMJ 82), we
determined the population health effects (fatal cancers and genetic
effects) that could be caused by radioactivity released from the
repository through each of these four release modes. In general, we
developed an estimated value for the health effects caused for each curie
of a particular radionuclide released through a particular release mode.
For this analysis, we assumed that releases to rivers ultimately become
releases to oceans (without reducing the ocean release for any depletion
due to tne processes encountered during transit in the river). Thus, we
added the health effects caused by a curie released to a river and an
ocean to develop a value for health effects per curie released to "surface
water." Table 6-1 displays the parameters we used to calculate the health
effects caused by releases to surface water, land surface, and the air.
The data used to develop these values are described in Smith, et al.
(SMJ 82).
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Table 6-1
Health Effects per Curie Released for Different Release Modes
Nuclide
Am-241
Am-243
C- 14
Cs-135
Cs-137
1-129
Np-237
Pu-238
Pu-239
Pu-240
Pu-242
Ra-226
Sr- 90
Tc- 99
Sn-126
U-234
Zr- 93
Releases to
Surface Water
7.31 E- 1
2.77 E 0
4.58 E- 2
3.83 E- 3
1.98 E- 2
1.09 E- 2
5.98 E- 1
2.29 E- 2
6.93 E- 2
6.54 E- 2
6.77 E- 2
3.17 E 0
1.21 E- 1
2.86 E- 4
1.20 E- 1
1.34 E 0
6.94 E- 2
Releases to
Land Surface
8.98 E- 2
1.03 E 0
2.58 E- 5
4.01 E- 4
5.62 E- 4
2.31 E- 5
3.22 E- 3
3.21 E- 3
5.55 E- 2
4.94 E- 2
5.63 E- 2
8.42 E- 2
9.75 E- 4
6.03 E- 8
4.13 E- 2
5.70 E -1
1.82 E- 1
Releases to
the Air
1.59 E- 1
1.14 E 0
2.04 E- 4
7.36 E- 4
6.91 E- 3
1.38 E- 3
8.03 E- 2
1.47 E- 2
5.18 E- 2
4.76 E- 2
5.13 E- 2
4.87 E- 1
1.63 E- 2
3.67 E- 5
1.12 E- 1
6.13 E- 1
1.55 E- 1
145
-------
Chapter 7 - RESULTS
We present the results of our analysis in terms of the consequences
(fatal cancers and genetic effects) and the probability of those health
effects. Our approach is to generate a probability and consequence for
each event and each event time selected, and to prepare a cumulative
complementary distribution function (CCDF). We also multiply each
probability (P) by its associated consequence (C) and sum the products to
obtain an overall risk, wnich we call the "(P)(C) risk", "expected value",
or the "expected health effects" over some period of time. To determine
the importance of different model assumptions we vary the characteristics
of the reference models.
To construct the CCDF graph, we first rank the consequences (highest
consequence first) and then associate with each consequence the sum of its
probability plus the probabilities of all the higher consequence events.
The consequence (horizontal axis) of the highest consequence event is
plotted against its probability (vertical axis). The next lower
consequence event is then chosen and its consequence is plotted against
the sum of its own probability plus the probability of the higher
consequence events. Each point on the resulting graph then gives the
probability of obtaining at least the indicated number of consequences or
health effects.
147
-------
The CCDF graph gives not only the "expected value" (by integrating
the area under the graph), Dut also indicates the distribution of
consequences. The consequences calculated can be fatal health effects,
genetic health effects, or weighted release ratios. The weighted release
ratios are the summation of the releases in curies of each radionuclide
divided by the quantity of each radionuclide corresponding to the release
limits in EPA's proposed environmental standards for high-level waste
disposal (EPA 82).
In developing the probabilities and consequences of the various
events, we identified three categories: (1) releases from events which are
not expected to occur within the time of interest (i.e., volcanoes,
meteorites, faults, breccia pipes), (2) releases from events which are
expected to occur a few times to hundreds of times during the time of
interest (i.e., human intrusion), and (3) releases which we expect will
occur continuously during the time of interest (i.e., normal groundwater
flow).
7.1 Releases from Low Probability Events
The frequencies at which the low probability events occur are assumed
to be constant annual rates. To calculate the necessary probability/
consequence information, we chose several time intervals and calculated
the cumulative probability of an event over each time interval using the
following equation:
pcum = Pann (*i+l - *i) (7-1)
148
-------
where P equals the total probability of an event with an annual
probability (Pann) occurring over the time interval t+-t. The
event is assumed to occur once in each time interval at the midpoint of
the interval:
te = (ti + ti+1)/2 (7-2)
The health effects are calculated for each event occurring at t , and
then integrated from t to the final time of interest t.
The CCDF curves can be obtained by matching sets of cumulative
probaoilities (Pcum) and integrated health effects. The expected number
of health effects for one event in a time interval is the product of the
cumulative probability Pcum for the time interval and the integrated
health effects for the event occurring in the time interval. The total
expected health effects for the event over the entire time of interest
(from t=0 to t=tf) can be calculated from equation 7-3:
total expected health effects = Pcum-Hei (7-3)
where: 1
pcum-j = pann(ti+l - *i)
He.j = integrated health effects from te to tf for each
i interval
te = (ti+1 + ti)/2
tf = 10,000 years, for most of our calculations.
149
-------
7.2 Releases from High Probability Events (Human Intrusion)
We expect inadvertant human intrusion to occur more than once during
the time of interest. The expected frequency of human intrusions into a
repository ranges from a drilling event every 400 years for granite to a
drilling event every 50 years for salt and shale (ADL 79d). An evaluation
of the total health effects from drilling events may cover thousands of
years — with tens to hundreds of drilling events expected during the time
of interest. Drilling events which may impact waste, however, are
expected to occur only once every one thousand drilling events. Even over
many thousands of years, it is possible that no direct impact of a
canister would occur. Thus, the direct hit of a canister is handled
mathematically as a low-probability event. Drilling events that do not
directly impact waste but do interact with contaminated groundwater in the
repository are expected to occur many times.
To evaluate these higher probability events in conjunction with the
low probability events, we must generate sets of probabilities and
consequences. Human intrusion may occur any time after institutional
controls have been removed — and can be assumed to be random in nature. We
assume that a binomial distribution, the fundamental statistical law that
governs random events, is applicable to human intrusion. The probability
that exactly n events will occur over a time period between t=0 and t=tf
can be expressed by:
(tf-nj!n! Pannn (l-Pann)tf~n (7-4)
150
-------
For convenience, we assume that—if n events do occur—they are
equally spaced over the time of interest. Thus, the average time between
events can be calculated from equation 7-5:
t. = institutional control time period, years
The first event time is t. +t , tne second event time is t. +2t
in av in av'
etc., until the final event time, which is t^-t . The integrated
T av
nealth effects are calculated for each event time and summed to obtain the
total health effects over the time of interest for n events. In this way
we have generated sets of cumulative probabilities and health effects for
the high probability of n events. From this data, the CCDF and the total
expected health effects can be calculated and integrated with the data
from the low probability events.
7.3 Releases from Normal Groundwater Flow
Releases from normal groundwater flow occur once with a probability
of one over all time. Thus, the integrated health effects are calculated
over the time of interest. This data can be used directly for the CCDF
and the expected health effects with a probability equal to 1. The
expected releases include bulk rock transport for granite, shale, and
basalt repositories and the leakage (if any) through boreholes and shafts
for the salt repositories.
151
-------
7.4 Results for Reference Repositories
To evaluate the effects of different assumptions on the long-term
risks from the five types of repositories, we first analyzed the risks
associated witn each of the reference repositories. The various
parameters of our reference repositories and the characteristics of the
release mechanisms have been presented throughout the report. For
convenience the parameters for the release mechanisms are summarized in
Tables 7-1 through 7-3.
We present the results for the reference repositories in two formats:
(1) graphs of cumulative probability versus premature cancer deaths
(CCDF curves) and (2) total expected premature cancer deaths (probability
times consequences). Most of our calculations evaluate a 10,000 year
period after repository closure. This time frame was chosen for two
reasons: (1) it is long enough for releases through groundwater to reach
the environment, thus allowing us to evaluate the importance of the
geochemical properties of the surrounding aquifers, and (2) it is short
enough for the probabilities and characteristics of geologic probabilities
and characteristics of geologic events which might disrupt the disposal
system to be reasonably predictable.
The CCDF curves for four of the five reference repositories are
presented in Figures 7-1 and 7-2. The CCDF curve for the salt dome
repository has not been included since it is essentially the same as the
one for bedded salt. The expected somatic health effects (premature
cancer deaths) for each event type and each repository are shown in
152
-------
Table 7-1
Characteristics of Low Probability Events
(Faults, Breccia Pipes, Volcanoes, Meteorites)
Faulting
Fraction of repository breached
Porosity of fault zone
Fraction of repository affected: Bedded Salt, Domed Salt
Granite, Shale, Basalt
Volume of repository affected (m3): Bedded Salt, Domed Salt
Granite, Shale, Basalt
Hydraulic conductivity of flow path
(m/yr): Bedded Salt, Domed Salt, Shale
Granite, Basalt
Cross-sectional area of fault (m)
Probability (yr"1):
Bedded Salt, Granite, Shale
Domed Salt
Basalt
Breccia Pipes (Bedded Salt Only)
Fraction repository breached
Fraction of repository affected
Probability after first 500 years (yr)
2
Flow area (m )
Porosity of flow path
Hydraulic conductivity of flow path (m/yr)
3 E- 3
1 E- 1
5 E- 2
1.0
1 E+ 5
2 E+ 6
31.5
3 E+ 3
4 E+ 3
2 E- 8
3 E- 7
5 E- 7
4 E- 3
1.6 E- 2
1 E- 8
3 E+ 4
2 E- 1
3 E+ 3
Volcanoes
Fraction of repository breached
Probability (yr ):
Bedded Salt, Domed Salt, Granite, Shale
Basalt
4 E- 3
1 E-10
6 E-10
Meteorites
Fraction of repository breached
Probability (yr"1)
1 E- 3
4 E-ll
153
-------
Table 7-2
Characteristics of Normal Groundwater Flow
Bulk Rock Transport (Granite, Basalt, Shale):
Granite Basalt Shale
K, hydraulic conductivity /, ^ .,
(after 100 years), m/yr 3x10"^ SxlO""3 3x10~J
A, cross-sectional area
of flow path, m2 8xl06 8xl06 8xl06
i(t) c(y) = ae~at + be~et where:
a = .0132 .132 .132
b = .0102 .102 .102
a = 1.6X10 ~3 1.6X10 ~3 1.6X10 ~3
8 = 3.1X10 ~4 3.1X10 "4 3.1X10 ~4
Shaft and Borehole Leakage (Bedded Salt, Domed Salt):
Initial Hydraulic conductivity of Shafts and Boreholes, m/yr 3.2xlO~3
2 £*
Annual change in Shaft seal, rn/y 3x10
Annual change in Borehole seal, my/yr 3xlO~4
Hydraulic gradient of upper aquifer:
Bedded Salt 1.3
Domed Salt 1.1
Viscosity Coefficient 5.0
o
Area of Main Shafts, m 100
Area of Boreholes, m2 Bedded Salt, 60 holes 6
Domed Salt, 50 holes 5
Repository Closure Time, years 200
Minimum recharge volume, m 20 000
Lithostatic gradient 7.9
154
-------
Table 7-3
Characteristics of High-Probability Events
in
en
(Human Intrusion by Drilling)
Characteristic
Drilling (hit canister)
Fraction of repository
(.15 of 1 canister)
Probability (yr~ )
Drilling (missed canisters)
Fraction of repository
Volume of affected
repository (m )
Volume of repository ?
removed by drill (m )
Initial permeability (m/yr)
Rate of change of hydraulic
conductivity (m/yr )
Porosity in flow path
Area of flow path (m )
Probability (yr"1)
Bedded
Salt
4E-6
2E-5
6E-5
.06
.06
3E-3
3E-4
.1
.5
2E-2
Domed
Salt
4E-6
2E-5
6E-5
.04
.04
3E-3
3E-4
.1
.5
2E-2
Granite
4E-6
2.5E-6
1.0
2E6
200
3E-3
3E-4
.1
.5
2.5E-3
Basalt
4E-6
1E-5
1.0
2E6
200
3E-3
3E-4
.1
.5
1E-2
Shale
4E-6
2E-5
1.0
2E6
200
3E-3
3E-4
.1
.5
2E-2
-------
Figure 7-1: COMPLEMENTARY CUMULATIVE DISTRIBUTION FUNCTIONS
(Bedded Salt and Granite)
f O
•o
Ol O
01 -H
u
X i-
(J
•i- 01
_Q 01
Q
Q. is
01
10
10
10
10
-6
-7
-8
-9
GRANITE
REPOSITORY
101 102 103 104 105 106
health effects over 10,000 years
10'
156
-------
Figure 7-2: COMPLEMENTARY CUMULATIVE DISTRIBUTION FUNCTIONS
(Basalt and Shale).
VI
IO
01
en o
01 O
01 i-l
u
X i-
01 0)
t- o
o
VI
4J U
••- 01
^ 1-
J3 01
<
VI
t.
10
01
OI O
c o
i- O
•a •
01 O
01 1-H
u
X i.
01 01
<<- o
o
VI
>. -M
•M U
>^v Ol
•r- >*.
JD ai
1 1
a.
-------
In Table 7-4. The contributions of the various radionuclides for the more
important events are presented in Table 7-5. The expected genetic effects
for each repository are also shown in Table 7-4; however, these are much
less than the somatic effects and will not be discussed further.
Figure 7-3 compares the total somatic effects for each of the reference
repositories, and Figures 7-4 and 7-5 depict the consquences and risks
from the various events for the bedded salt, granite, basalt, and shale
repositories.
In our tables, several significant figures are shown to facilitate
itemizing and comparing the risks from different events and radionuclides.
This is done strictly for convenience, we do not mean to imply that these
estimates are that precise—certainly no more than one significant figure
is meaningful in an absolute sense.
Each type of reference salt repository would cause about 200 health
effects, almost all of them premature cancer deaths. Nearly all of these
corne from releases of americium-243 and 241 due to drilling events which
hit contaminated brine pockets. The reference granite repository would
cause about 800 health effects, which are also dominated by releases of
americium-243 and 241 due to drilling. For the other hard rock
repositories, the risks are considerably larger: about 4500 for basalt and
about 7500 for shale. For these two reference repositories, normal
groundwater flow through bulk rock is a significant contributor to the
total number of projected nealth effects.
158
-------
Table 7-4
Expected Health Effects over 10,000 Years:
Reference Cases
Event
SOMATIC EFFECTS BY EVENT:
Normal Ground Water Flow
Drilling (misses canister)
Drilling (nits canister)
Faulting
Breccia Pipe
Meteorite
Volcano
Bedded
Salt
0
181
5
0.007
0.001
0.003
0.03
Domed
Salt
0
124
5
0.1
-
0.003
0.03
Granite
11
747
0.6
0.1
-
0.003
0.03
Basalt
1,420
2,960
2
3
-
0.003
0.2
Shale
1,420
5,910
5
0.1
-
0.003
0.03
TOTAL SOMATIC EFFECTS:
186
129
760
4,390
7,340
TOTAL GENETIC EFFECTS:
13
153
200
159
-------
Taole 7-5
Expected Health Effects over 10.000 Years by Radionuclide:
Reference Cases
Event
Norma 1
Ground Water
Flow
Drilling
(misses
canister)
Drilling
(nits
canister)
Faulting
TOTAL
Nucl ide
Sn-126
C- 14
Cs-135
1-129
Tc- 99
TOTAL
Am-243
Am-241
Sn-126
TOTAL
Am-241
Pu-239
Pu-240
Am-243
TOTAL
C- 14
Sn-126
Cs-135
1-129
Tc- 99
TOTAL
Arn-243
Am-241
Sn-126
C- 14
otners
TOTAL
Bedded
Salt
_
-
—
—
-
103
78
—
181
1.6
1.1
1.1
0.8
5
0.003
0.003
0.0005
0.0002
0.0002
0.007
104
79
0.02
0.005
2.4
186
Domed
Salt
_
—
—
—
-
69
55
—
124
1.6
1.1
1.1
0.8
5
0.05
0.04
0.007
0.004
0.003
0.1
70
57
0.05
0.05
2.4
129
Granite
5.8
4.7
0.6
0.3
_
11
671
75
2
747
0.2
0.1
0.1
0.1
0.6
0.07
0.04
0.01
0.005
0.0003
0.12
671
75
7.6
4.8
1.2
760
Basalt
954
399
47
23
0.3
1,420
2,650
304
7
2,960
0.8
0.5
0.5
0.4
2
1.6
1.1
0.2
0.1
0.006
3.1
2,650
305
959
401
73
4,390
Shale
954
399
47
23
0.3
1,420
5,290
607
14
5,910
1.6
1.1
1.1
0.8
5
0.07
0.04
0.01
0.005
0.0002
0.12
5,290
609
965
399
74
7,340
160
-------
ID -
ro
>, 3
^ 10 -
o
o
o
r,
o
1— <
0)
o
(/)
J_ i
^*
0
3 1 u
161
-------
Figure 7-4: CONSEQUENCES AND RISKS FOR DIFFERENT EVENTS
(Bedded Salt and Granite)
10 3 -
10 4-
10 3-
J2 10 2 -
1 «.'•
| 10°-
01
J= _J
Kf2-
io-3-
BEDDED SALT REPOSITORY , ,
—
\
%
^^^H
I
Nornwil Q»^*»*^ a
Water
Drilling Faulting
•M CV.
D-f
Vnlpsnrt
VU 1 (•AilU
Flow
10 5-
10 4-
10 3-
2 10 2 -
u
^ 10 x -
^ -1
10 L -
io-2-
io-3-
GRANITE REPOSITORY __
y/
%
%
w
•MNM
\
^^^
i
I
Normal D ...
Water
Flow
Drilling Faulting
Pipe Vo1cano
average consequences for one event
expected health effects over 10,000 years
162
-------
Figure 7-5: CONSEQUENCES AND RISKS FOR DIFFERENT EVENTS
(Basalt and Shale)
10
10
10
•2 10
5 _
4 _
3 _
2 _
C 10
0)
5 10 UH
fO
•S -i
10 H
10
10
-2.
-3 _
10
10
10
10
10
5 .
4 ..
3 .
2 .
1 .
10 u H
io'2H
io'3H
BASALT P
\
Normal
Water
Flow
SHALI
1
3ril
: RE
••••
EPO
I
Tin
POS
1
SITC
3 F
[TOR
RY
••••
aul
Y
I
ting
I
Breccia
Pipe
«•••
Vole
I
ano
I
Normal
Water Drilling Faulting
Flow
Breccia
Volcano
average consequences for one event
expected health effects over 10,000 years
163
-------
As Table 7-4 snows, only two types of events contribute significantly
to tne risks from the reference repositories: normal groundwater flow and
intrusion by drilling that contacts contaminated groundwater in the
repository. Although the consequences from some of the other events can
be large, their probabilities are so low that their risks are always small
relative to the two most important events. Therefore, as we compare the
risks from different types of repositories, we only consider the risks
from these two events.
The risks from the basalt and shale repositories are considerably
larger than those from granite and salt. This is primarily due to much
greater groundwater availability in the basalt and shale reference sites.
Tne granite site has relatively little water because there is no
underlying aquifer and the granite itself has a very low permeability;
both factors limit the recharge rate. Water movement is limited at the
salt sites because the salt will creep back into voids and fractures and
shut off pathways for water flow.
The risks for the granite repository are also lower than those for
basalt or shale because we assume that human intrusion by drilling is much
less likely for granite than for these other two rock types. A different
factor accounts for the small intrusion risks for the salt repositories.
Although the future intrusion rate for salt is assumed to be among the
highest, there is so little water in the reference salt repositories that
our assumed radionuclide solubility limits greatly reduce the potential
releases from intrusion.
164
-------
The two americium isotopes dominate the risks from releases to land
surface for two reasons: (1) they cause the most health effects per curie
released to the environment, and (2) the other alpha-emitting
radionuclides are restricted by much lower solubility limits. The
relatively high retardation factor for americium prevents these isotopes
from contributing to the risks due to normal groundwater flow, however.
Tin-126 and carbon-14 are the dominant radionuclides for the
groundwater flow pathway. Thus, for the salt and granite reference cases,
the americium isotopes contribute almost all of the risks because releases
to the land surface from intrusion dominate the results. For the basalt
and shale cases, tin-126 and carbon-14 are also significant because normal
groundwater flow causes a substantial part of the overall risks.
7.5 Effects of Different Assumptions
We performed a wide variety of sensitivity analyses to evaluate the
effects of different assumptions about the various parts of the repository
systems. We only considered bedded salt, granite and basalt in these
sensitivity analyses because our analyses for domed salt are very similar
to bedded salt and those for shale are similar to basalt. Our sensitivity
analyses address different waste form release rates, canister lifetimes,
solubility limits, retardation factors, event probabilities, and
integration periods.
165
-------
7.5.1 Different Waste Form Release Rates and Canister Lifetimes
Figure 7-6 snows how the expected health effects vary with different
waste form release rates. The risks increase in direct proportion to the
increased release rate with two exceptions: (1) the risks for the bedded
salt repository do not increase much above those for a 10~ parts per
year (ppy) release rate oecause of the solubility limits on the americium
isotopes, and (2) risks for the hard rock repositories do not increase
much beyond a 10 ppy rate because there is no more waste to dissolve
during the 10,000 year period of interest. Above this release rate,
dissolving the waste even faster has relatively little effect on the
overall results.
Figure 7-7 snows how expected health effects vary with different
canister lifetimes. Over the range we considered, canister lifetime has
much less effect on the results than the waste form release rate. The
primary effect of larger canister lifetimes is to shorten the period over
which risks from human intrusion and normal groundwater flow can occur.
Finally, to study the effect of varying both waste form release rate
and canister lifetime simultaneously, we did a series of parametric
analyses for the granite repository. These results are displayed in
Figures 7-8 and 7-9, and they reinforce the observation that release rates
have more effect on the overall risks than canister lifetimes.
166
-------
10
5 _
03
O
O
O
S-
Ol
10
4 .
10
3.
0)
.c
01
o
(1)
Q.
10
10
Figure 7-6:
EXPECTED HEALTH EFFECTS
OVER 10,000 YEARS
VS. DIFFERENT
WASTE FORM LEACH RATES
(parts per year)
BASALT
10"6 10"5 10"4 10"3
waste form leach rate (parts per year)
10
-2
167
-------
10J-T
to
o
CO
4->
U
-------
10
S-
o
CO
4->
o
a>
<*-
t-
a>
j=
•P
(O
-a
O)
u
(!)
a.
10
10 °H
10
10
Figure 7-8:
Expected Health Effects
Over 10,000 Years
vs. Different
Waste Form Leach Rates
GRANITE REPOSITORY
VARIOUS CANISTER LIFETIMES (years)
10
-6
10"° 10"H 10"°
waste form leach rate (parts per year)
100 years
500 years
1000 years
2000 years
3500 years
5000 years
10
-2
169
-------
10'
03
Ol
O
o
O
J-
O)
u
(U
OJ
-C
(U
TJ
OJ
+•>
o
(U
Q.
x
10
4J
10
3J
Figure 7-9:
Expected Health Effects
Over 10,000 Years
vs. Different Canister Lifetimes
GRANITE REPOSITORY
VARIOUS WASTE FORM LEACH RATES
(parts per year - ppy)
10"2 ppy
10"5 ppy
10J
1000 2000 3000 4000
canister lifetime (years)
5000
170
-------
7.5.2 Solubility Limits
We analyzed the effect of our solubility limits (Table 4-1) by
repeating our analyses without any solubility limits: any radionuclides
that could be removed from the waste form would directly enter the
groundwater. Table 7-6 shows these results.
Removing the solubility limits increases the risks substantially for
all of the repository types. However, the increase is most dramatic
(almost two orders of magnitude) for the salt repository. As noted
earlier, very little water enters the reference salt repository, which
makes the solubility limits (particularly the limits on plutonium and
americium) very important factors in limiting the risks from a salt
repository.
We also looked at the importance of waste form release rate and
canister lifetime on a salt repository without solubility limits. These
results are displayed in Figures 7-10 and 7-11, and they tend to reinforce
some previous observations: (1) without the effects of solubility limits,
risks -increase in direct proportion to the release rate up until a release
_o
rate of about 10 parts per year, and (2) reducing the release rate is
a more effective way to reduce risks than improving canister lifetime,
particularly if there are large uncertainties about the solubilities of
the radioactive wastes in the groundwater.
171
-------
Table 7-6
Expected Health Effects over 10,000 Years:
No Radionucllde Solubility Limits
Event
Bedded
Salt
Granite
Basalt
Normal Ground Water Flow
Drilling (misses canister)
Drilling (nits canister)
Faulting
Breccia Pipe
Meteorite
Volcano
0
14,700
5
0.009
0.001
0.003
0.03
14
2,770
0.6
0.2
0.003
0.03
1,640
11,000
2
4
0.003
0.2
TOTAL SOMATIC EFFECTS:
14,700
2,790
12,600
172
-------
10
10 H -
S_
-------
10s
Figure 7-11:
Expected Health Effects
Over 10,000 Years
vs. Different Canister Lifetimes
10
4 .
10
to
o
o
o
s-
O)
o
£ 10
o
-------
7.5.3 Different Retardation Factors
We evaluated the effects of different retardation factors by
performing two additional analyses. In one case, we replaced our
reference case retardation factors with retardation factors reported by
Denham, et al. (DE 73), which generally assume a greater level of
geochemical interaction with the surrounding rock formations (Table 4-1
lists both sets of factors). In the other case, we assumed that no
retardation took place and that all radionuclides moved with the same
velocity as the groundwater (although dissolution in the groundwater was
still subject to our solubility limits). Tables 7-7 and 7-8 display the
results of these two analyses.
The changes in retardation factors affect only those events which
involve significant groundwater flow pathways, such as faulting, breccia
pipe formation, and, of course, the normal groundwater flow expected in
the hardrock repositories. Use of the Denham factors generally reduces
these risks by only a little more than an order of magnitude, even though
many of the Denham factors assume up to a hundred times greater
retardation. This reduction in risk is relatively small because, for our
reference geologic settings, a retardation factor of about 15 is
sufficient to prevent a radionuclide from ever reaching the accessible
environment through groundwater flow in less than 10,000 years.
Increasing a retardation factor from 100 to 10,000 has no effect on our
analysis.
175
-------
Table 7-7
Event
Normal Ground Water Flow
Drilling (misses canister)
Drilling (hits canister)
Faulting
Breccia Pipe
Meteorite
Volcano
TOTAL SOMATIC EFFECTS:
Expected Health Effects over
Event
Normal Ground Water Flow
Drilling (misses canister)
Drilling (hits canister)
Faulting
Breccia Pipe
Meteorite
Volcano
Bedded
Salt
0
181
5
27
4
0.003
0.03
217
Table 7-8
Granite
36,800
747
0.6
458
-
0.003
0.03
38,000
Basalt
5,200,000
2,960
2
11,400
-
0.003
0.2
5,210,000
10,000 Years: Denham Retardation Factors
Bedded
Salt
0
181
5
0.006
0.0002
0.003
0.03
Granite
0.7
747
0.6
0.008
—
0.003
0.03
Basalt
87
2,960
2
0.2
_
0.003
0.2
TOTAL SOMATIC EFFECTS:
186
749
3,050
176
-------
On the other hand, assuming no retardation dramatically increases
tne risks for events involving groundwater flow. As shown by Table 7-7
and Figure 7-12, these increases change the relative importance of
different events in the overall risks. For the hard rock repositories,
normal groundwater flow becomes by far the most important source of
releases. For the basalt repository, even faulting becomes considerably
more important than human intrusion. Thus, it can be concluded that human
intrusion dominates the overall risks only for cases where the site
geochemistry and the chemical composition of the waste form insure
substantial protection by the geologic formations surrounding a repository.
We also looked at the importance of waste form release rate and
canister lifetime on a granite repository with no retardation. These
\
results are displayed in Figures 7-13 and 7-14. The shape of the curve
for different release rates is similar to previous curves, but
substantially higher at all release rates due to the lack of geochemical
retardation. The curve for different canister lifetimes (Figure 7-14)
leads to a new conclusion, however. Improving the canister lifetime is
considerably more effective in reducing risks for this case than for
others. In effect, the delay in releases through groundwater caused by a
longer-lived canister can substitute for the delay that would otherwise be
provided by geochemical retardation. In fact, for the granite repository,
where groundwater travel times increase significantly as the waste cools
down, canister lifetimes greater than 5,000 years can completely
compensate for a lack of geochemical retardation.
177
-------
Figure 7-12: Consequences and Risks for Different Events
(EFFECTS OF RETARDATION FACTORS)
10 6 -
10 5 -
10 4-
10 3-
2
10 !-
10 ° -
lo-1-
io-2-
io-3-
10 5-
10 4 -
10 3-
10 2-
10 1-
10°-
io-2-
io-3-
G
RANITE
\
REP(
}SIT
mmmm
Normal
Water Dril
Flow
GRANITE
REFERENCE C
^•^H
DRY
1
r/
W
%
%
v/
w
line
REPC
ASE
I
I
SIT
RET
Faul
DRY
ARD/i
m^^m
N
I
tin
TIO
I
0 RETARDATION
9 ''Pipe3
N FACTORS
/olc
^^H
1
ano
I
Normal Brprria
Water Drilling Faulting n
-------
to
s_
(O
O)
O
O
O
10
6 _
10
5J
Figure 7-13:
Expected Health Effects
Over 10,000 Years
vs. Different
Waste Form Leach Rates
(MOTE: vertical scale
different than
previous graphs)
NO RETARDATION
GRANITE REPOSITORY
EFFECTS OF RETARDATION FACTORS
O
a;
(O
O
a.
X
10
4J
10
3J
REFERENCE CASE
RETARDATION FACTORS
10
-6
10"D 10"* 10"°
waste form leach rate (parts per year)
10
-2
179
-------
10
5 _
S-
ro
OJ
•
O
O
O
s_
o>
O
I/)
•»->
(J
q-
i*-
-------
7.5.4 Summary of the Effects of Geochemical Factors
Taole 7-9 summarizes the overall risks from our examination of the
importance of solubility limits and retardation factors. Solubility
limits are more important for our reference salt repositories, where
little groundwater should enter the system and where releases caused by
human intrusion dominate the risks. Retardation factors are more
important for the hard rock repositories, where releases through
groundwater flow pathways are much more significant.
We also include in Table 7-9 the results if neither solubility limits
or retardation factors are considered. These analyses indicate that, even
without any protection from site geochemistry, there is a substantial
difference in overall risks between the basalt case and the salt and
granite cases. The additional protection provided by the reference salt
repository occurs (1) because there is no "normal" groundwater flow
through the salt itself and (2) because salt creep will tend to compress
the repository backfill and isolate the waste canisters from each other,
thus reducing the source term available for localized disruptive events.
The additional protection provided by the reference granite repository
occurs because tnere is no underlying aquifer to maintain an upward
hydraulic gradient as the wastes cool; thus, the driving force to remove
dissolved wastes from the repository is much reduced after about
1000 years. The basalt reference case has neither of these advantages.
181
-------
Table 7-9
Expected Health Effects over 10,000 Years:
Effects of Different Geochemical Factors
Event
Bedded
Salt
Granite
Basalt
Reference Case
Denham Retardation Factors
No Retardation
No Solubility Limits
No Solubility Limits
AND No Retardation
186
186
217
14,700
14,800
760 4,390
749 3,050
38,000 5,210,000
2,790 12,600
68,500 7,570,000
182
-------
7.5.5 Different Integration Periods
We also performed a number of analyses considering integration
periods other than 10,000 years. We wanted to know if stopping our
analysis at 10,000 years could substantially misrepresent the risks from
our reference repositories. To do this, we considered the average risk
per year for several integration periods. Figure 7-15 presents these
results, normalized to the average risk per year over 10,000 years, for
eacn of the three geologic media. Although 10,000 years does not
correspond to the largest average risk for any of the media, the average
risks for the other periods we studied were never more than 30 percent
higher than those at 10,000 years. Our results for the longer integration
times, those approaching 100,000 years, may be somewhat underestimated
because our models do not consider in-growth of Ra-226 and other
radionuclides in the long-lived decay chains stemming from the uranium and
plutonium in the wastes. However, we believe that the underestimates
would be quite small for our reference repositories. Figure 7-15 also
shows that cutting off the analyses at 1000 years would result in
substantial underestimates of the average risks, particularly for the hard
rock repositories.
183
-------
(O
O
o
O
O)
>
o
d)
CD
(O
i.
0)
fO
(O
OJ
O)
o
o
O)
O)
-------
7.5.6 Higner ProoaDlTitles
We considered uncertainties in the probabilities of releases by
repeating our analyses with a set of higher event probabilities that was
developed Dy Arthur D. Little, Inc. (ADL 79d). These higher probabilities
are discussed in Appendix D. As shown in Table 7-10, the expected health
effects are higher, particularly for human intrusion by drilling.
However, they are not dramatically higher. The increases in risks from
making much more conservative assumptions about event probabilities are
much smaller than the increases caused by making more conservative
assumptions about other aspects of our analyses.
185
-------
Table 7-10
Expected Health Effects over 10,000 Years:
Higher Event Probabilities
Bedded Domed
Event Salt Salt Granite Basalt Shale
SOMATIC EFFECTS BY EVENT:
Normal Ground Water Flow 0 0 11 1,420 1,420
Drilling (misses canister) 453 310 5980 14,800 14,800
Drilling (hits canister) 12 12 5 12 12
Faulting 0.07 17 50 60 1
Breccia Pipe 0.1 - -
Meteorite 0.003 0.003 0.003 0.003 0.003
Volcano 3 0.03 3 3*3
TOTAL SOMATIC EFFECTS: 468 339 6050 16,300 16,200
186
-------
Appendix A
REPOSITORY RADIONUCLIDE INVENTORY
187
-------
For our analysis of reference waste repositories, we have developed a
reference radionuclide inventory that is representative of the contents of
commercial radioactive waste that will be disposed in high-level waste
repositories. Projections of non-commercial waste comprise only a small
fraction of the total. The waste will either be in the form of
unreprocessed spent fuel from commercial reactors, or waste left from
reprocessing spent fuel to recover uranium and/or plutonium. Our
reference waste only includes spent fuel, which contains more isotopes
(per metric ton of heavy metal charged to the reactor) that are
important—because of their long half-lives, ease of environmental
transport, or biological significance—than does the waste from
reprocessing spent fuel.
Arthur D. Little, Inc. (ADL) has provided us with a detailed analysis
of the characteristics of high-level wastes (ADL 79a). ADL used the
ORIGEN computer program (BE 73) with an updated set of actinide data to
generate radioisotopic inventories for pressurized water reactor fuel with
a discharge exposure of 33,000 MWd/MTHM. Three alternative light water
reactor (LWR) fuel cycles were considered:
1. "throwaway" fuel cycle—spent fuel, no reprocessing
2. urainum only recycle
3. uranium and plutionium recycle
Figures A-l and A-2 compare the quantity of radioactivity (curies) of
the three fuel cycles and their decay heat generation by graphically
depicting the ORIGEN results. In terms of quantity of radioactivity,
189
-------
Figure A-l:
RADIOACTIVITY IN HIGH-LEVEL WASTE FROM
DIFFERENT LWR FUEL CYCLE OPTIONS
(from 100,000 MTHM)
10
10
— Spent Fuel (Throwaway Fuel Cycle)
"H •-. Uranium Recycle
Uranium and Plutonium Recycle
yl '•; i \--\-"
4u4O~
iiiiL
=4111
"i. MTj-l-nv-L- -'T"P"i-i iritii
4 +: l-'T^^p'rv-'firL'TnlTriJ!
i
'^tp
tuTUDfe
m
"3
10
10J
10"
DECAY TIME FROM DISCHARGE (YR)
190
-------
TTrrl \~-\-\ !
Figure A-2:
DECAY HEAT FROM HIGH-LEVEL WASTE FROM
DIFFERENT LWR FUEL CYCLE OPTIONS
(from 100,000 MTHM) I
rrTTTiT
— — — Spent Fuel (Throwaway Fuel Cycle)
Uranium Recycle
Uranium and Plutonium Recycle
-N4M—!-
I ; ',;••'
10
DECAY TIME FROM DISCHARGE (YR)
191
-------
all three options are comparable for about the first thousand years.
After a thousand years, the high-level waste activity from the
uranium-only recycle waste is generaly much lower. As indicated in
Figure A-2, the decay heat from the uranium-only recycle is also much
lower than either the "throwaway" fuel cycle or the uranium and plutonium
recycle wastes. Wastes from these latter two fuel cycles generate a
comparable amount of decay heat for about the first 10,000 years. Beyond
10,000 years, the heat of the "throwaway" fuel is much higher than that of
the uranium and plutonium recycle waste, because of the higher content of
Pu-239 and Pu-240 in the "throwaway" fuel cycle wastes. Therefore, we
have chosen the "throwaway" fuel cycle to characterize the reference
inventory of high-level radioactive wastes.
An overall picture of the "throwaway" fuel cycle inventory is shown
in Figure A-3 for a fuel charge of 100,000 MTHM, which is the quantity of
waste we chose for our reference geologic repository. The two major types
of radioactivity in spent fuel are the fission products, which dominate
for about the first one hundred years, and the actinides, including their
daughter radionuclides. A third, less significant, category of
radioactivity is the fuel assembly structural components, which comprise
only 0.1 to 1.0 percent of the total radioactivity in the repository at
any given time.
192
-------
Figure A-3:
TOTAL RADIOACTIVITY IN REFERENCE
REPOSITORY (from 100,000 MTHM)
Iplih, Fission Products
10
ION
DECAY TIME FROM DISCHARGE (YR)
193
-------
In order to make the analysis of the disposal of high-level and long
lived radioactive wastes easier, we developed a modified inventory based
on the ORIGEN output. The ORIGEN output provides a listing of the
radionuclides for various times after fuel discharge, and it categorizes
the inventory by type of activity (i.e., fission products, actinides and
daughters, and fuel assembly structural components). In order to ensure
that all radionuclides that significantly contribute to total
radioactivity are considered, we made a list of the five to ten most
abundant radionuclides for various times after reactor discharge for each
of the major categories of activity. Additional radionuclides are
included on the basis of long half-life, small geological retardation
factor, and large biological significance. Table 2-1 lists the resulting
principal isotopes extracted from the ORIGEN program output.
Since the activity associated with the fuel assembly structural
components comprises only a small fraction of the total radioactivity in
the repository at any given time, this category was not included in our
reference inventory; therefore it is excluded from Table 2-1. We should
also note that the estimate of the C-14 production as an activation
product in the fuel has been calculated separately, using the value of
0.561 Ci/MTU (DA 77). For our reference repository, this amounts to
56,100 Ci of C-14.
194
-------
Comparing our reference inventory with the ORI6EN output, our list
comprises 95 to 99 percent of the total curies of all the radionuclides
for almost all periods of interest. Figure A-4 depicts the radionuclide
inventory in a reference repository. For the first hundred years or so,
the fission product inventory is dominated by the Sr-90/Y-90 and the
Cs-137/Ba-137m decay chains. Beyond 600 years, Tc-99 dominates until
almost a million years. For the puposes of the analytical model used in
this report, the fission product inventories listed in Table 2-1 for ten
years after fuel discharge are used as the starting point; these
radionuclides inventories are taken directly from the ORIGEN program
output. For most fission product radionuclides, the inventory at any
subsequent time may be calculated by applying the appropriate radiological
half-life. However, for those radionuclides listed in Table 2-1 involved
in fission product decay chains—the Cs-137/Ba-137m chain, the
Zr-93/Nb-93m chain, and the Sn-126/Sb-126m/Sb-126 chain—we assume that
the activity of the daughters and parents are equal. Our assumption is
slightly conservative, as may be seen by examining the activities of the
decay chains in Table 2-1.
Because of long decay chains containing many radionuclides with
relatively long half-lives, the long-term behavior of individual actinide
and daughter isotopes is much more complicated. The ORIGEN program uses
Bateman equations to describe the ingrowth and decay of these isotopes.
We simplified the model for the actinide and daughter radionuclide source
195
-------
Figure A-4:
SIGNIFICANT FISSION PRODUCTS IN
REFERENCE REPOSITORY
(100,000 MTHM, throwaway fuel cycle)
NOTE: Not shown is 1-129, of which
about 1,900 curies are present
throughout this time period.
Sn-126,Sb-126m.Sb-126
10 -
DECAY TIME FROM DISCHARGE (YR)
196
-------
term in order to provide a more manageable model. First, the principal
actinide and daugnter radionuclides listed in Table 2-1 have been broken
down into respective decay chains.
1. Am-243—> Np-239—> Pu-239—> U-235
2. Pu-241—> Am-241—> Np-237—> Pa-233
3. Pu-238— > U-234 > Th-230—> Ra-226
4. Cm-244—> Pu-240
Of the four major decay chains, only the Pu-241 chain has a parent isotope
(Cm-245) that significantly contributes to the activity of the first
member of the chain. Based on the ORIGEN output, the parent isotopes of
Am-243, Pu-238, and Cm-244 all have lower activity levels compared to
their respective daughters.
These four decay chains account for all of the principal isotopes in
Table 2-1 except Pu-242. This isotope is formed by the decay of both
Am-242 and Cm-246. The ORIGEN output shows that, upon discharge of the
fuel from reactors, only very small quantities of Am-242 and Cm-246 are
present relative to Pu-242. Therefore, Pu-242 is treated as decaying to
U-238, ignoring any contribution from Am-242 and Cm-246.
In our simplified model for actinides and daughters, the
radionuclides are treated in pairs. We assume radionuclide A, with an
initial inventory A , decays into radionuclide B, which has an initial
197
-------
Inventory B , and which concurrently decays according to its half-life.
Tnerefore, the rate of change of the number of B atoms may be expressed
as:
^r= Axx - Bx2 (A-l)
where A and B are the number of atoms of A and B, respectively, at any
time t, and x, and x~ are the respective decay constants for A and B.
Since: A = A0e~Xlt (A-2)
equation A-l may be rewritten as
- X2B (A-3)
The solution to this linear differential equation for B as a function of
time, considering initial amounts of A and B (A and B respectively), is:
B = ApXile - e )/(x2 _ H) + 2 (A_4)
This equation describes the number of atoms of B at any time. A more
convenient form expressed in terms of radioactivity may be achieved by
multiplying both sides of equation A-4 by x:
°Bf = x2 B = L x^e- - e ^r (A_5)
198
-------
Equation A-5 describes the activity of radionuclide B at any time,
given initial activities of A and B. We used this equation to estimate
the ingrowth and decay among the actinides and daughters in the four major
decay chains listed above.
Figure A-5 illustrates the results of applying Equation A-5 to the
decay chains for the principal actinides as compared to the ORIGEN
output. Agreement for the principal radionuclides is such that
differences between the two models is 10 percent or less; most results
agree so well that it is impossible to detect the difference.
Presently, the decay chains leading to the buildup of Ra-226 have not
been modeled or included in the results of this paper. These decay chains
are very difficult to model for releases to an aquifer. Fortunately for
the event times during a 10,000 year period, the buildup of Ra-226 does
not seem to be very important. Generally two types of releases are
analyzed in this report—direct releases to the air or land surface and
long term releases through the aquifer pathway. All the direct releases
occur during the 10,000 year time period. Thus, very little Ra-226 is
released directly. The parent radionuclides of Ra-226 that are released
directly are effectively removed from the accessible environment within a
few hundred years after the release. The environmental "sinks" for these
radionuclides are either the lower soil layers or the ocean sediments.
These parent radionuclides are thus effectively removed from the
environment prior to any signficant growth of Ra-226.
199
-------
Xs-
10
SIGNIFICANT ACTINIDES AND DAUGHTERS IN
REFERENCE REPOSITORY
(100,000 MTHM, throwaway fuel cycle)
NOTE: ORIGEN data shown by solid
lines.- EPA model projections by
dashed lines where they are more
than 10% different than ORIGEN.
—-"--rv* , -
pu-240 IV i :
11ii i iiijin iimi i^iiiji in
Am-243 & Np-239
DECAY TIME FROM DISCHARGE (YR)
200
-------
The transport of radionuclides through the aquifer to the environment
is another matter. Releases through this pathway can occur over very long
time periods. The buildup of Ra-226 in our reference aquifer can become
significant. If the releases are integrated only through a 10,000 year
time period, the transit time of Ra-226 in our reference aquifer is too
long for it to be released in significant amounts to the environment.
However, if the integration of releases is extended to hundreds of
thousands of years, it would be prudent to specifically analyze the
potential releases of Ra-226 via the aquifer pathway.
201
-------
Appendix B
RADJONUCLIDE TRANSPORT IN GROUNDWATER
203
-------
The analytical solution of a radionuclide transport equation in a
groundwater stream can be greatly simplified if the diffusion effect is
neglected (BH 80); however, this may introduce some modeling error. This
Appendix evaluates the modeling error introduced by this simplification.
For the purpose of this discussion, we assume the effect of
radionuclide retardation in the host formation is negligible. Therefore,
the basic equations may be written as
(B-l)
at Rd aX RdaX
The boundary condition with a source term representing a drilling
event which hits a canister may be written by assuming that the contents
of the canister are released directly into the aquifer with little or no
resistance from the host rock or drilling borehole. That is:
Q = fLQ0e-e e--eu(t _ te) (B_2)
In these equations:
•
Q = the rate of radionuclide passing through a section.
D = the coefficient of hydrodynamic dispersion
Rd = tne retardation factor of the overlying aquifer
v = the groundwater velocity
A = the decay constant
L = the release rate constant
Q = the initial inventory of radionuclide
205
-------
X = the space coordinate
t = the time of interest
t = the event time.
f = the fraction of repository affected
The analytical solution for equation B-l — neglecting the dispersion
term and using equation B-2 as the boundary condition — is:
Q = fLQ0e-xte e-L(t-te-RdX/v) u(t_te_Rdx/v) (B-3)
The analytical solution without neglecting the dispersion term, on the
other hand, is (ADL 79d):
-L(t - te) (vX/2D-xt-GX) . _ _ x _ _
Q = 1LV e e erfcLX/2 Rd7DTt-te) -^T[t-te)/Rd]
2 (IM)
where 6 is:
G = v_2 RdL (B-5)
4D D
We have calculated health effects using the environmental dose
commitment of the total quantity of radionuclides released to the
biosphere over a specified time period. Although integration of
equation B-4 with respect to time cannot be obtained analytically, we can
integrate equation B-3. Therefore, the modeling process can be simplified
by neglecting the dispersion term. In order to evaluate the error
introduced by omitting tne dispersion effect, we investigated four
radionuclides that are expected to contribute the major portion of health
effects from groundwater transport pathways. They are technetium-99,
206
-------
neptunium-237, strontium-90 and plutonium-239. We analyzed the
relative error of neglecting the dispersion effect for the postulated
hydrogeological conditions employed in this analysis. The results
presented in Table B-l indicate the relative errors are generally low for
all radionuclides except plutonium-239. Although there is a significant
difference in the case of plutonium-239, the net release of radioactivity
is expected to be small enough to be negligible.
We therefore conclude that we can neglect the dispersion effect under
the assumed hydrogeological conditions without introducng significant
error in our assessments of health effects.
207
-------
Table B-l
Relative Error Due to Omission of Diffusion Effect
Radio-
nuclide
Tc-99
Np-237
Sr-90
Pu-239
Retarda-
tion
Factor
1.0
100
1UO
10000
Decay
Number
0.00176
0.00017
12.2
0.0151
Total
Released
With
Diffusion
9. 982 9x1 O"1
Q.SSlSxlO'1
0.0000
1.5 506x1 0~64
Activity
Downstream (Ci/Ci)1
Without
Diffusion
9.9824xlO~1
9.8314X10"1
0.0000
2.6396xlO~66
Error
(percent)
0.005
0.0013
0.0000
•••Note: Total activity in curies released at downstream end due
to impulse release of activity at upstream end.
208
-------
Appendix C
DERIVATIONS OF EQUATIONS
209
-------
C.I Solution to Equation 5-3a
= c _ xvc(t) (5_3a)
-xt -L(t - t )
where: Qc(t) = QQe e u (5-3b)
Equation 5-3a is a differential equation of the form:
P(s)y + y' = q(s)
that can be rewritten as:
xC(t) + dC(t)/dt = ^QCU)
with: p(t) = x
q(t) = f Qc(t) = Lf [Qoe-^e-L(t - V]
An integrating factor, y(t), is:
ft ft
J p(s)ds J xds xt
e = e = e
Multiplying equation 5-3a by the integrating factor:
xt lf -xt -L(t-t ) xt
e [xC(t) + dC(t)/dtJ = [iL QQe e ] e
and integrating yields:
f
tJ
. _ Lf r 0 e-L(t-t )
dt - ue c
d(t) - v ; o
211
-------
Evaluating this equation gives:
At, xt f 1 -L(t-t ) -L(0)
C(t.)e ' - C(tc)e c = ^ F£) QQ [e - e
But tne concentration at tne time of canister failure, C(t ), is zero,
L»
therefore:
At fQ -L(t - t ) fQ
C(t.) e 1 = --^e 1 C ^
which simplifies to:
fQn -At. -L(t - t )
C(t.) » -^e 1 [1 - e n C ] (5-4)
giving the concentration at any time, t-j.
C.2 Solution to Equation 5-5:
VdC(t)/dt = LfQc(t) - AVC(t) - V(t)*C(t) (5-5)
where: Qc(t) = Q0e-xt e-L(t-tc) (5-3b)
Equation 5-5 is a differential equation of the form:
P(s)y + y' = q(s)
which can be seen by rewriting equation 5-5 in the form:
LA + (V*(t)/V)] C(t) + dC(t)/dt = ^ Qc(t)
and setting: p(t) = A + V*(t) / V
q(t) = Lf Qc(t) = Lf ^-At e-L(t - tc)]
212
-------
An integrating factor, p(t), is given by:
/ p(s)ds / [x + V*(s)/V] ds
w(t) =
the solution is of the form:
where: t = time release was initiated (the event time)
C(t ) = the concentration of the radionuclide immediately
before the event time (equation 5-4).
C.3 Solution to Equation 5-7
Equation 5-7 is a differential equation of the form:
P(s)y + y' = q(s)
which can be seen by rewriting equation 5-7 in the form:
(5_7)
and setting p(t) = x + Vaq/V
if Lf -xt
q(t) = f Qc(t) = f QQe e
An integrating factor is given by:
rt ft
I p(s) ds / [x + V /V] ds xt tV /V
(t) = e = e H = e e H
213
-------
The solution is of the form:
C(t.) =
y(s)q(s)ds
C(tjp(ta )
,
Lt
C(t)u(t)
ee
where:
t. = the time of interest
t = time of event (assuming t. _> t _> t )
fQ0 ~^e - L( t - t )
C(te) = ^ e e [1 - e J (from Equation 5-4)
214
-------
C.4 Solution to Equation 5-18
= LQc(t)/V(t) - xC(t)
can be written in the form:
P(s)y + y' = q(s)
dC(t) LQft)
as: xC(t) + = —
dt V(t)
with: p(s) = x
q(t) = L Qc(t) / V(t)
rt
J p(s)ds xt
u(t) = e = e
The solution is of the form:
t
1 (
-TFT /
u(tj TJ
u(s)q(s)ds
rch
where: Trcn = saturation time
xt ft xs C(Trch)eXTrch
C(t) = e~xt / [eXSLQJs)/V(s)Jds + r-^—.F
Trch
This equation must be solved numerically.
215
-------
C.5 Solution to Equation 5-5 witn V*(t) from equation 5-20
,*>
VdC(t)/dt = LfQc(t) - xVC(t) - V (t)C(t) (5-5)
V*(t)= KAi(t)c(y)= K A (ae-at + be-** + iace-irt + ia) (5-20)
From Section C.2, equation 5.5 is of the form:
P(s)y + y' = q(s)
_xt _L(t - t )
witn: q(t) = f- [QQ e e J
p(t) = x + Vx(tj/V = x + K A i(t) c(y) / V
= x + K A (ae~at + be-^t + iace-Yt + ia) / v
ft
I P(s)ds
w(t) = e
Tne solution is of tne form:
i r*1
c(ti)= Trr "(
p(t }
and, in this case, C(t ) = 0, so the last term vanishes.
\*
216
-------
C.6 Solution to Equation 5-28
= LfQ e e - xVC(t) - Ki (t)c(y)AC(t) (5-28)
is of the form:
P(s)y + y' = q(s)
with: p(t) = x + V*(t) / V = x + K i(t) c(y) A / V
q(t) = LfQ0 e-xt e -L(t-tc)
ft ft *
/ p(s)ds xt / V (s)/V ds
J j
= e e
r*
xt J [Ki(s)c(u)A/V] ds
^ e e
and: i(t)c(u) = ae-at + be~^ + ^ce-^ + ia
be~es+ i ce~YS+ i )A/Vj ds
so: y(t) = eAU e" a a
The solution is of the form:
i f* cty^p)
C(t) =—rn- / u(s)q(s)ds + —
e
and, since the brine pocket is empty initially:
C(te) = 0
217
-------
Tne total quantity of radionuclide released is
t
Q = f C(s)V*(s) ds
wnere C(t) is either the solution to Equation 5-28 or, for a solubility
limited radionuclide, C , the solubility limit. The volumetric flow,
*
V (tj, is eitner:
V*(t) = K(t)i(t)c(y)A
or, for a volumetric flow limited by the aquifer:
V=^ = tne flow limit of the aquifer.
aq
218
-------
Appendix D
MORE CONSERVATIVE PROBABILITY ESTIMATES
219
-------
In their report Arthur D. Little, Inc. (ADL) provides more
conservative assumptions concerning various events affecting a repository,
which they have labeled "second" estimates (ADL 79d). We have not
utilized all of their second estimates, but we have examined the effects
of the higher probabilities of various events. The bases for these second
estimates are discussed below. The calculated values of the second
estimate probabilities are presented in Table D-l, where they are compared
with ADL's "first" estimates.
D.I Human Intrusion, Drilling
The second estimate probabilities of drilling into a bedded salt,
domed salt, shale or basalt repository are based on the reference
probability of drilling into a bedded salt repository. ADL's first
estimate for a bedded salt repository is based on exploratory drilling for
oil and minerals. The more conservative values also include occasional
drilling for water. ADL's second estimate for granite is based on
drilling for water, geothermal, and mineral exploration and possible
development of geothermal wells.
D.2 Faulting
The second estimate faulting probabilities are based on different
geologic eras in selected locations. The technique for calculating the
probabilities is presented in Chapter 5. Calculations differ for each
repository, thus they will be discussed briefly according to repository
type. ADL chose f equal to 5 as the number of faults expected per
repository.
221
-------
(X)
rv>
Table D-l
More Conservative ("Second Estimate") Frequencies of Occurrence for Various Events
Event
Drilling * 2nd estimate
1st estimate
Faulting 2nd estimate
1st estimate
Breccia 2nd estimate
Pipe + 1st estimate
Volcano 2nd estimate
1st estimate
Meteorite
(Events
Bedded
Salt
5xlO~2
2xlO~2
4xlO~7
2xlCT8
IxlCT6
1x1 CT8
1x1 0~8
IxlO-10
For all
per year) (ADL
Domed
Salt
5xlO~2
2xlO~3
1x1 0~5
3xlO~7
—
IxlO-10
IxlO-10
79d)
Granite
2xlO~2
IxlO'2
IxlO"5
2xlO"8
—
IxlO"8
MO'10
media, both 1st and 2nd
Basalt
5xlO~2
lxlO~2
lxlO~5
5xlO~7
—
1x1 0~8
6xlO-10
estimates are:
Shale
5xlO~2
2xlO~2
4xlO~7
2xlO~8
—
lxlO~8
IxlO-10
4xlO~U
* Occurrence rate is assumed to be zero during the first 100 years after disposal, and
somewhat higher than the rates shown during the second 100 years after disposal.
+ Occurrence rate is assumed to be zero during first 500 years after disposal.
-------
D.2.1 Bedded Salt
The second estimate for faulting in bedded salt is based on
mid-Tertiary faulting in the Paradox Basin with N = 25 million years.
D.2.2 Domed Salt
The second estimate for faulting in domed salt is based on Gulf Coast
faulting, with the latest faulting occurring during the Quaternary period
and a minimum age of one million years.
D.2.3 Shale
The second estimate for faulting in shale is based on the same
assumptions as for bedded salt.
D.2.4 Granite
The second estimate for faulting in granite is based on an active
site in the basin and range province in the Southwestern United States.
The age would be at least one million years.
D.2.5 Basalt
The second estimate for basalt is based on a site where the most
recent faulting is more recent than the Quaternary age of one million
years.
D.3 Breccia Pipe
The ADL second estimate for oreccia pipes is discussed in
Section 5.2.4 of Chapter 5—a value of 1 x 10" events per year.
223
-------
D.4 Volcanoes
For the second estimates, ADL assumed that repository sites are
located near areas that have experienced volcanic activity over the past
ten million years. A number of volcanic fields were considered, such as
the Flagstaff, Arizona, area where 85 vents are estimated to exist in an
2
area 6400 km (ADL 79d). The time over which these developed is thought
to be at least 10 years. It is important to note the value calculated
for the second estimate should not be applied to the specific volcano
fields from whose parameters they have been calculated. They represent
only averages, and detailed site investigation could introduce other
factors that might significantly alter the estimate for an individual
site. Ue believe thay are reasonable for generic calculations.
Many other calculations yielded similar values, and so we selected a
—ft
frequency of 1 x 10 events per year for second estimates for all media
except salt domes. In the case of salt domes, the second estimate is the
same as the reference case estimate.
D.5 Meteorites
Since the calculated probability for meteorites is a statistically
derived estimate and independent of location, the second estimate has the
same value as the reference estimate.
224
-------
Appendix E
FORTRAN LISTING OF COMPUTER PROGRAM
(REPRISK)
225
-------
Q***** QQ. QQQ **********************************************************
C
C
C
C
C
C
C
C
C
Q*****
REPRISK
MARCH 13, 1981
— MODIFIED TO TREAT EERF ENVIRONMENTAL PATHWAY MODELS
(PATHWAY INPUT FILES OF FT03 AND 04 ARE LABELED)
— MODIFIED TO INCLUDE NEW A.D.LITTLE RELEASE MODELS
— MODIFIED TO TREAT MULTIPLE DRILLING EVENTS
FOR INPUT INSTRUCTIONS SEE REPRISK INPUT GUIDE DATED JAN 21, 1981
*
*
*
*
*
*
*
C-
C
: 000 **********************************************************
COMMON /BLOCK1/ E1,TAX,V,AREA(10),K1(10),RNLDX(20),NC,ND,Y1X,IEX
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
DIMENSION F(6),A(4),HELAB(6),RT(16),PROBT(8),CNT(8)
DIMENSION TITLE(120),DASH(33),FMTA(10),FMTB(11),FMTC(10),HFA(5),
1 HFB(8,5),HFC(5),STARS(29),EVENT(4),HFSTIT(19),HFGTIT(19),
2 SOMLAB(6),GENLAB(6),RROLAB(6),CURLAB(6)
DIMENSION AMEAN1(12,10)
DIMENSION TEDC (12), NOUT ( 7)
DIMENSIOf
1 EVNT <
2 NEVTT
3 FHIT
4 FTANK
5 VTANK
6 EDES
7 PORS (
8
9
A KPRIM
B
C NDCASE
D VDRILL
E
F
G
H
n
^
10),
;io),
10 ,
10),
10),
,10,4),
10),
,10),
[10),
[10),
j\j i ri
PROB (10,
CNS (10,
CNG 10,
CNR 10,
NRSMX 10,
NRGMX(10,
NRRMX(10,
x(io,
Y 10,
FRATE(10,
NDEVS(10,
RISKS(IO),
RISKG(IO),
RISKR(IO),
CNSR (10,
CNGR (10,
CNRR (10,
25),
25),
25 ,
25),
25),
25),
25),
25),
25),
25),
25),
TEVNT(25),
NENTT(25),
TOBND(25),
25,
25,
25,
RNID (20)
NRNTY(20)
RNLD 20)
RNQO (20)
RNDS (20)
RNDA (20)
RNDS1(20)
RNDS2(20)
LAMS (20)
RNLD1 (20),
RNQ01 (20),
RNKD (20),
RNSOL (20),
RNQOX (20),
LR (20),
RLMT(3,20),
RRISKS 20),
RRISKG(20),
RRISKR(20),
20)
20)
20)
C-
C
CSR(200,20),CGR(200,20),CRR(200,20)
NEVSM ** NEVSM ** — NEVTM ** NRNM ** NRNM **
227
-------
DIMENSION
1
2
3
4
5
HFS1 (20),
HFS2 (20),
HFS3 (20),
HFS4 (20),
HFS5 (20),
HFS6 (20),
NRNM **
HFS7 (20),
HFS8 (20),
HFS9 (20),
HFS10(20),
HFS11(20),
HFS12(20),
NRNM **
HFG1 (20),
HFG2 (20),
HFG3 (20),
HFG4 (20),
HFG5 (20),
HFG6 (20),
NRNM **
HFG7 (20),
HFG8 (20),
HFG9 (20),
HFG10(20),
HFG11(20),
HFG12(20)
NRNM **
c
REAL*8 DDASH/8H /
REAL*8 CNS,CNG,CNR,PROB,PROBT,CNT,X,Y,RISKS,RISKG,RISKR,TRISKS,
1 TRISKG.TRISKR
REAL*4 LAMS,LAMR,LAMG,LAMW,MESS1N,MESSA,MESS1A,MESSAA,LR,K1,KPRIM
C
DATA TITLE/120*4H /, DASH/33*4H /, STARS/29*4H****/,
1 BLANKS/4H /
DATA SOMLAB/4H SOM,4HATIC,4H HEA.4HLTH ,4HEFFE,4HCTS /
DATA GENLAB/4H GEN,4HETIC,4H HEA,4HLTH ,4HEFFE,4HCTS /
DATA RROLAB/4H ,4H REL,4HEASE,4H RAT,4HIOS ,4H /
DATA CURLAB/4H ,4H CUR.4HIES ,4HRELE,4HASED,4H /
DATA EVENT/4H ,4H EVE,4HNT ,4H /
DATA FMTA/4H( ,4H1H ,,4H17X,,4H8( 2,4HX, ,4H I6,,4H' YE,4HARS',
1 4H )/,4HlH )/
DATA FMTB/4H( ,4H1H ,,4H4A4,,4H'*',,4H7( 5,4HX,1P,4HE9.2,4H ),,
1 4H1( 5,4HX,A9,4H ))/
DATA FMTC/4H( ,4H1H .,4H 4X,,4HF5.1,4H,7X,,4H'*',,4H8( 6,4HX, ,
1 4H2A4 ,4H ))/
DATA HFA /4H4(16,4H5(11,4H6( 7,4H7( 4,4H8( 2/
DATA HFB /4H1(19,4H2(19,4H3(19,4H4(19,4*4H
1 4H1(14,4H2(14,4H3(14,4H4(14,4H5(14,3*4H
2 4H1(10,4H2(10,4H3(10,4H4(10,4H5(10,4H6(10,2*4H
3 4H1( 7,4H2( 7,4H3( 7,4H4( 7,4H5( 7,4H6( 7,4H7( 7,4H
4 4H1( 5,4H2( 5,4H3( 5,4H4( 5,4H5( 5,4H6( 5,4H7( 5,4H8( 5/
DATA HFC /4H4(20,4H5(15,4H6(11,4H7( 8,4H8( 6/
DATA AFORMA,AFORM6/4H ),,4HX,A9/
C
DATA TEDC /12*0.0/
DATA EVNT /10*0.0/
DATA TEVNT /25*0.0/
DATA TOBND /25*0.0/
DATA RNID /20*0.0/
C
DO 1246 I = 1,10
CVA(I) = 0.
ALPH(I) = 1.
1246 CONTINUE
C
228
-------
CALL ERRSET(208,0,-1,1)
NDCTM = 12
NEVTM = 25
NOUT8 = (NEVTM/8) + 1
NEVSM = 10
NRNM = 20
C
NDCT = 0
NEVT = 0
NEVS = 0
NRN = 0
C
IX =0
IPATH = 0
IRLMT = 1
NINT = 0
C
TDINT = 0.0
CVC = 0.0
NCOF = 10
C
C
DO 1234 1=1,NEVTM
DO 1234 J=l,NEVSM
FRATE(J.I) = 0.0
1234 PROB(J,I) = 0.0
C
DO 1244 1=1,NRNM
RNLDl(I) =0.0
RNQOl(I) = 0.0
RNLDX(I) = 0.0
1244 RNQOX(I) =0.0
C
555 NDOT = 0
C
READ (5,13,ERR=999) NLINE,IREP,NSG,NINT,NMAT,NPCA,NPCP,NDOO,NN,NT,
1 IDRILL
WRITE (6,72)
IF (NINT .LE. 1)
1 WRITE (6,16) NLINE,IREP,NSG,NINT,NMAT,NPCA,NPCP,NDOO,NN,NT,IDRILL
16 FORMAT (1H ,10X,16I5)
13 FORMAT (1615)
IF (NSG .EQ. 0) NSG = 3
IF (NINT .EQ. 0) NINT = 2
IF (NMAT .EQ. 0) NMAT = 2
IF (NPCA .EQ. 0) NPCA = 2
IF (NPCP .EQ. 0) NPCP = 1
IF (NDOO .EQ. 0) NDOO = 3
IF (IDRILL .EQ. 0) IDRILL = 1
229
-------
251
GO TO (251,252,253,254,255,256,257), NSG
IMP A
NPB
NPC
NTS
NTS
NTR
GO TO 258
252
NPA
NPB
NPC
NTS
NTG
NTR
2
2
1
0
1
0
GO TO 258
253
NPA
NPB
NPC
NTS
NTG
NTR
3
3
I
0
0
1
254
GO TO 258
NPA
NPB
NPC
NTS
NTG
NTR
1
2
1
1
1
0
GO TO 258
255 NPA
NPB
NPC
NTS
NTG
NTR
1
3
2
1
0
1
GO TO 258
256 NPA
NPB
NPC
NTS
NTG
NTR =
2
3
1
0
1
1
257
GO TO 258
NPA
NPB
NPC
NTS
NTG
NTR
1
3
1
1
1
1
258 IF (NDOO .EQ. 2) NDOT = 1
230
-------
N2 = NLINE + 1
GO TO (100,102,103,104,105,106,107), N2
CALL ERROR (1,N1,N2,F,A,IX)
102 READ (5,11) (TITLE(I),I=1,20)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,20)
11 FORMAT (20A4)
12 FORMAT (18X,20A4)
GO TO 108
103 READ (5,11) (TITLE(I),I=1,40)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,40)
GO TO 108
104 READ (5,11) (TITLE(I),I=1,60)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,60)
GO TO 108
105 READ (5,11) (TITLE(I),1=1,80)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,80)
GO TO 108
106 READ (5,11) (TITLE(I),I=1,100)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,100)
GO TO 108
107 READ (5,11) (TITLE(I),I=1,120)
IF (NINT .LE. 1) WRITE (6,12) (TITLE(I),1=1,120)
108 CONTINUE
C
Q***** Q£- QQQ **************************************************
C ' *
C REPRISK INPUT *
C *
C REFER TO INPUT GUIDE FOR ASSISTANCE *
C *
c***** ££. ooo *********************************************************
100 READ (5,10,ERR=999,END=190) N1,N2,(F(I),I=1,6),(A(I),I=1,4)
IF (NINT .LE. 1) WRITE (6,25) Nl,N2,(F(I),1=1,6),(A(I),1=1,4)
25 FORMAT(1H ,10X,I2,2X,I2,6(2X,1PE10.2),2X,4A4)
10 FORMAT (2I2,6E10.4,4A4)
C
Q***** ££. 000 *******************************************************
C
C***** TYPE 10 CARD ENTERS DOSE INTEGRATION TIME *
C *
C ** IF SET EQUAL TO ZERO, DOSE INTEGRATION IS TAKEN TO BE THE *
C ** TIME PERIOD OVER WHICH EVENTS ARE CONSIDERED (THE DOSE *
C ** COMMITMENT TIME) *
C *
Q***** Q£; 000 *******************************************************
IF (Nl .NE. 10) GO TO 200
C
TDINT = F(l)
GO TO 100
231
-------
r***** rr- 000 *******************************************************
C ' *
c***** JYPE 11 CARDS ENTER DOSE COMMITMENT TIMES *
C
r***** CC' 000 *******************************************************
200 IF (Ml .NE. 11) GO TO 300
C
DO 1001 1=1,6
IF (F(I) .EQ. 0.0) 60 TO 1001
DO 1002 J=1,NDCTM
IF (TEDC(J) .NE. 0.0) GO TO 201
TEDC(J) = F(I)
NDCT = J
GO TO 1001
201 IF (F(I) .EQ. TEDC(J)) GO TO 1001
IF (F(I) .61. TEDC(J)) GO TO 1002
SAVEA = TEDC(J)
TEDC(J) = F(I)
JJ = J + 1
DO 1003 K=JJ,NDCTM
IF (TEDC(K) .NE. 0.0) GO TO 202
TEDC(K) = SAVEA
NDCT = K
GO TO 1001
202 SAVEB = TEDC(K)
TEDC(K) = SAVEA
1003 SAVEA = SAVEB
1002 CONTINUE
1001 CONTINUE
GO TO 100
Q***** Q£. 000 *******************************************************
C *
C***** TYPE 20 CARDS ENTER EVENT TIMES *
C *
Q***** QQ. 000 *******************************************************
300 IF (Ml .NE. 20) GO TO 400
C
DO 2001 1=1,6
IF (F(I) .EQ. 0.0) GO TO 2001
DO 2002 J=1,NEVTM
IF (TOBND(J) .NE. 0.0) GO TO 301
TOBND(J) = F(I)
NEVT = J
GO TO 2001
301 IF (F(I) .EQ. TOBND(J)) GO TO 2001
IF (F(I) .GT. TOBND(J)) GO TO 2002
SAVEA = TOBND(J)
TOBND(J) = F(I)
JJ = J + 1
232
-------
DO 2003 K=JJ,NEVTM
IF (TOBND(K) .NE. 0.0) GO TO 302
TOBND(K) = SAVEA
NEVT = K
GO TO 2001
302 SAVEB = TOBND(K)
TOBND(K) = SAVEA
2003 SAVEA = SAVEB
2002 CONTINUE
2001 CONTINUE
GO TO 100
C *
£***** QQ. QQQ *******************************************************
C *
c***** TYPE 22 CARD ENTERS ASSUMPTIONS ON DISTRIBUTION OF MATERIAL *
c***** RELEASED TO THE ATMOSPHERE *
C *
£***** QQ. QQQ *******************************************************
400 IF (Ml .NE. 22) GO TO 450
C
FAL = F(l)
FLL = F(2)
FAW = F(3)
GO TO 100
C
£***** QQ. QQQ *******************************************************
C ' *
C***** TYpE 23 AND 24 CARDS ENTER CHARACTERIZATIONS OF EVENT EFFECTS *
c***** ON THE REPOSITORY *
C *
Q***** QQ. QQQ *******************************************************
450 IF (Nl .NE. 23) GO TO 451
C
DO 3001 I=1,NEVSM
IF (EVNT(I) .EQ. 0.0) GO TO 402
IF (EVNT(I) .NE. F(l)) GO TO 3001
NEVTT(I) = N2
FHIT(I) = F(2]
FTANK(I) = F(3]
VTANK(I) = F(4)
VDRILL(I) = F(5)
DO 3002 J=l,4
3002 EDES(I.J) = A(J)
GO TO 100
3001 CONTINUE
233
-------
402 NEVS = NEVS + 1
EVNT(NEVS) = F(l)
NEVTT(NEVS) = N2
FHIT(NEVS) = F(2)
FTANK(NEVS) = F(3)
VTANK(NEVS) = F(4)
VDRILL(NEVS) = F(5)
DO 3003 0=1,4
3003 EDES(NEVS.O) = A(0)
GO TO 100
C
451
C
IF (Nl .NE.
DO 3101 1=1
IF (EVNT(I)
IF (EVNT(I)
KPRIM(I) =
PORS(I) =
24) GO TO
,NEVSM
.EQ. 0.0)
.NE. F(l))
F(2)
F(3)
F(4)
460
GO
GO
TO 999
TO 3101
AREA(I) = F(5)
GO TO 100
3101 CONTINUE
GO TO 999
C
Q***** QQ; QOO *******************************************************
C ' *
C***** TYPE 25 CARDS ENTER EVENT FAILURE RATE DATA *
C *
C ** THE AVERAGE FAILURE RATE OF EACH EVENT TYPE OCCURRING WITHIN *
C ** EACH EVENT TIME PERIOD MUST BE ENTERED ON TYPE 24 CARDS. *
C ** FAILURE RATES MUST BE ASSOCIATED WITH INCREASING EVENT TIME *
C ** PERIODS REGARDLESS OF THE ORDER ON THE TYPE 20 CARDS *
C *
C***** QQ: 000 *******************************************************
460 IF (Nl .NE. 25) GO TO 470
C
DO 3004 I=1,NEVSM
IF (EVNT(I) .EQ. 0.0) GO TO 999
IF (EVNT(I) .NE. F(l)) GO TO 3004
GO TO (403,404,405,406,407,408), N2
CALL ERROR (3,N1,N2,F,A,IX)
403 DO 3005 0=2,6
3005 FRATE(I.J-l) = F(0)
GO TO 100
404 DO 3006 0=2,6
3006 FRATE(I,0+4) = F(0)
GO TO 100
405 DO 3007 0=2,6
3007 FRATE(I,0+9) = F(0)
GO TO 100
234
-------
406 DO 3008 J=2,6
3008 FRATE(I,J+14) = F(J)
GO TO 100
407 DO 3009 J=2,6
3009 FRATE(I,J+19) = F(J)
GO TO 100
408 DO 3010 J=2,6
3010 FRATE(I,J+24) = F(J)
GO TO 100
3004 CONTINUE
GO TO 999
C
Q***** CQ. QQQ *******************************************************
C *
C***** JYPE 26 CARDS ENTER EVENT INITIAL PROBABILITY (INSTEAD OF *
c***** FAILURE RATE DATA) *
C *
Q***** QQ. QOO *******************************************************
470 IF (Ml .NE. 26) GO TO 500
C
DO 3011 I=1,NEVSM
IF (EVNT(I) .EQ. 0.0) GO TO 999
IF (EVNT(I) .NE. F(l)) GO TO 3011
PROB(I,1) = F(2)
GO TO 100
3011 CONTINUE
GO TO 999
C
Q***** QQ; QQQ *******************************************************
C ' *
C***** TYPE 30, 31, AND 32 CARDS ENTER RADIONUCLIDE DATA *
C *
£***** QQ. QQQ *******************************************************
500 IF (Nl .NE. 30) GO TO 501
C
DO 4001 I=1,NRNM
IF (RNID(I) .EQ. 0.0) GO TO 502
IF (RNID(I) .NE. F(l)) GO TO 4001
NRNTY(I) = N2
RNLD(I) = 0.693/F(2)
RNQO(I) = F(3)
LR(D = F(4)
RNDA(I) = F(5)
RNSOL(I) = F(6)
RNDSl(I) = A(l)
RNDS2(I) = A(2)
GO TO 100
4001 CONTINUE
235
-------
502
501
4002
503
4003
NRN = NRN
RNID(NRN)
NRNTY(NRN)
RNLD(NRN)
RNQO(NRN)
LR(NRN)
RNDA(NRN)
RNSOL(NRN)
RNDSl(NRN)
RNDS2(NRN)
GO TO 100
+ 1
= F(l)
= N2
= 0.693/F(2)
= F(3)
= F(4
= F(5)
= F(6)
- A(2)
IF (Nl .N£.
DO 4002 1=1
IF (RNID(I)
IF (RNID(I)
LAMS(I) =
RNKD(I) =
RLMT(IJ) =
RLMT(2,I) =
RLMT(3,I) =
GO TO 100
CONTINUE
GO TO 999
31) GO
,NRNM
.EQ.
.NE.
F(2)
F(3)
F(4)
F(5)
F(6)
TO 503
0.0) GO TO 999
F(l)) GO TO 4002
IF (Nl .NE.
DO 4003 1=1,,
IF (RNID(I)
IF (RNID(I) .NE. F(l)) GO TO 4003
32) GO TO 600
,NRNM
.EQ. 0.0) GO TO 999
IF (F(2) .NE. 0.0) RNLDl(I)
RNQOl(I) = F(3)
IF (F(4) .NE. 0.0) RNLDX(I)
RNQOX(I) = F(5)
GO TO 100
CONTINUE
GO TO 999
0.693/F(2)
0.693/F(4)
*******************************************************
*
C
C***** QC:
C
C***** TYPE 50 CARD ENTERS AQUIFER FLOW SYSTEM DATA *
C *
Q***** Q£. QQQ *******************************************************
600 IF (Nl .NE. 50) GO TO 700
XA
XS
XKA
XIA
PORA
AQAREA
F(D
F(2)
F(3)
F(4)
F(5
F 6
236
-------
VAQ = XKA * XIA * AQAREA
WTIME = XA * PORA / (XKA * XIA)
GO TO 100
C
Q***** QQ. QQQ *******************************************************
C *
c***** TYPE 51 CARD ENTERS HYDRAULIC GRADIENT DATA *
C *
Q***** QQ. 000 *******************************************************
700 IF (Nl .NE. 51) GO TO 740
C
DO 741 I = l.NCOF
IF ( CVA(I) .NE. 0.0) GO TO 741
ALPH(I) = F(l)
CVA(I) = F(2)
IF (F(3) .EQ. 0.0) GO TO 742
CVC = F(3)
742 CONTINUE
GO TO 100
741 CONTINUE
C
Q***** QQ. 000 *******************************************************
C ' *
c***** TYRE 52 CARD ENTERS LEACH RATE, CANISTER LIFETIME, AND *
C***** OTHER MISCELLANEOUS DATA *
C *
Q***** QQ. 000 *******************************************************
740 IF (Nl .NE. 52) GO TO 750
C
WFLR = F(l)
CLIFE = F(2)
VR = F(3
TIC = F(4)
EXPECT = F(5)
NTIC = TIC
GO TO 100
C
Q***** QQ. 000 *******************************************************
C ' *
Q***** TYPE 53 CARD ENTERS DATA FOR EXPECTED RELEASES FROM *
Q***** A SALT REPOSITORY *
C *
Q***** QQ; 000 *******************************************************
750 IF (Nl .NE. 53) GO TO 760
C
TCLOS = F(l)
VMIN = F(2)
XHGH = F(3
XLOW = F(4)
XILTH = F(5)
GO TO 100
237
-------
r***** cc* 000 *******************************************************
c ' *
c***** TYPE 60 CARD ENTERS ENVIRONMENTAL TRANSFER FACTORS *
C *
£***** QQ- QOO *******************************************************
760 IF (Nl .NE. 60) 60 TO 800
C
GLMS = F(l)
LAMR = F(2)
LAMG = F(3]
LAMW = F(4i
GO TO 100
C
£***** QQ. QOO *******************************************************
C ' *
C***** TYPE 70 CARD ENTERS OCEAN ENVIRONMENTAL PATHWAY DATA *
C *
£***** £Q. 000 *******************************************************
800 IF (Nl .NE. 70) GO TO 900
C
S1IO = F(l)
S2IO = F(2)
TAU1 = F(3
TAU2 = F(4)
GO TO 100
C
900 IF (Nl .LT. 96) GO TO 999
IF (Nl .EQ. 99) GO TO 998
WRITE (6,21)
21 FORMAT (1H ,9X,'ANOTHER PROBLEM WILL FOLLOW, BASED UPON THE ',
1 'INPUTS TO THIS PROBLEM AND ANY PREVIOUS PROBLEMS')
GO TO 190
C
998 WRITE (6,20)
20 FORMAT (1H ,9X,'INPUT DATA WAS CORRECTLY TERMINATED')
GO TO 190
C
999 CALL ERROR (5,N1,N2,F,A,IX)
GO TO 100
C
190 IF (IPATH .EQ. 1) GO TO 194
C
Q***** QQ. 000 *********************************************************
c *
C***** EERF TAPES 3 3 4 READ IN HEALTH EFFECTS FACTORS *
C *
C***** £Q. 000 *********************************************************
c
238
-------
188
15
14
C
C
1600
C
192
189
C
C
1700
C
READ (3,15,ERR=999) (HFSTIT(I ) ,1=1,19)
I PATH = 1
READ (3,14,ERR=999,END=192) (F(I ) ,1=1,13)
FORMAT (1X.19A4)
FORMAT (1X,F8.3,1P6E10.3/1X,1P6E10.3)
DO IbOO I=1,NRNM
IF (RNID(I) .EQ. 0.0) GO TO 188
IF (RNID(I) .NE. F(l)) GO TO 1600
HFS1 (I) = F( 2)
HFS2 (I) = F( 3)
HFS3 (I) = F( 4)
HFS4 (I) = F( 5)
HFS5 (I) = F( 6)
HFS6 (I) = F( 7)
HFS7 (I) = F( 8)
HFS8 (I) = F( 9)
HFS9 (I) = F 10
HFSIO(I) = F(ll)
HFSll(I) = F(12)
HFS12(I) = F(13)
GO TO 188
CONTINUE
GO TO 188
READ (4,15,ERR=999) (HFGTIT(I ) ,1=1 ,19)
READ (4,14,ERR=999,END=193) (F(I), 1=1,13)
DO 1700 I=1,NRNM
IF (RNID(I) .EQ. 0.0) GO TO 189
IF (RNID(I) .NE. F(l)) GO TO 1700
HFG1 (I) = F( 2)
HFG2 (I) = F( 3)
HFG3 (I) = F( 4)
HFG4 (I) = F( 5)
HFG5 (I) = F( 6)
HFG6 (I) = F( 7)
HFG7 (I) = F( 8)
HFG8 (I) = F( 9)
HFG9 (I) = F(10)
HFGIO(I) = F(ll)
HFGll(I) = F(12)
HFG12(I) = F(13)
GO TO 189
CONTINUE
GO TO 189
239
-------
193 REWIND 3
REWIND 4
C
194 DO 1800 1=1, NRN
IF (HFS1(I) .NE. 0.0) GO TO 1800
WRITE (6,67) RNDS1(I),RNDS2(I)
67 FORMAT (lOX.'NO DATA WAS ENTERED FOR',2A4)
IX = 1
1800 CONTINUE
C
IF (IX .NE. 1) 60 TO 191
WRITE (6,40)
40 FORMAT (1H ,' PROBLEM TERMINATED DUE TO INPUT ERRORS')
STOP 1001
Q • 000 *******************************************************
C ' *
C***** SET UP NPRT AND NOUT(I) FOR OUTPUT FORMATS BASED UPON NEVT *
C***** NEVT = NUMBER OF EVENT TIMES *
C *
Q***** QQ. 000 *******************************************************
C
191 IF (NEVT .GT. 8) GO TO 140
NPRT = 1
NOUT(l) = NEVT
GO TO 195
140 DO 1101 I=2,NOUT8
NK = NEVT / I
IF (NK .GT. 8) GO TO 1101
NR = NEVT - I * NK
NPRT = I
143 IF (NR .GT. 0) GO TO 141
DO 1102 0=1, NPRT
1102 NOUT(J) = NK
GO TO 195
141 IF (NK .GE. 8) GO TO 142
DO 1103 J=1,NPRT
NOUT(J) = NK + 1
NR = NR - 1
IF (NR .GT. 0) GO TO 1103
JJ = J + 1
DO 1104 K=JJ,NPRT
1104 NOUT(K) = NK
GO TO 195
1103 CONTINUE
CALL ERROR (8, NPRT, NEVT, F, A, IX)
142 NPRT =1+1
NK = NEVT / NPRT
NR = NEVT - NPRT * NK
GO TO 143
240
-------
1101
195
145
7002
CONTINUE
CONTINUE
DO 7002 I=1,NEVT
IF (I .NE. 1) GO TO
TEVNT(I) = TOBND(I)
GO TO 7002
TEVNT(I) = (TOBND(I)
CONTINUE
145
/ 2.0
+ TOBND(I-l)) / 2.0
1064
1061
1062
1060
1063
7088
DO 7088 I = l.NEVS
DO 1063 NA = l.NDCT
AMEAN1(NA,I) = 0.0
DO 1060 J=1,NEVT
IF ( TOBND(J) .GT. TEDC(NA) ) GO TO 1060
IF ( NA .EQ. 1 ) GO TO 1064
CONTINUE
IF (J .NE. 1) GO TO 1061
TBAND = TOBND(J)
GO TO 1062
TBAND = TOBIMD(J) - TOBND(J-l)
IF (FRATE(I.J) .EQ. 0.0) FRATE(I,J
IF (FRATE(I,J) .LT. 0.0) FRATE(I,J
CA = TBAND * FRATE(I.J)
.EQ. 2 .AND
.EQ. 3 .AND
146
147
148
149
7004
7003
IF (NEVTT(
IF (NEVTT(
I)
I)
TOBND(J
TOBND(J
+ CA
AMEANl(NA.I) = AMEANl(NA.I)
CONTINUE
CONTINUE
CONTINUE
DO 7003 I=1,NEVS
IF (PROB(I.l) .NE. 0.0) GO TO 7003
DO 7004 J=1,NEVT
IF (J .NE. 1) GO TO 146
TBAND = TOBND(J)
GO TO 147
TBAND = TOBND(J) - TOBND(J-l)
IF (FRATE(I.J) .EQ. 0.0) FRATE(I
IF (FRATE(I.J) .LT. 0.0) FRATE(I.J)
CA = TBAND * FRATE(I.J)
IF (NEVTT(I) .EQ. 2 .AND. TOBND(J)
IF (NEVTT(I) .EQ. 3 .AND. TOBND(J)
IF (CA .GT. 0.04) GO TO 148
PROB(I.J) = CA
GO TO 7004
IF (CA .LT. 100.0) GO TO 149
PROB(I.J) = 1.0
GO TO 7004
PROB(I.J) = 1.0 - EXP (-CA)
CONTINUE
CONTINUE
= FRATE(I.J-l)
= 0.0
LE. TIC) CA = 0.0
LE. TIC CA = 0.0
J) = FRATE(I.J-l)
0.0
,LE.
.LE.
TIC)
TIC)
CA = 0.0
CA = 0.0
241
-------
DO 7001 J=1,NEVTM
7001 NENTT(J) = TEVNT(J)
EQ.
EQ.
0.0) RNQOX(I
0.0) RNLDX(I
0.0) LR(I)
0.0) LAMS(I)
= RNQO(I)
= RNLD(I)
= WFLR
= GLMS
DO 7005 1=1,NRN
IF (RNQOX(I) .EQ
IF (RNLDX(I) .EQ
IF (LR(I)
IF (LAMS(I)
OLMT = 0.0
DO 7007 J=l,3
7007 IF (RLMT(J.I) .NE. 0.0) OLMT = RLMT(J.I)
IF (OLMT .EQ. 0.0) OLMT = 1.0
DO 7008 J=l,3
7008 IF (RLMT(J.I) .EQ. 0.0) RLMT(J.I) = OLMT
7005 IF (RLMT(l.I) .NE. 1.0) IRLMT = 0
C
DO 1245 I = l.NCOF
IF ( ALPH(I) .EQ. 0. ) ALPH(I) = 1.0
1245 CONTINUE
DO 7006 I=1,NEVS
IF (VTANK(I) .EQ. 0.0) VTANK(I) = VR
IF (VDRILL(I) .EQ. 0.0) VDRILL(I) = VTANK(I)
7006 IF (FTANK(I) .EQ. 0.0) FTANK(I) = 1.0
C
NCT = NEVT * NEVS
C
Q***** QQ. QQQ *******************************************************
C ' *
C***** START DOSE COMMITMENT TIME LOOP (1000) *
c***** SUBSCRIPT = NA *
C *
Q***** QQ. QQQ *******************************************************
C
350 DO 1000 NA=1,NDCT
C
IEX = 0
TA = 0.0
NTA = 0
NTE = TEDC(NA)
TC = TEDC(NA)
IF (NA .EQ. 1 .OR. NDOT .EQ. 1) GO TO 196
TA = TEDC(NA-l)
NTA = TA
196 IF (TDINT .NE. 0.0) GO TO 197
TB = TEDC(NA)
NTB = NTE
GO TO 198
197 IF (TEDC(NA) .61. TDINT) CALL ERROR (25.N1,Nl.F.A.IX)
TB = TDINT
NTB = TB
242
-------
198 DO 1236 I=1,NEVTM
DO 1236 J=1,NEVSM
NDEVS(J,I) = 0
CNS(J,I) = 0.0
CNG(J,I) = 0.0
CNR(J.I) = 0.0
NRSMX(J,I)= 0.0
NRGMX(J,I)= 0.0
NRRMX(J,I)= 0.0
DO 1236 K=1,NRNM
CNSR(J,I,K) = 0.0
CNGR(J,I,K) = 0.0
1236 CNRR(J,I,K) = 0.0
DO 1237 I = l.NEVSM
1237 NDCASE(I) = 0
C
Q***** QQ. 000 *******************************************************
C *
C***** START EVENT (3000) AND EVENT TIME (2000) LOOPS *
C***** SUBSCRIPTS = NC AND NB *
C *
Q***** QQ- 000 *******************************************************
C
DO 3000 NC=1,NEVS
DO 2000 NB=1,NEVT
C
IF (TEVNT(NB) .61. TEDC(NA)) GO TO 2000
C
C
CONSM =0.0
CONGM =0.0
CONRM =0.0
CONST =0.0
CONGT =0.0
CONRT =0.0
C
Q***** Q£. 000 *******************************************************
C ' *
C EVENT BRANCHING *
C***** BRANCH TO METEORITE, VOLCANO, DRILLING DIRECT IMPACT (110), *
C***** NO HIT DRILLING (111), FAULTING, BRECCIA PIPES (112), *
C***** OR NORMAL GROUNDWATER FLOWS - NONSALT (113) OR SALT (117) *
C *
Q***** Q£. 000 *******************************************************
NGA = NEVTT(NC)
GO TO (110,110,111,112,113), NGA
CALL ERROR (9,NEVTT(NC),NC,F,A,IX)
C
243
-------
Q***** QQ- QQO *******************************************************
c ' *
Q***** BRANCH 110 *
c***** START RADIONUCLIDE LOOP (4100) FOR METEORITES, VOLCANOES, *
c***** AND DRILLING DIRECT IMPACT *
C *
r***** CC' 000 *******************************************************
C
110 DO 4100 ND=1,NRN
C
SF1 = S1IO * RNKD(ND)
SF2 = S2IO * RNKD(ND)
C
NGB = NRNTY(ND)
GO TO (150,151), NGB
CALL ERROR (20,NRNTY(IMD),ND,F,A,IX)
C
150 CA = RNLD(ND) * TEVNT(NB)
IF (CA .GE. 20.0) GO TO 4100
CA = EEXP (-CA.IEX)
QALS = FHIT(NC) * RNQO(ND) * CA
GO TO 159
C
151 CA = RNLD(NDJ * TEVNT(NB)
CA1 = RNLDl(ND) * TEVNT(NB)
CA = EEXP (-CA.IEX)
CA1 = EEXP (-CA1.IEX)
CB = RNLD(ND) / (RNLD(ND) - RNLDl(ND))
QALS = FHIT(NC) * (CB * RNQOl(ND) * (CAl - CA) + RNQO(ND) * CA)
IF (QALS .EQ. 0.0) GO TO 4100
C
159 IF (NGA .EQ. 2) GO TO 152
C
Q***** CQ. goo *******************************************************
c *
c***** BRANCH 110 *
C***** AIR PATHWAY CALCULATIONS FOR METEORITES AND VOLCANOES *
C *
Q***** QQ. 000 *******************************************************
C
CALL SMESS1
1 (RNLD(ND),LAMG,LAMS(ND),LAMR,TEVNT(NB),TB,MESS1N,MESSA,IEX)
TF3 = TFAC3 (RNLD(ND),LAMS(ND),TEVNT(NB),TB,IEX)
TF4 = TFAC4 (RNLD(ND),LAMS(ND),LAMR,TEVNT(NB),TB,IEX)
TF5 = TFAC5 (RNLD(ND),LAMS(ND),LAMR,TEVNT(NB),TB,IEX)
TF6 = SMESSN (RNLD(ND),LAMU,SF1,SF2,TAU1,TAU2,TEVNT(NB),TB,IEX)
IF (TA .67. TEVNT(NB)) GO TO 153
244
-------
CONS = QALS * (FAL * HFS7(ND) * MESS1N + FAL * HFS8(ND) * MESSA
1 + FLL * HFS9(ND) * TF3 + FLL * HFSIO(ND) * TF4
2 + FLL * HFSll(ND) * TF5 + FAW * HFS12JND) * TF6)
CONG = QALS * (FAL * HFG7(ND) * MESS1N + FAL * HFG8(ND) * MESSA
1 + FLL * HFG9(ND) * TF3 + FLL * HFGIO(ND) * TF4
2 + FLL * HFGll(ND) * TF5 + FAW * HFG12(ND) * TF6)
CONR = QALS / RLMT(1,ND)
GO TO 154
153 CALL SMESS1
1 (RNLD(ND),LAMG,LAMS(ND),LAMR,TEVNT(NB),TA,MESS1A, MESSAA, IEX)
TF3A = TFAC3 (RNLD(ND) ,LAMS(ND) ,TEVNT(NB) ,TA,IEX)
TF4A = TFAC4 RNLD(ND) , LAMS ND) ,LAMR,TEVNT(NB) ,TA, IEX)
TF5A = TFAC5 (RNLD(ND) ,LAMS(ND) ,LAMR,TEVNT(NB) ,TA,IEX)
TF6A = SMESSN (RNLD(ND) ,LAMW,SF1 ,SF2,TAU1 ,TAU2,TEVNT(NB) ,TA,IEX)
CONS =
1
2
3
4
5
CONG =
1
2
3
4
5
QALS *
+
+
+
+
+
QALS *
+
+
+
+
+
(FAL
FAL
FLL
FLL
FLL
FAW
(FAL
FAL
FLL
FLL
FLL
FAW
*
*
*
*
*
*
*
*
*
*
*
*
HFS7(ND)
HFS8(ND)
HFS9(ND)
HFSIO(ND)
HFSll(ND)
HFS12(ND)
HFG7(ND)
HFG8(ND)
HFG9(ND)
HFGIO(ND)
HFGll(ND)
HFG12(ND)
*
*
*
*
*
*
*
*
*
*
*
*
(MESS1N
(MESSA
(TF3 -
(TF4 -
(TF5 -
(TF6 -
(MESS1N
(MESSA
(TF3 -
(TF4 -
(TF5 -
(TF6 -
- ME SSI A)
- MESSAA)
TF3A)
TF4A)
TF5A)
TF6A))
- MESS1A)
- MESSAA)
TF3A)
TF4A)
TF5A)
TF6A))
CONR = QALS / RLMT(l.ND)
GO TO 154
C
0***** QQ. QQO *******************************************************
C ' *
Q***** BRANCH 110 *
C***** LAND SURFACE PATHWAY CALCULATIONS FOR DRILLING DIRECT IMPACT *
C *
Q***** ££• 000 *******************************************************
C
152 TF3 = TFAC3 (RNLD(ND).LAMS(ND) ,TEVNT(NB),TB,IEX)
TF4 = TFAC4 (RNLD(ND) ,LAMS(ND) ,LAMR,TEVNT(NB) ,TB,IEX)
TF5 = TFAC5 (RNLD(ND),LAMS(ND) ,LAMR,TEVNT(NB),TB,IEX)
IF (TA .GT. TEVNT(NB)) GO TO 155
C
CONS = QALS * (HFS4(ND) * TF3 + HFS5(ND) * TF4 + HFS6(ND) * TF5)
CONG = QALS * (HFG4(ND) * TF3 + HFG5(ND) * TF4 + HFG6(ND) * TF5)
CONR = QALS / RLMT(2,ND)
GO TO 154
C
155 TF3A = TFAC3 (RNLD(ND).LAMS(ND) ,TEVNT(NB) ,TA,IEX)
TF4A = TFAC4 (RNLD(ND) ,LAMS(ND) ,LAMR,TEVNT(NB) ,TA,IEX)
TF5A = TFAC5 (RNLD(ND) ,LAMS(ND) ,LAMR,TEVNT(NB) ,TA5IEX)
245
-------
CONS = QALS * (HFS4(ND) * (TF3 - TF3A) + HFS5(ND) * (TF4 - TF4A)
1 + HFS6(ND) * (TF5 - TF5A))
CONG = QALS * (HFG4(ND) * (TF3 - TF3A) + HFG5(ND) * (TF4 - TF4A)
1 + HFG6(ND) * (TF5 - TF5A))
CONR = QALS / RLMT(2,ND)
C
154 IF (CONS .LE. CONSM) GO TO 166
CONSM = CONS
NRSMX(NC.NB) = ND
C
166 IF (CONG .LE. CONGM) GO TO 167
CONGM = CONG
NRGMX(NC.NB) = ND
C
167 IF (CONR .LE. CONRM) GO TO 168
CONRM = CONR
NRRMX(NC.NB) = ND
C
168 CONST = CONST + CONS
CONGT = CONGT + CONG
CONRT = CONRT + CONR
C
CNSR(NC,NB,ND) = CONS
CNGR(NC,NB,ND) = CONG
CNRR(NC,NB,ND) = CONR
C
4100 CONTINUE
CNS(NC,NB) = CONST
CNG(NC,NB) = CONGT
CNR(NC.NB) = CONRT
GO TO 2000
C
Q***** ££• QQQ *******************************************************
C *
C***** BRANCH 113 3 112 *
C***** NORMAL GROUNDWATER FLOWS - NONSALT (113) AND FAULTING OR *
C***** BRECCIA PIPE EVENTS (112)
C *
Q***** QQ. 000 *******************************************************
C
113 IF (IREP .EQ. 1) GO TO 117
IF (NB .GT. 1) GO TO 2000
112 FRAC = FTANK(NC) - FHIT(NC)
C
V = VTANK(NC)
TFAIL = TEVNT(NB)
C
IF (CLIFE .GE. TFAIL) TFAIL = CLIFE
C
C
246
-------
VX = VOLFLO(IEX,TFAIL)
VY = AREA(NC) * Kl(NC)
VX = VX * VY
C
TDEL1 = TDELI(XS,TFAIL,PORS(NC),K1(NC),IEX,TB;
TDEL1A = TDELI(XS,TEVNT(NB),PORS(NC),K1(NC),TB;
TB1 = TB
C
C.
Q***** QQ. QQQ *******************************************************
C ' *
C 112 LOOP FOR FAULTING AND BRECCIA PIPE EVENTS *
C***** BRANCH 112 *
C***** START RADIONUCLIDE LOOP (4000) FOR 112 BRANCH *
C *
Q***** QQ- QQQ *******************************************************
C
DO 4000 ND=1,NRN
C
TSOL = 0.
TVAQ = TFAIL
AMT = FRAC * RNQOX(ND)
BOXS = 0.0
BOXG = 0.0
BOXR = 0.0
PIPES = 0.0
PIPEG = 0.0
PIPER = 0.0
TDEL2 = TFAIL + RNDA(ND) * WTIME
C
TDEL = TDEL1 + TDEL2
TMAX = TB1 - TDEL + TFAIL
TMIN = TFAIL
C
IF (VX .LE. VAQ) GO TO 5102
C
TVAQ = EQUAL (VY,VAQ,NT,Ti*lAX,TMIN, IEX)
5102 CONTINUE
C
IF (TDEL .GT. TB) GO TO 4050
IF (TDEL * RNLDX(ND) .GT. 20.0) GO TO 4050
IF(RNSOL(ND) .EQ. 0.0) GO TO 846
C
£***** ££• Q(JQ *******************************************************
C
C***** BRANCH 112 *
C***** TSOL IS CALCULATED *
C***** JSOL IS WHEN THE RADIONUCLIDE CONCENTRATION BECOMES *
C***** LOWER THAN ITS SOLUBILITY LIMIT *
C *
P***** QQ- QQQ *******************************************************
C
247
-------
TSOL = -1.0
DEL = 100.
NOON =(TMAX - TFAIL) / DEL
Yl = 0.0
CHECK = AMI / V
IF ( CHECK .LE. RNSOL(ND)) GO TO 847
IF ( TFAIL .EQ. CLIFE ) GO TO 5105
TG = TFAIL - CLIFE
CHECK2 = CHECK * EEXP(-RNLDX(ND)-* TFAIL,IEX)
CHECK2 = CHECK2 * (1. - EEXP(-LR(ND) * TG, IEX))
IF (CHECK2 .LE. RNSOL(ND) ) GO TO 847
5105 NX = NOON + 2
DO 840 K=1,NX
Tl = TFAIL + DEL * (K-2)
IF( Tl * RNLDX(ND) .61. 20.0) GO TO 847
IF(K .EQ. 1) Tl = TFAIL
IF(K .EQ. 2) Tl = TFAIL + 10.
IF(Y1 .NE. 0.) GO TO 842
IF(T1 .GE. TVAQ) GO TO 852
CX = CONVQ(T1,IEX,VAQ,RNSOL(ND),RNLDX(ND),AMT,V,
1 CLIFE,TFAIL,TVAQ,AREA(NC),K1(NC),LR(ND))
IF(CX .LT. RNSOL(ND)) GO TO 840
IF ( K .LE. 2 ) GO TO 845
K = K - 1
Tl = Tl - DEL
845 CONTINUE
Yl = 1.0
TSOLI = Tl
GO TO 840
852 IF(K .LE. 2) GO TO 859
C A8 = MOD(K,10)
C IF(A8 .NE. 0.) GO TO 840
859 IF(T1 .67. 10000.) GO TO 860
CX = CONVT(T1,VAQ,RNSOL(ND),RNLDX(ND),AMT,V,
1 CLIFE,TFAIL,TVAQ,AREA(NC),K1(NC),LR(ND))
860 IF(T1 .GT. 10000.) CX = CONHYD(T1,IEX,RNSOL(ND),RNLDX(ND),AMT,V,
1 CLIFE,TFAIL,TVAQ,AREA(NC),K1(NC),LR(ND))
IF(CX .LT. RNSOL(ND)) GO TO 840
IF ( K .LE. 2 ) GO TO 849
K = K - 1
Tl = Tl - DEL
849 CONTINUE
Yl = 1.0
TSOLI = Tl
GO TO 840
842 IF(T1 .GE. TVAQ) GO TO 843
TSOL = VQSOL(T1,IEX,VAQ,RNSOL(ND),RNLDX(ND),AMT,V,
1 CLIFE,TFAIL,TVAQ,AREA(NC),K1(NC),LR(ND))
IF(TSOL .EQ. -1.0) GO TO 840
GO TO 846
248
-------
843 TSOL = V7SOL(T1,IEX,VAQ,RNSOL(ND),RNLDX(ND),AMT,V,
1 CLIFE,TFAIL,TVAQ,AREA(NC),K1(NC),LR(ND))
IF(TSOL .EQ. -1.0) GO TO 840
GO TO 846
840 CONTINUE
847 IF(Y1 .EQ. 1.0) TSOL = TB1
IF(Y1 .EQ. 0.0) TSOL = TFAIL
846 CONTINUE
C
Q***** QQ. QQQ *************************************************
C " *
c***** BRANCH 112 *
C***** CONSEQUENCES CALCULATED AS CURIES RELEASED a HEALTH EFFECTS *
C *
Q***** £Q: 000 *********************************************************
c
c
SOL = RNSOL(ND)
IF ( TSOL .EQ. TFAIL .AND. Yl .EQ. 0. ) SOL = 0.
IF ( TSOL .LT. TFAIL ) SOL = 0.
TMAX = TB1 - TDEL + TFAIL
IF ( TMAX .67. TSOL .AND. SOL .NE. 0. ) TMAX = TSOL
C
IF (TA .67. TDEL) TMIN = 7A - TDEL + TFAIL
IF (TA - TDEL + TFAIL .67. 7VAQ) TVAQ = TA - TDEL + TFAIL
X8 = 0.0
Y8 = 0.
IF (SOL .NE. 0.0) GO TO 5103
C
IF (TFAIL .EQ. TVAQ) GO TO 5250
C
X8 = ENT1A (TVAQ,7MIN,VAQ,CLIFE,LR(ND),V,TFAIL,RNLDX(ND),AM7,IEX)
C
5250 IF (TVAQ .EQ. TMAX) GO TO 5104
C
Y8 = SALT (VY,LR(ND),V,7FAIL,7VAQ,7MAX,NN,IEX,CLIFE,AM7,RNLDX(ND),
1 VAQ)
GO TO 5104
C
5103 TV = TVAQ
IF ( TVAQ .67. 7MAX ) 7V = 7MAX
IF ( 7MAX .LE. 7FAIL ) 7V = 7FAIL
X8 = VAQ * SOL * (7V - 7FAIL)
IF ( 7VAQ .6E. 7MAX ) GO 70 5104
Y8 = EN7CO (VY,SOL,7MAX,7VAQ,IEX)
5104 Z = -RNLDX(ND) * (7DEL - 7FAIL)
Z = EEXP (Z.IEX)
QSW = (X8 + Y8) * Z
C
249
-------
BOXS = QSW * (HFSl(ND) + HFS2(ND) / (LAMS(ND) + RNLDX(ND)))
BOXG = QSW * (HFGl(ND) + HFG2(ND) / (LAMS(ND) + RNLDX(ND)))
BOXR = QSW / RLMT(3,ND)
C
4050 IF ( FHIT(NC) .EQ. 0. ) GO TO 4051
TDEL2 = TEVNT(NB) + RNDA(ND) * WTIME
TDEL = TDEL1A + TDEL2
C
IF (TDEL * RNLDX(ND) .GT. 20.0) GO TO 4000
IF (TDEL .GT. TB1) GO TO 4000
C
TMAX = TB1 - TDEL + TEVNT(NB)
TMIN = TEVNT(NB)
C
5199 Yl = -RNLDX(ND) * TEVNT(NB)
Yl = EEXP (Y1,IEX)
IF (TA .GT. TDEL) TMIN = TA - TDEL + TEVNT(NB)
IF (TA - TDEL + TEVNT(NB) .GT. TVAQ) TVAQ = TA - TDEL + TEVNT(NB)
C
X10 = LR(ND) * TEVNT(NB)
X10 = EEXP (X10.IEX)
X10 = X10 * LR(ND) * FHIT(NC) * RNQOX(ND) / (LR(ND) + RNLDX(ND))
X8 = -TMIN * (LR(ND) + RNLDX(ND))
X8 = EEXP (X8.IEX)
Y8 = -TMAX * (LR(ND) + RNLDX(ND))
Y8 = -EEXP (Y8.IEX)
X8 = X8 * X10
Y8 = Y8 * X10
5106 Z = -RNLDX(ND) * (TDEL - TEVNT(NB))
Z = EEXP (Z.IEX)
QSW = (X8 + Y8) * Z
C
PIPES = QSW * (HFSl(ND) + HFS2(ND) / (LAMS(ND) + RNLDX(ND)))
PIPEG = QSW * (HFGl(ND) + HFG2(ND) / (LAMS(ND) + RNLDX(ND)))
PIPER = QSW / RLMT(3,ND)
C
4051 CONS = BOXS + PIPES
CONG = BOXG + PIPEG
CONR = BOXR + PIPER
C
IF (CONS .LE. CONSM) GO TO 131
CONSM = CONS
NRSMX(NC.NB) = ND
131 IF (CONG .LE. CONGM) GO TO 132
NRGMX(NC,NB) = ND
CONGM = CONG
132 IF (CONR .LE. CONRM) GO TO 133
CONRM = CONR
NRRMX(NC.NB) = ND
250
-------
133 CONST = CONST + CONS
CONGT = CONGT + CONG
CONRT = CONRT + CONR
C
CNSR(NC,NB,ND) = CONS
CNGR(NC,NB,ND) = CONG
CNRR(NC,NB,ND) = CONR
C
4000 CONTINUE
C
CNS(NC,NB) = CONST
CNG(NC.NB) = CONGT
CNR(NC,NB) = CONRT
C
2000 CONTINUE
C
GO TO 3000
C
Q***** QQ• QQQ *******************************************************
C ' *
c***** BRANCH 111 *
C***** NO HIT DRILLING EVENTS(lll) - PROBABILITIES *
C *
Q***** QQ. QQQ *******************************************************
111 AMEAN = AMEAN1(NA,NC)
TIC1 = TIC
IF ( TC .EQ. TIC1 ) P = 0.
IF ( TC .EQ. TIC1 ) GO TO 1528
P = AMEAN1(NA,NC) / (TC - TIC1)
1528 SIGMA = AMEAN * (1.0 - P)
SIGMA = SQRT (SIGMA)
IX = 12
IF (AMEAN .GT. 6.00) GO TO 1529
X8 = 3.0 * SIGMA + AMEAN
IX = INT (X8)
IF (AMEAN .LT. 0.5) IX = 3
IX = IX + 1
1529 RR = 0.0
C
DO 5000 1=1,IX
IF (AMEAN .GT. 6.00) GO TO 5015
R = I - 1.0
NOC = I - 1
PROB(NC.I) = BINOM (TC,R,P)
GO TO 5001
5015 RL = AMEAN + SIGMA * (I - 7) * .5
IF (RL .LT. 0.) RL = 0.
IF (RR .GT. 0.0) RL = RR
RR = AMEAN + SIGMA * (I - 6) * .5
IF (RR .LT. 0.) RR = 0.
251
-------
RM = (RL + RR) / 2
IM = INT (RM)
RM = IM
NOC =
IF(I .
IF(I .
IF(I .
IF(I .
IF(I .
IF(I .
IM
EQ.
EQ.
EQ.
EQ.
EQ.
EQ.
1
2
3
4
5
6
.OR.
.OR.
.OR.
.OR.
.OR.
.OR.
.0
I
I
I
I
I
I
.EQ.
.EQ.
.EQ.
.EQ.
.EQ.
.EQ.
12)
11)
10)
9)
8)
7)
X8 =
X8 =
X8 =
X8 =
X8 =
X8 =
.005
.0165
.050
.090
.150
.190
PROB(NC.I) = X8
5001 NDCASE(NC) = IX
IF (AMEAN .61. 6.) GO TO 5026
IF (NOC .EQ. 0) GO TO 5025
5026 CONST =0.0
CONGT =0.0
CONRT =0.0
NOCT = NOC
IF (AMEAN .LE. 6.) GO TO 5002
NOCT = INT(AMEAN)
IF (I .61. 1) GO TO 5003
5002 XX = TIC1
XI = NOCT +1.0
DEL = (TC - TIC1) / XI
C
C
Q***** QQ. 000 *******************************************************
C ' *
C***** BRANCH 111 *
C***** NO HIT DRILLING EVENTS - RELEASES TO LAND SURFACE *
C***** CONSEQUENCES CALCULATED AS CURIES RELEASED 3 HEALTH EFFECTS *
C *
Q***** £Q. QOO *******************************************************
C
DO 5005 J=1,NOCT
XX = XX + DEL
TDRILL = XX
C
IF (CLIFE .6E. TDRILL) GO TO 5005
C
DO 5006 ND=1,NRN
IF (TDRILL * RNLD(ND) .67. 20.0) GO TO 5006
NGB = NRNTY(ND)
FRINV = FTANK(NC) * RNQO(ND)
C
CA = TANK (VTANK(NC).LR(ND),CLIFE,TDRILL,FRINV,RNLD(ND),IEX)
C
IF ( NGB .EQ. 1 ) GO TO 1500
252
-------
CAD = DTANK (VTANK(NC),LR(ND),CLIFE,TDRILL,FTANK(NC),RNQO(ND),
1 RNLD(ND),RNQ01(ND),RNLD1(ND),IEX)
C
CA = CA + CAD
1500 IF (RNSOL(ND) .EQ. 0.0) GO TO 1901
C
IF (CA .61. RNSOL(ND)) CA = RNSOL(ND)
1901 QALS = CA * VTANK(NC)
IF (QALS .EQ. 0.0) 60 TO 5006
QALS = QALS * VDRILL(NC) / VTANK(NC)
C
TF3 = TFAC3 (RNLD(ND),LAMS(ND).TDRILL,TB,IEX)
TF4 = TFAC4 (RNLD ND ,LAMS(ND),LAMR,TDRILL,TB.IEX)
TF5 = TFAC5 (RNLD(ND),LAMS(ND),LAMR,TDRILL,TB,IEX)
C
IF (TA .61. TDRILL) GO TO 1550
C
CONS = QALS * (HFS4(ND) * TF3 + HFS5(ND) * TF4 + HFS6(ND) * TF5)
CON6 = QALS * (HF64(ND) * TF3 + HFG5(ND) * TF4 + HFG6(ND) * TF5)
CONR = QALS / RLMT(2,ND)
GO TO 1540
C
1550 TF3A = TFAC3 (RNLD(ND),LAMS(ND),TDRILL,TA,IEX)
TF4A = TFAC4 (RNLD(ND),LAMS(ND),LAMR,TDRILL,TA.IEX)
TF5A = TFAC5 (RNLD(ND),LAMS(ND),LAMR,TDRILL,TA.IEX)
C
CONS = QALS * (HFS4(ND) * (TF3 - TF3A) + HFS5(ND) * (TF4 - TF4A)
HFS6(ND
CONG = QALS * (HFG4(ND
1 + HFG6(ND
CONR = QALS / RLMT(2,ND)
C
1540 CONST = CONST + CONS
CON6T = CON6T + CON6
CONRT = CONRT + CONR
C
CSR(J.ND) = CONS
C6R J,ND) = CONG
CRR(J,ND) = CONR
C
5006 CONTINUE
5005 CONTINUE
C
IF (IDRILL .EQ. 1) GO TO 5025
C
* (TF5 - TF5A))
* (TF3 - TF3A) + HFG5(ND) * (TF4 - TF4A)
* (TF5 - TF5A))
253
-------
r***** cc- 000 *******************************************************
C ' *
Q***** BRANCH 111 *
C***** NO HIT DRILLING - RELEASES TO GROUNDWATER *
C***** CONSEQUENCES CALCULATED AS CURIES RELEASED 3 HEALTH EFFECTS *
C *
Q***** pp. QQQ *******************************************************
C
XX = TIC1
504 DO 5007 J=1,NOCT
XX = XX + DEL
TDRILL = XX
C
IF (CLIFE .GE. TDRILL) TDRILL = CLIFE
C
AA = AREA(NC)
C
TDEL1 = TDELKI (XS,TDRILL,PORS(NC),K1(NC),KPRIM(NC),IEX,TB)
C
DO 5008 ND=1,NRN
C
TDEL2 = RNDA(ND) * WTIME + TDRILL
TDEL = TDEL1 + TDEL2
C
IF (TDEL .GT. T6) GO TO 5008
IF (TDEL * RNLD(ND) .GT. 20.0) GO TO 5008
C
TI = TDRILL
IF (TA .GT. TDEL) TI = TA - TDEL + TDRILL
Q = FTANK(NC) * RNQOX(ND) * EEXP(-RNLDX(ND)*TDRILL,IEX)/VTANK(NC)
IF ( Q .LT. RNSOL(ND) ) GO TO 5008
C
IF (RNSOL(ND) .EQ. 0.0) GO TO 5009
TSOL = TSOLDR (VTANK(NC),LR(ND),CLIFE,RNQO(ND),RNLD(ND),
1 FTANK(NC),TB,TI,RNSOL(ND),IEX)
TF = TB - TDEL + TDRILL
IF (TSOL .EQ. -1.) GO TO 5009
IF ( TF .GT. TSOL ) TF = TSOL
C
QSW = ENTANK (AA.Kl(NC),KPRIM(NC),0.0,RNSOL(ND),1.0,TF,TI,0.0,
1 CLIFE,IEX.NN)
GO TO 5020
C
5009 CONTINUE
C
QSW = ENTANK (AA.Kl(NC),KPRIM(NC),RNLD(ND),RNQOX(ND),VTANK(NC),
1 TF,TI,LR(ND),CLIFE,IEX.NN)
5020 Y8 = -RNLD(ND) * (TDEL - TDRILL)
C
QSW = QSW * EEXP (Y8.IEX)
C
254
-------
CONS = QSW * (HFSl(ND) + HFS2(ND) / (LAMS(ND) + RNLDX(ND)))
CONG = QSW * (HFGl(ND) + HFG2(ND) / (LAMS(ND) + RNLDX(ND)))
CONR = QSW / RLMT(3,ND)
C
CONST = CONST + CONS
CONGT = CONGT + CONG
CONRT = CONRT + CONR
C
CSR(J.ND) = CONS + CSR(J,ND)
CGR(0,ND) = CONG + CGR(J.ND)
CRR(J.ND) = CONR + CRR(J.ND)
C
5008 CONTINUE
5007 CONTINUE
C
5025 CNS(NC,I) = CONST
CNG(NC,I) = CONGT
CNR(NCJ) = CONRT
CNSX = CONST
CNGX = CONGT
CNRX = CONRT
DO 4998 NO = l.NRN
NOCM = NOCT - 1
UO 4999 J = l.NOCM
CSR(NOCT,ND) = CSR(J,ND) + CSR(NOCT,ND)
CGR(NOCT,ND) = CGR(J,ND) + CGR(NOCT,ND)
CRR(NOCT,ND) = CRR(J.ND) + CRR(NOCT.ND)
4999 CONTINUE
4998 CONTINUE
C
5003 NDEVS(NC.I) = NOC
C
5000 CONTINUE
C
IF (AMEAN .LE. 6.0) GO TO 5004
DO 6111 I = 1,IX
XIX = NDEVS(NC.I)
FX1X = XIX / INT(AMEAN)
CNS(NC,I) = CNSX * FX1X
CNG(NC,I = CNGX * FX1X
6111 CNR(NC,I) = CNRX * FX1X
DO 4997 ND = 1,NRN
DO 4996 I = 1,IX
XIX = NDEVS(NC,I)
FXIX = XIX / INT(AMEAN)
CNSR(NC,I,ND) = FXIX * CSR(NOCT,ND)
CNGR(NC,I,ND) = FXIX * CGR(NOCT,ND)
CNRR(NC,I,ND) = FXIX * CRR(NOCT.ND)
255
-------
4996 CONTINUE
4997 CONTINUE
5004 GO TO 3000
000 *******************************************************
*
c***** CC:
c
c***** BRANCH 117
c***** NORMAL GROUNDUATER FLOW - SALT MEDIA (117)
C
£***** QQ
C
117 XXG
CEE
CFF
*
*
*
*******************************************************
= XHGH / XLOW
= Kl(lMC) * XXG * AREA(NC)
= KPRIM(NC) * XXG * AREA(NC)
VOLSH = CEE + CFF * TCLOS
IF (VOLSH .LE. VMIN) GO TO 591
DVV = (VTANK(NC) - VMIN) / TCLOS
DA = CFF / 2.0
DB = CEE + DVV
DC = - VTANK(NC)
TRCH = ROOT (DA,DB,DC)
VRCH = VTANK(NC) - DVV * TRCH
DEE = CEE * XILTH / XXG
OFF = CFF * XILTH / XXG
DA = OFF / 2.0
DB = DEE + OFF * TRCH
DC = - (VRCH - VMIN)
TVMIN = ROOT (DA,DB,DC)
TRR = TVMIN + TRCH
TLLMT = TRCH
IF (TRCH .17. CLIFE) TLLMT = CLIFE
IF (DEE + OFF * TLLMT .67. DVV) GO TO 920
IFLOW = 1
DA = XILTH * KPRIM(NC) / (2.0 * PORS(NC))
DB = Kl(NC) + KPRIM(NC) * TRCH
DB = DB * XILTH / PORS(NC)
DC = - XLOW
TDEL1 = ROOT (DA,DB,DC)
GO TO 921
920 IFLOW = 2
TRR = TCLOS
TDEL1 = XLOW *
PORS(NC) * AREA(NC) / DVV
921 IF (TRR .LE. CLIFE) GO TO 592
DO 4090 ND=1,NRN
CA = LR(ND) * CLIFE
WLRDT = LR(ND) * EEXP (.CA.IEX)
256
-------
CB = LR(ND) * (TLLMT - CLIFE)
CGB = EEXP (-CB.IEX)
C
QINT = 0.0
TOEL2 = RNDA(ND) * WTIME
TDEL = TDEL1 + TDEL2
TOUT = TLLMT + TDEL
IF (TOUT .GE. TB) GO TO 4090
IF (TOUT*RNLDX(ND) .GE. 20.0) GO TO 4090
C
CA = RNLDX(ND) * TDEL
DECAYD = EEXP (-CA.IEX)
ITRIG = 0
C
TMAX = TB - TDEL
IF (TRR .LT. TMAX) TMAX = TRR
DELT = 1.00
IT = (TLLMT + DELT) / DELT
IMAX = TMAX / DELT
C
DO 4091 I=IT,IMAX
C
FI = I
T = FI * DELT
C
IF (I .EQ. IMAX) T = TMAX
IF (ITRIG .EQ. 1) GO TO 911
CINTOA = CINTA (TLLMT,DEE,OFF,VRCH,TRCH,LR(ND),DVV,IFLOW,IEX,
1 VTANK(NC))
TOLDA = TLLMT
AREAX =0.0
C
911 THALF = (T + TOLDA) / 2.0
CA = (T - TOLDA) / 6.0
CINTH = CINTA (THALF,DEE,OFF,VRCH,TRCH,LR(ND),DVV,IFLOW,IEX,
2 VTANK(NC))
CINTN = CINTA (T,DEE,DFF,VRCH,TRCH,LR(ND),DVV,IFLOW,IEX,
3 VTANK(NC))
CB = CINTOA + 4.0 * CINTH + CINTN
CC = CA * CB
AREAX = AREAX + CC
TOLDA = T
CINTOA = CINTN
C
CA = RNLDX(ND) * T
DECAY = EEXP (-CA.IEX)
CONC = WLRDT * RNQOX(ND) * FTANK(NC) * DECAY * AREAX
IF (TLLMT .EQ. CLIFE) GO TO 912
CC = (RNQOX(ND) * FTANK(NC) / VRCH) * DECAY * (1.0 - CGB)
CONC = CONC + CC
257
-------
912 IF (RNSOL(ND) .EQ. 0.0) GO TO 913
IF (CONC .LT. RNSOL(ND)) GO TO 913
C
IF (ITRIG .EQ. 1) GO TO 914
TRNST = TDEL + TLLMT
GO TO 915
914 TRNST = TDEL + T - DELT
GO TO 915
C
913 IF (ITRIG .EQ. 1) GO TO 916
QRTO =0.0
TROLD = TLLMT
C
916 VOLF = DEE + OFF * T
IF (IFLOW .EQ. 2) VOLF = DVV
QRTN = VOLF * CONC * DECAYD
CC = 0.5 * (QRTN + QRTO) * (T - TROLD)
QINT = QINT + CC
QRTO = QRTN
TROLD = T
ITRIG = 1
4091 CONTINUE
GO TO 930
C
915 CA = RNSOL(ND) * DECAYD
IF (IFLOW .EQ. 1) GO TO 917
CB = - DVV * TDEL * CA
CC = DVV * CA / 2.0
GO TO 918
917 CB = (DEE - DFF * TDEL) * CA
CC = DFF * CA / 2.0
918 TULMT = TRR + TDEL
IF (TULMT .61. TB) TULMT = TB
CD = CB * (TULMT - TRNST)
CE = CC * (TULMT**2.0 - TRNST**2.0)
QINT = QINT + CD + CE
C
930 CONS = QINT * (HFSl(ND) + HFS2(ND) / (LAMS(ND) + RNLDX(ND)))
CONG = QINT * (HFGl(ND) + HFG2(ND) / (LAMS(ND) + RNLDX(ND)))
CONR = QINT / RLMT(3,ND)
C
IF (CONS .LE. CONSM) GO TO 931
CONSM = CONS
NRSMX(NC.l) = ND
931 IF (CONG .LE. CONGM) GO TO 932
NRGMX(NC,1) = ND
CONGM = CONG
932 IF (CONR .LE. CONRM) GO TO 933
CONRM = CONR
NRRMX(NC.l) = ND
258
-------
933
CONST = CONST + CONS
CONGT = CONGT + CONG
CONRT = CONRT + CONR
CNSR(NC,1,ND)
CNGR(NC,1,ND)
CNRR(NC,1,ND)
CONS
CONG
CONR
4090 CONTINUE
CNS(NC,1) = CONST
CNG(NC,1) = CONGT
CNR(NC,1) = CONRT
c
c
591
592
593
GO TO
I SALT
GO TO
I SALT
CNS(NC
CNG(NC
CNR(NC
3000
= 1
593
= 2
,1) =
,1 =
,1 -
0
0
0
.0
.0
.0
3000 CONTINUE
DO 7024 ND=1,NRN
DO 7024 NC=1,NEVSM
DO 7024 NB=1,NEVTM
RIS=PROB(NC,NB)*CNSR(NC,NB,ND)
7024 CONTINUE
c
£***** £
C
C***** RISKS CALCULATED
000 **************************************************
*
*
c *
Q***** QQ. QQQ *******************************************************
C
DO 6100 NC=1,NEVSM
RISKS(NC) = 0.0
RISKG(NC) = 0.0
6100 RISKR(NC) = 0.0
C
DO 6103 ND=1,NRNM
RRISKS(ND) = 0.0
RRISKG(ND) = 0.0
6103 RRISKR(ND) = 0.0
C
IRRSK = 0
C
259
-------
TRISKS = 0.0
TRISKG = 0.0
TRISKR = 0.0
C
DO 6101 NC=1,NEVSM
DO 6102 NB=1,NEVTM
RISKS(NC) = PROB(NC.NB) * CNS(NC,NB) + RISKS(NC)
RISKG(NC) = PROB(NC,NB) * CNG(NC,NB) + RISKG(NC)
RISKR(NC) = PROB(NC.NB) * CNR(NC,NB) + RISKR(NC)
DO 6102 ND=1,NRNM
RRISKS(ND) = PROB(NC,NB) * CNSR(NC,NB,ND) + RRISKS(ND)
RRISKG(ND) = PROB(NC,NB) * CNGR(NC,NB,ND) + RRISKG(ND)
6102 RRISKR(ND) = PROB(NC,NB) * CNRR(NC,NB,ND) + RRISKR(ND)
TRISKS = RISKS(NC) + TRISKS
TRISKG = RISKG(NC) + TRISKG
6101 TRISKR = RISKR(NC) + TRISKR
C
Q***** QQ. QQQ ***************************************************
C ' *
c***** PRINTOUTS - REMAINDER OF MAIN IS FORMAT AND WRITE STATEMENTS *
C ' *
Q***** QQ. QQQ *******************************************************
C
IF (NMAT .EQ. 1) GO TO 250
WRITE (6,72)
72 FORMAT (1H1)
WRITE (6,30) (DASH(I),I=1,33)
30 FORMAT (1H ,33A4/1H )
WRITE (6,31) (TITLE(I),I=1,20)
WRITE (6,31) (TITLE(I),1=21,40)
31 FORMAT (1H ,26X,20A4)
WRITE (6,32) (DASH(I),I=1,33)
32 FORMAT (1H /1H ,33A4)
C
WRITE (6,70) TRISKS,TRISKG
70 FORMAT (1H ,'*****',4X,'THE (P)(C) RISK FOR THIS DOSE1,
1 ' COMMITMENT PERIOD IS',1PE9.2,' FOR SOMATIC1,
2 ' EFFECTS, AND1,1PE9.2,' FOR GENETIC EFFECTS',
3 5X,'*****')
WRITE (6,71) (DASH(I),1=1,33)
71 FORMAT (1H ,33A4)
WRITE (6,74)
74 FORMAT (1H ,'*****',4X,'THE (P)(C) RISK BY EVENT IS:',90X,'*****')
DO 6110 I=1,NEVS
6110 WRITE (6,75) EVNT(I),(EDES(I,L),L=1,4),RISKS(I),RISKG(I)
75 FORMAT (1H ,'*****',23X,'EVENT',F6.1,2X,4A4,2X,1PE9.2,
1 ' FOR SOMATIC EFFECTS',5X,1PE9.2, ' FOR GENETIC EFFECTS',
2 5X,'*****')
WRITE (6,71) (DASH(I),1=1,33)
WRITE (6,76)
260
-------
76 FORMAT (1H ,'*****',4X,'THE (P)(C) RISK BY RADIONUCLIDE IS:',83X,
1 '******\
DO 6120 1=1,NRN
IF (RRISKS(I) .NE. 0.0) 60 TO 610
IRRSK = 1
GO TO 6120
610 WRITE (6,77) RNDS1(I),RNDS2(I),RRISKS(I),RRISKG(I)
77 FORMAT (1H ,'*****',42X,2A4,4X,1PE9.2,' FOR SOMATIC EFFECTS',5X,
1 1PE9.2,' FOR GENETIC EFFECTS',5X,'*****•)
6120 CONTINUE
IF (IRRSK .EQ. 1) WRITE (6,78)
78 FORMAT (1H ,'*****',43X,'CONTRIBUTION FROM ALL OTHER ',
1 'RADIONUCLIDES WAS ZERO',29X,'*****')
WRITE (6,71) (DASH(I),1=1,33)
C
DO 6001 K=1,NEVS
IF (NEVTT(K) .NE. 3) GO TO 651
6001 CONTINUE
GO TO 851
C
C
651 DO 6000 I=NPA,NPB,NPC
C
IF (I .EQ. 3 .OR. I .NE. NPA) GO TO 652
WRITE (6,33
33 FORMAT (1H
WRITE (6,34
34 FORMAT (1H ,'EACH ENTRY IN THE FOLLOWING TABLES REPRESENTS THE ',
1 'FOLLOWING DATA:'//
21H ,5X, '1. THE TOTAL NUMBER OF HEALTH EFFECTS FROM ONE ',
3 'SUCH EVENT INCURRED IN THIS DOSE COMMITMENT PERIOD.'/
41H ,5X, '2. THE RADIONUCLIDE CONTRIBUTING THE MOST HEALTH ',
5 'EFFECTS WITHIN THIS TOTAL.1/
61H ,5X, '3. THE PROBABILITY OF AT LEAST ONE EVENT OF THIS ',
7 'TYPE OCCURRING WITHIN THE TIME PERIOD REPRESENTED ',
8 'BY THIS EVENT TIME1)
WRITE (6,33)
GO TO 160
C
652 IF (IRLMT .EQ. 1) GO TO 653
WRITE (6,33)
WRITE (6,39)
39 FORMAT (1H ,'EACH ENTRY IN THE FOLLOWING TABLES REPRESENTS THE ',
1 'FOLLOWING DATA:1//
21H ,5X, '1. THE TOTAL RELEASE RATIO FROM ONE ',
3 'SUCH EVENT INCURRED IN THIS DOSE COMMITMENT PERIOD.'/
41H ,5X, '2. THE RADIONUCLIDE CONTRIBUTING THE LARGEST PART ',
5 'OF THIS RELEASE RATIO.1/
61H ,5X, '3. THE PROBABILITY OF AT LEAST ONE EVENT OF THIS ',
7 'TYPE OCCURRING WITHIN THE TIME PERIOD REPRESENTED ',
8 'BY THIS EVENT TIME')
261
-------
WRITE (6,33)
GO TU 160
C
653 WRITE (6,33)
WRITE (6,42)
42 FORMAT (1H ,'EACH ENTRY IN THE FOLLOWING TABLES REPRESENTS THE ',
1 'FOLLOWING DATA:1//
21H ,5X, '1. THE TOTAL NUMBER OF CURIES RELEASED FROM ONE ',
3 'SUCH EVENT INCURRED IN THIS DOSE COMMITMENT PERIOD.'/
41H ,5X, '2. THE RADIONUCLIDE CONTRIBUTING THE MOST ',
5 'CURIES WITHIN THIS TOTAL.1/
61H ,5X, '3. THE PROBABILITY OF AT LEAST ONE EVENT OF THIS ',
7 'TYPE OCCURRING WITHIN THE TIME PERIOD REPRESENTED ',
8 'BY THIS EVENT TIME')
WRITE (6,33)
C
160 IF (I .NE. 1) GO TO 161
DO 6061 J=l,6
b061 HELAB(J) = SOMLAB(J)
GO TO 165
161 IF (I .NE. 2) GO TO 162
DO 6062 0=1,6
6062 HELAB(J) = GENLAB(J)
GO TO 165
162 IF (IRLMT .EQ. 1) GO TO 163
DO 6063 J=l,6
6063 HELAB(J) = RROLAB(J)
GO TO 165
163 DO 6064 J=l,6
6064 HELAB(J) = CURLAB(J)
165 NSA = 1
C
DO 7000 J=1,NPRT
C
WRITE (6,30) (DASH(L),L=1,33)
WRITE (6,35) NTA,NTB,(HELAB(L),L=1,6)
35 FORMAT (1H ,3X,'DOSE COMMITMENT PERIOD = ',17,' YEARS TO ',17,
1 ' YEARS',47X.6A4)
WRITE (6,36)
36 FORMAT (1H /1H ,60X,'EVENT TIMES'/1H )
C
NFC = NOUT(J)
NFCC = 2 * NFC
NFA = NOUT(J) - 3
IF (NFA .LT. 1) NFA = 1
NSB = NSA + NFC - 1
FMTA(4) = HFA(NFA)
WRITE (6.FMTA) (NENTT(L),L=NSA,NSB)
WRITE (6,41) (STARS(L),L=1,29)
41 FORMAT (17X,29A4/1H ,16X,'*')
FMTC(7) = HFC(NFA)
262
-------
IF (TEVNT(NSB) .61. TEDC(NA)) GO TO 170
/
FMTB(5) = HFB(NFC.NFA)
FMTB(8) = BLANKS
FMTB(9) = BLANKS
FMTB(10)= BLANKS
DO 8000 K=1,NEVS
•»
IF (NEVTT(K) .EQ. 3) GO TO 8000
IF (I .NE. 1) GO TO 175
WRITE (6,FMTB) (EVENT(L),L=1,4),(CNS(K,L),L=NSA,NSB)
DO 8001 M=1,NFC
NRA = NRSMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 172
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDSZ(NRA)
GO TO 8001
172 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8001 CONTINUE
GO TO 176
175 IF (I .NE. 2) GO TO 174
WRITE (6,FMTB) (EVENT(L),L=1,4),(CNG(K,L),L=NSA,NSB)
DO 8002 M=1,NFC
NRA = NRGMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 173
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDS2(NRA)
GO TO 8002
173 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8002 CONTINUE
GO TO 176
174 WRITE (6,FMTB) (EVENT(L),L=1,4),(CNR(K.L),L=NSA,NSB)
DO 8006 M=1,NFC
NRA = NRRMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 171
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDS2(NRA)
GO TO 8006
171 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8006 CONTINUE
176 WRITE (6.FMTC) EVNT(K),(RT(L),L=1,NFCC)
WRITE (6.FMTB) (EDES(K.L),L=1,4),(PROB(K,L),L=NSA,NSB)
WRITE (6,37)
37 FORMAT (1H ,16X,'*')
8000 CONTINUE
WRITE (6,71) (DASH(L),L=1,33)
263
-------
NSA = NSB +1
IF (TEVNT(NSA) .61. TEDC(NA)) GO TO 6000
GO TO 7000
C
170 FMTB(8) = AFORMA
FMTB(IO) = AFORMB
DO 8003 L=NSA,NSB
IF (TEVNT(L) .LE. TEDC(NA)) GO TO 8003
MFD = L - NSA
IF (NFD .LT. 1) NFD = 1
NFE = NFD + 1
NFF = NFC - NFD
FMTB(5) = HFB(NFD.NFA)
FMTB(9) = HFB(NFF,NFA)
DO 8005 K=NFE,NFC
RT(2*K-1) = DASH(i;
8005 RT(2*K) = DASH(1,'
GO TO 177
8003 CONTINUE
C
177 DO 8100 K=1,NEVS
C
IF (NEVTT(K) .EQ. 3) GO TO 8100
IP = 1
DO 8201 M=NSA,NSB
PROBT(IP) = PROB(K.M)
8201 IP = IP + 1
DO 8202 NhNFE.NFC
8202 PROBT(M) = DDASH
C
IF (I .NE. 1) GO TO 178
IP = 1
DO 8203 I4=NSA,NSB
CNT(IP) = CNS(K,M)
8203 IP = IP + 1
DO 8204 M=NFE,NFC
8204 CNT(M) = DDASH
WRITE (6.FMTB) (EVENT(L),L=1,4),(CNT(L),L=1,NFC)
DO 8102 M-l.NFD
NRA = NRSMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 179
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDS2(NRA)
GO TO 8102
179 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8102 CONTINUE
GO TO 180
178 IF (I .NE. 2) GO TO 182
IP = 1
264
-------
DO 8205 M=NSA,NSB
CNT(IP) = CNG(K,M)
8205 IP = IP + 1
DO 8206 M=NFE,NFC
8206 CNT(M) = DDASH
WRITE (6.FMTB) (EVENT(L),L=1,4),(CNT(L),L=1,NFC)
DO 8103 M=1,NFD
NRA = NRGMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 181
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDS2(NRA)
GO TO 8103
181 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8103 CONTINUE
GO TO 180
182 IP = 1
DO 8207 M=NSA,NSB
CNT(IP) = CNR(K.M)
8207 IP = IP + 1
DO 8208 I4=NFE,NFC
8208 CNT(M) = DDASH
WRITE (6.FMTB) (EVENT(L),L=1,4),(CNT(L),L=1,NFC)
DO 8104 M=1,NFD
NRA = NRRMX(K,NSA+M-1)
IF (NRA .LE. 0) GO TO 183
RT(2*M-1) = RNDSl(NRA)
RT(2*M) = RNDS2(NRA)
GO TO 8104
183 RT(2*M-1) = BLANKS
RT(2*M) = BLANKS
8104 CONTINUE
180 WRITE (6.FMTC) EVNT(K),(RT(L),L=1,NFCC)
WRITE (6.FMTB) (EDES(K,L),L=1,4),(PROBT(L),L=1,NFC)
WRITE (6,37)
8100 CONTINUE
WRITE (6,71) (DASH(L),L=1,33)
GO TO 6000
7000 CONTINUE
C
6000 CONTINUE
C
DO 8501 K=1,NEVS
IF (NEVTT(K) .EQ. 3) GO TO 851
8501 CONTINUE
GO TO 259
C
851 WRITE (6,71) (DASH(I),1=1,33)
WRITE (6,81) NTIC.NTE
265
-------
81 FORMAT (1H /1H ,'FOR RELATIVELY LIKELY HUMAN INTRUSION EVENTS, ',
1 'MULTIPLE OCCURRENCES ARE ASSUMED. THE EVENT TIMES FOR ',
2 'EACH OCCURRENCE ARE EVENLY'/
3 1H , 'SPACED THROUGHOUT THE PERIOD FROM LOSS OF INSTITUTIONAL ',
4 'CONTROLS (',15,' YEARS) TO THE END OF THE EVENT ',
5 'PERIOD (',16,' YEARS).1/
6 1H , 'FOR EACH CASE, THE CONSEQUENCES ARE SUMMED OVER ',
7 'THESE MULTIPLE OCCURRENCES.'/1H )
WRITE (6,71) (DASH(I),1-1,33)
DO 8500 K=1,NEVS
C
IF (NEVTT(K) .NE. 3) GO TO 8500
NDCS = NDCASE(K)
WRITE (6,82) NDCS,EVNT(K),NTIC,(EDES(K,L),L=1,4),NTE
82 FORMAT (1H /1H ,5X,'EVENT1,15X,12,' CASES WERE RUN FOR ',
1 'DIFFERENT EXPECTED NUMBERS OF OCCURRENCES.1/
2 1H , 4X,F5.1,16X,'FROM',I6,' YEARS'/
3 1H , 4A4,9X,'TO ',16,' YEARS'/1H )
IF (IRLMT .NE. 1) WRITE (6,83)
83 FORMAT (1H ,21X,'NUMBER OF',9X,'PROBABILITY OF',
1 12X,'SOMATIC',16X,'GENETIC'/
2 1H , 20X,'OCCURRENCES',10X,'THIS NUMBER',
3 IX,2(9X,'HEALTH EFFECTS'),9X,'RELEASE RATIOS')
IF (IRLMT .EQ. 1) WRITE (6,85)
85 FORMAT (1H ,21X,'NUMBER OF',9X,'PROBABILITY OF',
1 12X,'SOMATIC',16X,'GENETIC'/
2 1H , 20X,'OCCURRENCES',10X,'THIS NUMBER',
3 IX,2(9X,'HEALTH EFFECTS'),8X,'CURIES RELEASED1)
WRITE (6,33)
C
DO 8510 1=1,NDCS
8510 WRITE (6,84) NDEVS(K.I),PROB(K,I),CNS(K,I),CNG(K,I),CNR(K,I)
84 FORMAT (1H ,23X,I3,15X,1PE9.2,3(14X,1PE9.2))
WRITE (6,32) (DASH(I),I=1,33)
C
8500 CONTINUE
C
C*a*a
C WRITE (6,72)
C WRITE 6,61 ((I,J,PROB(I,J),CNS(I,J),J=1,NEVT),I=1,NEVS)
C WRITE (6,63)
C WRITE (6,61) ((I,J,PROB(I,J),CNG(I,J),J=1,NEVT),I=1,NEVS)
C 61 FORMAT (4(1H ,2I3,1P2E9.2))
C 63 FORMAT (1H )
C*a*a
C
250 IF (NMAT .NE. 1) GO TO 259
IF (NA .EQ. 1) WRITE (6,72)
WRITE (6,32) (DASH(I),1-1,33)
266
-------
WRITE (6,64) NTA.NTB
64 FORMAT (1H ,4X,'THE (P)(C) RISK FOR THE DOSE COMMITMENT PERIOD ',
1 17,' YEARS TO ',17,' YEARS IS:1)
DO 6010 I=NPA,NPB,NPC
IF (I .EQ. 1) WRITE (6,65) TRISKS,(SOMLAB(L),L=1,6)
IF (I .EQ. 2) WRITE (6,65) TRISKG,(GENLAB(L),L=1,6;
IF (I .EQ. 3 .AND. IRLMT .NE. 1)
1 WRITE (6,65) TRISKR,(RROLAB(L),L=1,6)
IF (I .EQ. 3 .AND. IRLMT .EQ. 1)
1 WRITE (6,65) TRISKR,(CURLAB(L),L=1,6)
65 FORMAT (1H ,99X,1PE9.2,' FOR',6A4)
6010 CONTINUE
WRITE (6,32) (DASH(I),1-1,33)
C
259 IF (NTS .EQ. 1)
1 CALL PCPLOT (PROB,CNS,NCT,NEVS,NEVT,NEVSM,NEVTM,NPCA,NPCP,X,Y)
IF (NTG .EQ. 1)
1 CALL PCPLOT (PROB,CNG,NCT,NEVS,NEVT,NEVSM,NEVTM,NPCA,NPCP,X,Y)
IF (NTR .EQ. 1)
1 CALL PCPLOT (PROB,CNR,NCT,NEVS,NEVT,NEVSM,NEVTM,NPCA,NPCP,X,Y)
C
IF (IEX .EQ. 1) WRITE (6,73)
73 FORMAT (1H1.10X,'CAUTION: AN OVERFLOW CONDITION HAS OCCURRED IN ',
1 'FUNCTION EEXP IN THIS TIME PERIOD.1)
C
1000 CONTINUE
C
IF (NDOO .EQ. 1 .OR. NDOT .EQ. 1) GO TO 360
NDOT = 1
GO TO 350
C
360 WRITE (6,50)
50 FORMAT (1H //1H ,9X,'PROBLEM COMPLETED1)
C
IF (Nl .NE. 96) GO TO 371
C
WRITE (6,21)
DO 3012 I-l.NEVSM
3012 EVNT(I) = 0.0
NEVS = 0
DO 1235 I=1,NEVTM
DO 1235 J=1,NEVSM
FRATE(J.I) = 0.0
1235 PROB (J,I) = 0.0
GO TO 555
C
371 IF (Nl .NE. 97) GO TO 372
C
WRITE (6,21)
DO 4004 I-l.NRNM
267
-------
RNLD(I) = 0.0
RNLDl(I) = 0.0
RNLDX(I) = 0.0
RNQOl(I) = 0.0
RNQOX(I) = 0.0
4004 RNID(I) = 0.0
NRN = 0
I PATH = 0
IRLMT = 1
GO TO 555
C
372 IF (Nl .NE. 98) GO TO 370
WRITE (6,21)
GO TO 555
C
370 STOP 1000
END
268
-------
£***** QQ. QQQ *******************************************************
C ' *
C***** FUNCTIONS AND SUBROUTINES *
C *
£*********************************************************************
C
SUBROUTINE SMESS1
1 (RNLD,LAMG,LAMS,LAMR,TEV,T,MESS1N,MESSA,IEX)
C
REAL*4 LAMG,LAMS,LAMR,MESS1N,MESSA,MSN,M6N
C
A5N = - (RNLD + LAM6)
B6N = - (RNLD + LAMS + LAMR)
B4N = - (A5N + B6N)
C4N = A5N * B6N - LAMG * LAMR
C
CA = (B4N**2 - 4.0 * C4N)**0.5
C
M5N = (- B4N + CA) / 2.0
M6N = (- B4N - CA) / 2.0
C
CB = M6N - A5N
CC = M6N - MSN
CD = A5N - MSN
CE = MSN * (T - TEV)
CF = M6N * (T - TEV)
C
CE = EEXP (CE.IEX) - 1.0
CF = EEXP (CF.IEX) - 1.0
C
CG = CB * CE / (MSN * CCi
CH = CD * CF / (MSN * CC]
C
MESS1N = CG + CH
C
CI = - CD * CB / (LAMR * CC)
CJ = CE / MSN - CF / M6N
C
MESSA = CI * CJ
C
RETURN
END
269
-------
FUNCTION CINTA (S,DA,DB,VRCH,TRCH,WLR,DVV,I,IEX,VR)
C
60 TO (10,20), I
C
10 DK = VRCH + DA * TRCH + DB * TRCH**2.0 / 2.0
DC = WLR * S
DC = EEXP (-DC.IEX)
C
DD = DK - DA * S - DB * S**2.0 / 2.0
C
GO TO 30
20 DK = VR
DC = WLR * S
DC = EEXP(-DC.IEX)
C
DD = DK - DVV * S
C
30 CINTA = DC / DD
C
RETURN
END
270
-------
FUNCTION SMESSN (RNLD,LR,SF1,SF2,TAU1,TAU2,TDEL,T,IEX)
C
REAL*4 M1N,M2N
REAL LR
C
A1N = - (RNLD + SF1 + TAU1)
B2N = - (RNLD + SF2 + TAU2)
WN = - (RNLD + LR)
B3N = - (A1N + B2N)
C3N = A1N * B2N - (TAU1 * TAU2 + TAU2 * SF1)
C
CA = (B3N**2 - 4.0 * C3N)**0.5
C
M1N = (- B3N + CA) / 2.0
M2N = (- B3N - CA) / 2.0
C
CB = M1N * (T - TDEL)
CC = M2N * (T - TDEL)
CD = WN * (T - TDEL)
C
CB = EEXP (CBJEX) - 1.0
CC = EEXP (CC.IEX - 1.0
CD = EEXP (CDJEX) - 1.0
C
CE = (A1N - M2N) * CB / ((WN - M1N) * M1N)
CF = (A1N - M1N) * CC / ((WN - M2N) * M2N)
CG = (M2N - M1N) * (WN - B2N) * CD /
1 ((WN - M2N) * (WN - M1N) * WN)
C
SMESSN = (CE - CF + CG) / (M2N - M1N)
C
RETURN
END
FUNCTION QINTT (RNLD,LR,TDEL,T,IEX)
REAL LR
C
CA = - RNLD * TDEL
CB = - (RNLD + LR) * T + LR * TDEL
C
QINTT = EEXP (CA.IEX) - EEXP (CBJEX)
C
RETURN
END
271
-------
SUBROUTINE PCPLOT (P,C,NCT,NEVS,NEVT,NSM,NTM,NA,NP,X,Y)
C
DIMENSION X(NCT),Y(NCT),P(NSM,NTM),C(NSM,NTM)
C
REAL*8 X,Y,P,C,XSAVE1,XSAVE2,YSAVE1,YSAVE2
C
DATA IUNIT/10/
C
DO 1100 1=1,NCT
X(I) = 0.0
1100 Y(I) = 0.0
NNUM = 0
C
DO 1500 I=1,NEVS
DO 1000 L=1,NEVT
C
IF (P(I,L) .LE. 0.0) GO TO 1000
IF (C(I,L) .LE. 0.0) GO TO 1000
C
ITRIG = 0
NNUM = NNUM + 1
C
DO 2000 0=1,NCT
C
IF (ITRIG .EQ. 1) GO TO 100
IF (C(I,L) .LT. X(J)) GO TO 2000
C
XSAVE1 = X(J)
YSAVE1 = Y(J)
X(J) = C(I,L)
IF (0 .EQ. 1) GO TO 101
Y(J) = Y(J-l) + P(I,L)
IF (XSAVE1 .EQ. 0.0) GO TO 1000
ITRIG = 1
GO TO 2000
101 Y(J) = P(I,L)
IF (XSAVE1 .EQ. 0.0) GO TO 1000
ITRIG = 1
GO TO 2000
C
100 XSAVE2 = X(J)
YSAVE2 = Y(J)
X(J) = XSAVE1
Y(J) = YSAVE1 + P(I,L)
IF (XSAVE2 .EQ. 0.0) GO TO 1000
XSAVE1 = XSAVE2
YSAVE1 = YSAVE2
C
2000 CONTINUE
1000 CONTINUE
1500 CONTINUE
C
272
-------
DO 3000 I=1,NNUM
IF (Y(I) .LT. 0.04) 60 TO 3000
Y(I) = 1.0 - DEXP (-Y(I))
3000 CONTINUE
C
C*ot*
IF (NA .EQ. 1) GO TO 200
WRITE (6,10) NNUM,NCT,NEVS,NEVT
10 FORMAT (1H /1H ,10X,4I6)
WRITE (6,12)
C WRITE (6,13) ((I,J,P(I,J),C(I,J),J=1,NEVT),I=1,NEVS)
C 13 FORMAT (4(1H ,2I3,1P2E9.2))
11 FORMAT (1H .1P14E9.2)
WRITE (6,12)
WRITE (6,11) (Y(I),X(I),I=1,NNUM)
12 FORMAT (1H )
C*a*
C
200 IF (NP .EQ. 1) GO TO 300
DO 4000 I=1,NNUM
4000 WRITE (IUNIT) Y(I),X(I)
REWIND IUNIT
IUNIT = IUNIT + 1
C
300 RETURN
END
273
-------
SUBROUTINE ERROR (IN,NA,NB,F,A,IX)
C
DIMENSION F(6),A(4)
C
IF (IN .GT. 5) GO TO 100
C
WRITE (6,10) IN,NA,NB,(F(I),1=1,6),(A(I),1=1,4)
10 FORMAT (1H ,'ERROR ',I2,10X,I2,2X,I2,6(2X,1PE10.2),2X,4A4)
WRITE (6,11)
11 FORMAT (1H ,10X,'THE ABOVE INPUT CARD IS INCORRECT1)
IF (IX .NE. 1) IX = 1
RETURN
C
100 WRITE (6,10) IN,NA,NB,(F(I),I=1,6),(A(I),I=1,4)
STOP 1002
END
FUNCTION BINOM (TB,R,P)
C
IF (R .EQ. 0.0) GO TO 300
C
Y = TB / R
X = (1 - P)**Y
Z = 1.0
JR = R
C
DO 100 1=1,JR
Z = (TB + 1 - I) * Z * P * X / ((R + 1 - I) * (1 - P))
100 CONTINUE
GO TO 200
C
300 Z = (1 - P)**TB
C
200 BINOM = Z
C
RETURN
END
274
-------
FUNCTION EQUAL (VY,VAQ,NT,TMAX,TMIN,IEX)
C
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
IMIN = TMIN
IF (IMIN .EQ. 0) IMIN = 1
IMAX = TMAX
TIME = -1.0
C
DO 100 I=IMIN,IMAX,NT
TI = I
VT = VOLFLO(IEX,TI)
VT = VY * VT
IF (VT .61. VAQ) GO TO 100
TIME = I
GO TO 200
100 CONTINUE
C
IF (TIME .EQ. -1.0) TIME = TMAX
C
200 EQUAL = TIME
C
RETURN
END
275
-------
FUNCTION ENT1A (TF,TI,VAQ,CL,LR,VR,TEVNT,RNLD.RNQO.IEX)
REAL LR
All = (VAQ / VR) - LR
AL2 = RNLD + VAQ / VR
Al = LR * CL
Al = EEXP (Al.IEX)
Al = Al * RNQO / VR
El = Al * LR / AL1
Gl = VAQ * TEVNT / VR
G2 = -LR * CL
G3 = AL1 * TEVNT
PI = AL2 - AL1
P3 = El / PI
Ql = -TI * AL2
Q2 = -TF * AL2
Rl = - PI * TF
R2 = - PI * TI
P4 = P3 * VAQ
P4 = ALOG (P4)
P5 = El * VAQ / AL2
P5 = ALOG (P5)
P6 = Al * VAQ / AL2
P6 = ALOG (P6)
SI = P4 + Rl
S2 = P4 + R2
S3 = Q2 + P5 + G3
S4 = Q2 + P6 + Gl + G2
S5 = Q2 + P6 + G3
S6 = Ql + P5 + G3
S7 = Ql + P6 + Gl + G2
S8 = Ql + P6 + G3
SI = EEXP (Sl.IEX)
S2 = EEXP (S2.IEX)
S3 = EEXP (S3.IEX)
S4 = EEXP (S4.IEX)
S5 = EEXP (S5.IEX)
S6 = EEXP (S6,IEX)
S7 = EEXP (S7.IEX)
S8 = EEXP (S8.IEX)
ENT1A =- SI + S2 + S3 - S4 + S5 - S6 + S7 - S8
RETURN
END
276
-------
FUNCTION ENTCO (VY,RNSOL,TF,TI,IEX)
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
VA = 0.0
VB = 0.0
DO 1 I = 1,NCOF
AX = - ALPH(I) * TF
BX = - ALPH(I) * TI
VA = VA + EEXP(AX,IEX) * CVA(I) / ALPH(I
VB = VB + EEXP(BX,IEX) * CVA(I) / ALPH(I
1 CONTINUE
Fl = VB - VA
F2 = CVC * (TF - TI)
ENTCO = (Fl + F2) * RNSOL * VY
RETURN
END
FUNCTION ENTANK (AA,K1,KPRIM,RNLD,RNQO,VR,TF,TI,LR,CL,IEX,NN)
C
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
REAL KPRIM,Kl.LR
C
Al = LR * CL
Cl = RNQO / VR * (Kl - KPRIM * TI)
C2 = EEXP (Al.IEX)
C3 = RNQO * KPRIM / VR
IF (LR .EQ. 0.0) C2 = 0.0
GA1 = RNLD + LR
X = 0.
H = (TF - TI) / NN
C
YN = FUNC(AA,C1,C2,C3,GA1,TF,RNLD,IEX)
YO = FUNC(AA,C1,C2,C3,GA1,TI,RNLD,IEX)
C
DO 100 I = 2,NN,2
IF (I .EQ. NN) GO TO 200
T = TI + I * H
Z = FUNC(AA,C1,C2,C3,GA1,T,RNLD,IEX)
X=X+2. *Z
200 T = TI + (1-1) * H
Z = FUNC(AA,C1,C2,C3,GA1,T,RNLD,IEX)
X = X + 4.* Z
100 CONTINUE
C
ENTANK = ( YO + YN + X ) * H /3.
C
RETURN
END
277
-------
FUNCTION FUNC (AA,C1,C2,C3,GA1,T,RNLD,IEX)
Fl = Cl + C3 * T
F2 = - RNLD * T
F2 = EEXP(F2,IEX)
F3 = - GA1 * T
F3 = C2 * EEXP(F3,IEX)
F4 = ( F2 - F3 ) * Fl
Gl = AA * VOLFLO(IEX,T)
G3 = F4 * Gl
FUNC = G3
RETURN
END
FUNCTION TANK (VR,LR,CL,T,RNQO,RNLD,IEX)
C
REAL LR
C
A = -LR * (T - CL)
B = -RNLD * T
A = EEXP (A.IEX)
B = EEXP (B,IEX)
C = (1.0 - A) * B
C
TANK = (C * RNQO) / VR
C
RETURN
END
278
-------
FUNCTION TDELI (X,TS,POR,XK,IEX,TB)
C
DIST = 0.0
T = TS
ITB = TB
DELT = 1.0
C
DO 1000 1=1,ITB
C
CD = XK * VOLFLO(IEX,T)
C
DDEL = (CD / POR) * DELT
DIST = DIST + DDEL
C
IF (DIST .61. X) GO TO 100
T = T + DELT
C
1000 CONTINUE
C
100 TDELI = T - TS
C
RETURN
END
FUNCTION TDELKI (X,TS,POR,XK1,XKPR,IEX.TB)
C
DIST = 0.0
T = TS
ITB = TB
DELT = 1.0
C
DO 1000 1=1,ITB
C
CA = VOLFLO(IEX,T)
CB = XK1 * CA
CE = XKPR * T * CA
CG = CB + CE
C
DDEL = (CG / POR) * DELT
DIST = DIST + DDEL
C
IF (DIST .GT. X) GO TO 100
T = T + DELT
1000 CONTINUE
C
100 TDELKI = T - TS
C
RETURN
END
279
-------
FUNCTION EEXP (X,IX)
C
IF (X .61. -100.0) GO TO 10
EEXP = 0.0
RETURN
C
10 IF (X .LT. 172.00) GO TO 20
EEXP = 4.0E75
IX = 1
RETURN
C
20 EEXP = EXP (X)
RETURN
END
FUNCTION DTANK (V,LR,CL,T,FR,RNQO,RNLD,RNQ01,RNLD1,IEX)
C
REAL LR
C
A = RNLD * RNQO * FR / V
B = CL * LR
CO = A / (RNLD - RNLD1)
Al = -RNLD1 * T
Al = EEXP (Al.IEX)
Bl = -RNLD * T
Bl = EEXP (Bl.IEX) * CO
Cl = RNQ01 * FR / V
C3 = Cl + CO
C2 = - LR * T
C2 = EEXP(C2,IEX)
B = EEXP(B,IEX)
C
X = - C3 * Al * B * C2 + ( CO + Cl * B ) * Al
C
Y = Bl * ( B * C2 - 1. )
C
DTANK = X + Y
C
RETURN
END
280
-------
FUNCTION TFAC3 (RNLD,LAMS,TEV,T,IEX)
C
REAL*4 LAMS
C
CA = RNLD + LAMS
CB = - CA * (T - TEV)
CB = EEXP (CB.IEX)
C
TFAC3 = (1.0 - CB) / CA
C
RETURN
END
FUNCTION TFAC4 (RNLD,LAMS,LAMR,TEV,T,IEX)
C
REALM LAMS,LAMR
C
CA = RNLD + LAMS + LAMR
CB = - CA * (T - TEV)
CB = EEXP (CB,IEX)
C
TFAC4 = LAMR * (1.0 - CB) / CA
C
RETURN
END
FUNCTION TFAC5 (RNLD,LAMS,LAMR,TEV,T,IEX)
C
REAL*4 LAMS,LAMR
C
CA = RNLD + LAMS
CB = - CA * (T - TEV)
CB = EEXP (CB.IEX)
CC = (1.0 - CB) / CA
C
CD = RNLD + LAMS + LAMR
CE = - CD * (T - TEV)
CE = EEXP (CE.IEX)
CF = (CE - 1.0) / CD
C
TFAC5 = CC + CF
C
RETURN
END
281
-------
FUNCTION SALT(VY,LR,VR,TE,TItTFfNN,IEX,CL,RNQO,RNLD,VAQ)
INTEGER IER
REAL LR,DCADRE,AF1,A,AERR,RERR,ERROR,C
EXTERNAL API
COMMON /BLOCK3/ VAR,VAY,P1,C1,D1,E1,F1,IEX1
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
VAR = VR
VAY = VY
IEX1 = IEX
X=0.0
CX = 0.0
NL = NN + 1
CC = VY * CVC
P1=-LR+CC/VR
A1=-LR*CL
B1=-LR*TE
E1=(LR*RNQO/VR)*EEXP(-A1,IEX)
R1=(RNQO/VR)
R1=ALOG(R1)
Wl = VAQ / VR
W2 = VAQ / VR -LR
W3 = RNLD + VAQ / VR
E2 = El / W2
E2 = ALOG(E2)
G1=-RNLD-CC/VR
W4 = - 61 * TI
W5 = E2 - W3 * TI
W6 = W2 * TI
W7 = W2 * TE
W8 = Rl - Al + Wl * TE - W3 * TI
B2=EEXP(B1,IEX)
A3=EEXP(A1,IEX)
DO 2 I=1,NCOF
AX = - ALPH(I) * TI
CX = CX - CVA(I) * EEXP(AX.IEX) * VY / ( VR * ALPH(I))
CONTINUE
A4 = CX
H3 = (TF - 110. - TI) / (NN - 20)
H4 = 10.
H2 = 1.
DO 100 I = 1,NL
TI = I - 1
IF (I .61. 11) H2 = H4
IF I .GT. 11) TI = 10. * (I - 11) + 10.
IF (I .GT. 21) H2 = H3
IF (I .GT. 21) TI = 110. + H2 * (I - 21)
T = TI + TI
XA=G1*T
CX = 0.0
282
-------
DO 1 J=1,NCOF
AX = - ALPH(J) * T
CX = CX + CVA(J) * EEXP(AX.IEX) * VY / ( VR * ALPH(J))
1 CONTINUE
F1=XA+CX
F2 = Fl + W5 + W6 + W4 + A4
F2 = EEXP(F2,IEX)
F3 = Fl + W5 + W7 + W4 + A4
F3 = EEXP(F3,IEX)
F4 = F1+ W8 + W4 + A4
F4=EEXP(F4,IEX)
H1=F4*(A3-B2)+F2-F3
RERR = .095
AERR = 0.0
Y = DCADRE(AF1,TI,T,AERR,RERR,ERROR,IER)
IF (IER .LT. 100) GO TO 200
200 CT = Y + HI
VT = VY * VOLFLO(IEX,T)
FIX1 = CT * VT * H2
IF (I .EQ. 1 .OR. I .EQ. NL) 60 TO 101
IF (I .EQ. 21) GO TO 300
IF (I .EQ. 11) GO TO 400
FIX1 = 4. * FIX1
IF ((MOD(I,2)) .EQ. 0) GO TO 101
FIX1 = FIX1 / 2.
GO TO 101
300 FIX1 = FIX1 * (10. + H3) / H2
GO TO 101
400 FIX1 = FIX1 * (1. +10.) / H2
101 CONTINUE
100 X = X + FIX1
IEX = IEX1
SALT = X / 3.
RETURN
END
283
-------
FUNCTION AF1(S)
REAL S
COMMON /BLOCKS/ VAR,VAY,P1,C1,D1,E1,F1,IEX1
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
AX = 0.0
DO 1 I = l.NCOF
BX = - ALPH(I) * S
AX = AX - EEXP(BX,IEX1) * CVA(I) * VAY / ( VAR * ALPH(I))
1 CONTINUE
Cl = AX
Al = PI * S + Cl
A2=ALOG(E1)
A3=A1+A2+F1
AF1 = EEXP(A3,IEX1)
RETURN
END
FUNCTION ROOT (A,B,C)
C
IF (A .NE. 0.) GO TO 100
ROOT = - C / B
100 CA = B**2.0 - 4.0 * A * C
CA = SQRT (CA)
ROOT = (CA - B) / (2.0 * A)
RETURN
END
FUNCTION VOLFLO(IEX.T)
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
VX = 0.0
DO 1 1= l.NCOF
AX = -ALPH(I) * T
VX = VX + CVA(I) * EEXP(AX.IEX)
1 CONTINUE
VOLFLO = VX + CVC
RETURN
END
284
-------
FUNCTION VTSOL (TT,IEX,VAQ,kNSOL,RNLDX,RNQOX,VR,CLIFE,
1 TFAIL,TVAQ,AREA,Kl.LR)
COMMON /BLOCK2/ CVA(10),ALPH(10),CVC,NCOF
REAL LR,K1
X = VAQ * RNSOL / RNLDX
Y = RNQOX
A = RNLDX *TFAIL
B = RNLDX * TVAQ
Al = X * EEXP(AJEX) + Y
Z = VR * RNSOL
IF ( TFAIL .EQ. CLIFE ) Y = Y + VR * RNSOL * EEXP(RNLDX*CLIFE,IEX)
IF(TFAIL .GE. TVAQ) ACTVAQ = Y * EEXP(-AJEX) - VR * RNSOL
XI = AREA * Kl * RNSOL
C = RNLDX * TT
Yl = CVC / RNLDX
VX = 0.
AX = 0.0
BX = 0.0
DO 100 I=1,NCOF
VX = VX + CVA(I) * (EEXP(-ALPH(I) * TT,IEX))
A4 = ALPH(I) - RNLDX
AX = AX + CVA(I) * EEXP(-ALPH(I) * TVAQ,IEX) / A4
BX = BX + CVA(I) * EEXP(-ALPH(I) * TT.IEX) / A4
100 CONTINUE
VX = ( VX + CVC ) * XI
A = Al * EEXP(-B,IEX) - X - AX * XI + Yl * XI
IF ( TVAQ .LE. TFAIL ) A = Y * EEXP(-B.IEX) + XI * Yl - XI * AX
ACT = A * EEXP( B-C , IEX ) + XI * BX - Z - XI * Yl
GT = RNLDX * RNSOL * VR + VX
GT = GT / ACT
IF (GT .GE. LR) VTSOL = TT
IF (GT .LT. LR) VTSOL = -1.0
RETURN
END
SUBROUTINE UERTST(IER.X)
IF (IER .GT. 66) WRITE(6,100) IER
100 FORMATUH ,'IER = ' ,13,' (ANSWERS MAY NOT BE WITHIN THE SPECIFIED
1ERROR RANGE DUE TO AN ILL BEHAVED FUNCTION)1)
RETURN
END
285
-------
FUNCTION VQSOL(T1,IEX,VAQ,RNSOL,RNLDX,RNQOX,VR,CLIFE,
1 TFAIL,TVAQ,AREA,K1,LR)
REAL LR,K1
X = RNSOL * (RNLDX * VR + VAQ)
Y = RNQOX
Z = EEXP(RNLDX * TFAIL,IEX) * VAQ * RNSOL / RNLDX
U = EEXP(-RNLDX*T1,IEX)
ACTVAQ = (Y + Z) * U - X / RNLDX
FTVAQ = X / ACTVAQ
IF (FTVAQ .GE. LR) 60 TO 100
VQSOL = -1.0
RETURN
100 VQSOL =T1
RETURN
END
FUNCTION AF2(S)
REAL S,LR,K1
COMMON /BLOCK1/ El,TAX,V,AREA(10),K1(10),RNLDX(20),NC,ND,Y1X,IEX
X = ALOG(El)
Y = -XMU(TAX,IEX,V,AREA(NC),K1(NC),RNLDX(ND))
Z = XMU(S,IEX,V,AREA(NC),K1(NC),RNLDX(ND))
W = -Y1X * S
VM=X+Y+Z+W
AF2 = EEXP(VM,IEX)
RETURN
END
FUNCTION XMU(T,IEX,VR,AREA,Kl,RNLDX)
COMMON /BLOCK2/ CVA(IO),ALPH(10),CVC,NCOF
REAL Kl
VA = 0.0
DO 100 I = 1,NCOF
VA = VA - CVA(I) * EEXP(-ALPH(I) * T , IEX ) / (ALPH(I) * VR)
100 CONTINUE
VA = (VA + T * CVC / VR ) * AREA * Kl + RNLDX *T
XMU = VA
RETURN
END
286
-------
FUNCTION CONVT(TA,VAQ,RNSOL,XRNLDX,RNQOX,XVR,CLIFE,
1 TFAIL,TVAQ,XAREA,XK1,LR)
INTEGER IER
REAL LR,DCADRE,AF2,A,AERR,RERR,ERROR,C,K1
EXTERNAL AF2
COMMON /BLOCK1/ El,TAX,V,AREA(10),K1(10),RNLDX(20),NC,ND,Y1X,IEX
TT = TA
TAX = TT
Y1X = LR + XRNLDX
Al = -LR * CLIFE
Bl = -LR * TFAIL
El = (LR * RNQOX / XVR) * EEXP(-A1,IEX)
Rl = (RNQOX / XVR)
R1=ALOG(R1)
Wl = VAQ / XVR
W2 = VAQ / XVR - LR
W3 = XRNLDX + VAQ / XVR
E2 = El / W2
E2 = ALOG(E2)
W5 = E2 - W3 * TVAQ
W6 = W2 * TVAQ
W7 = W2 * TFAIL
W8 = Rl - Al + Wl * TFAIL - W3 * TVAQ
B2=EEXP(B1,IEX)
A3=EEXP(A1,IEX)
XI = XMU(TVAQ,IEX,XVR,XAREA,XK1,XRNLDX)
X2 = XMU(TT,IEX,XVR,XAREA.XK1,XRNLDX)
X3 = EEXP(X1 - X2 ,IEX)
CTVAQ = EEXP(W5 + W6.IEX) - EEXP(W5 + W7.IEX)
CTVAQ = CTVAQ + EEXP(W8,IEX) * (A3-B2)
HI = CTVAQ * X3
RERR = .095
AERR = 0.0
Y = DCADRE(AF2,TVAQ,TT,AERR,RERR,ERROR,IER)
IF (IER .LT. 100) GO TO 200
200 CT = Y + HI
CONVT = CT
RETURN
END
287
-------
FUNCTION CONVQ (TT,IEX,VAQ,RNSOL,RNLDX,RNQOX,VR,CLIFE,
1 TFAIL,TVAQ,AREA,K1,LR)
REAL LR,K1
All = (VAQ / VR) - LR
AL2 = RNLDX + VAQ / VR
AL3 = - LR - RNLDX
A2 = LR * CLIFE
Al = RNQOX / VR
El = Al * LR / AL1
Gl = VAQ * TFAIL / VR
G2 = -LR * CLIFE
G3 = AL1 * TFAIL - AL2 * TT
Yl = El
Y2 = EEXP(AL3*TT+A2,IEX) - EEXP(G3+A2,IEX)
Y3 = Al
Y4 = 1.- EEXP(-LR * TFAIL+A2.IEX)
Y5 = EEXP(-AL2 * TT+G1.IEX)
CT = Yl * Y2 + Y3 * Y4 * Y5
CONVQ = CT
RETURN
END
FUNCTION CONHYD(TT,IEX,VAQ,RNSOL,RNLDX,RNQOX,VR,CLIFE,
1 TFAIL,TVAQ,AREA,K1,LR)
REAL LR.K1
Al = CVC * AREA * Kl / VR
A4 = VAQ / VR
IF ( Al .GT. A4 ) Al = A4
A2 = LR * RNQOX * EEXP(LR * CLIFE,IEX) / VR
A3 = Al - LR
TCUT = 10000.
IF(TVAQ .GE. TCUT) CX = CONVQ(TCUT,IEX,VAQ,RNSOL,RNLDX,RNQOX,
1 VR,CLIFE,TFAIL,TVAQ,AREA,Kl.LR)
IF(TVAQ .LT. TCUT) CX = CONVT(TCUT,VAQ,RNSOL,RNLDX,RNQOX,
1 VR,CLIFE,TFAIL,TVAQ,AREA,Kl.LR)
XI = EEXP(-(RNLDX + LR) * TT.IEX)
X2 = RNLDX + Al
X3 = - X2 * TT + A3 * TCUT
X4 = EEXP(X3,IEX)
X5 = EEXP(X2 * (TCUT - TT),IEX)
CONHYD = A2 * (XI - X4) / A3 + CX * X5
RETURN
END
288
-------
FUNCTION TSOLDR (VR,LR,CLIFE,RNQO,RNLD,FTANK,TB,TI,RNSOL,IEX)
REAL LR
TSOL = TB
FR = FTANK * RNQO
A = VR * RNSOL
B = (FR + VR * RNSOL * EEXP(RNLD*CLIFE,IEX))
C = RNLD * A
DEL = ( TB - TI ) / 100.
NN = 100
DO 4 I = 1,NN
T = TI + I * DEL
CA = TANK(VR,LR,CLIFE,T,FR,RNLD,IEX)
IF ( CA .GE. RNSOL ) GO TO 5
4 CONTINUE
GO TO 3
5 DO 1 I = 1,NN
T = TI + I * DEL
ACT = B * EEXP(-RNLD*T,IEX) - A
FT = C / ACT
IF ( FT .GE. LR ) TSOL = T
IF ( FT .GE. LR ) GO TO 2
1 CONTINUE
2 TSOLDR = TSOL
RETURN
3 TSOLDR = -1
RETURN
END
289
-------
Appendix F
INPUT GUIDt FOR REPRISK
291
-------
INPUT GUIDE FOR REPOSITORY RISK CODE (REPRISK)
January 21, 1981
Input for this code consists of one job control card, a variable number of
alphanumeric title cards, and a variable number of standardized format
cards which enter the remainder of the data required for a problem.
With some exceptions, the standardized format cards may be entered in any
order; exceptions are indicated in this guide. The job control card must
oe the first input card, followed by the title cards, and the standardized
format cards.
In many cases, the code will assume values or instructions if no quantity
is entered for a particular parameter. These default options are also
indicated below.
The program dimension statements may be changed (and the program
recompiled) to treat problems of different sizes. The amount of allowable
input is affected by these dimensions, and the appropriate limiting
parameters are indicated in this guide. These parameters are the
following, which are clearly indicated in the dimension statements of the
program:
NDCTM Maximum numoer of dose commitment times
NEVTM Maximum number of event times
NEVSM Maximum number of events
NRNM Maximum number of radionuclides
If requested, the code will write data files to create "complementary
cumulative distribution function (ccdf)" plots of the results of a run
(see Appendix G). The number of files written by each run is determined
by four input variables. These variables are indicated in this input
guide by a "plot file" designation (see pages 294, 295, and 298) together
with instructions on associating a number with each variable. The product
of these four "plot file" numbers determines how many files will be
written. Appropriate file-handling control cards must be included for
this number of files for the run to oe completed.
For further information contact: Dan Egan (703) 557-8610
Office of Radiation Programs (ANR-460)
U. S. Environmental Protection Agency
Washington, DC 20460
293
-------
JOB CONTROL CARD (Format 1615) - CONTINUED ON FOLLOWING PAGE
NLINE Number of title cards to be read (0 to 6)
IREP Type of repository strata to be considered
1 = salt
2 = non-salt
NSG Tnree types of consequence calculations are performed
by the code:
Somatic health effects (S)
Genetic health effects (G)
"Release Ratios" (R)
("release ratios" become curies released if
no release limits are entered on the
radionuclide data cards)
This variable is an index to determine which
consequences will be displayed in the detailed output,
including ccdf plots. The following table indicates
the various combinations ("x"), and also shows
appropriate "plot file" numbers for determining the
number of ccdf plots
"plot file"
S G R number
1
I
1
2
2
2
3
NINT Index for type of input reproduction selected
1 = unformatted "echo" of input cards
2 = descriptive display of input (not yet available)
Default = 2
NMAT Index to determine printer output format
1 = print summed risks for each problem
2 = print matrix of consequences and probabilities
for each event and event time
Default = 2
1 =
2 =
3 =
4 =
5 =
6 =
7 =
X
—
_
X
X
—
X
Default
_
X
—
X
—
X
X
= 3
_
—
X
_
X
X
X
294
-------
JOB CUNTRUL CARD (Format 1615) - CONTINUED (see previous page)
NPCA Index to determine whether raw data for pc plots are
printed
1 = do not print
2 = print
Default = 2
NPCP Index to determine whether ccdf plot files are
prepared "plot file" no.
1 = do not write plot files 0
2 = write plot files 1
Default = 1
NDOO Index to determine whether cumulative (0-A, 0-B, etc.)
and/or incremental (0-A, A-B, etc.) dose commitments
are calculated."plot file" no.
1 = cumulative 1
2 = incremental 1
3 = both cumulative and incremental 2
Default = 1
NN Indicates tne number of time steps used in functions
witn numerical integration techniques. Must be an even
number (recommended between 20 and 50)
NT Indicates the time step size used in the functions
which calculate the groundwater transit times from the
repository to the overlying aquifer.
(Recommendation, set to 1)
IDRILL Index to determine whether aquifer releases are
considered for drilling events which do not hit canister
1 = do not consider
2 = consider
Default = 1
295
-------
TITLE CARDS (Format 20A4)
Up to six cards may be used for entering title.
First two cards will be used to title all sets of matrix output.
Remaining title cards will only be printed at introduction of problem.
Number of title cards must be indicated on Job Control Card as NLINE.
STANDARDIZED FORMAT CARDS (Format 212, 6E10.4.4A4)
These cards enter tne remainder of the data for a proolem. The first
integer field enters the "type" of card to identify the data being
provided. Thus, a card with a "10" in first field is a "Type 10" card.
This nomenclature will be used in the remainder of this guide.
The fields of tnis card are designated Nl, N2, F(l through 6), and
A(l tnrougn 4). The entries on tne following sheets correspond to these
designations.
296
-------
TYPE 10 CARD Dose Integration Time Period
Nl 10
N2
F(l) TDINT End of Dose Integration Time Period (years), which
is assumed to start at time = zero.
This entry is intended to allow integration of
health effects over a longer period that the dose
commitment time periods defined on the Type 11
cards.
This entry must be larger than any of the dose
commitment time periods.
Default: If no entry is made, doses are integrated
to the end of the dose commitment time period(s)
established by the Type 11 cards.
297
-------
TYPE 11 CARDS Dose Commitment Time Periods
Ml 11
N2
F(l - 6) TEDC(I) End of Dose commitment time periods (years), which
are assumed to start at time = zero or the next
smaller dose commitment time period—depending
upon the entry for NDOO on the Job Control Card.
Up to NDCTM times may be entered to define dose
commitment periods for consideration of release
events.
Tnese times may oe entered in any order, since the
code will sort them in increasing order.
"p lot file" number = the number of dose commitment time period entries
298
-------
TYPE 20 CARDS Event Time Periods
Nl 20
N2
F(l - 6) TOBND(I) Event time period outer bounds (years).
Up to NEVTM times may be entered to define the
outer bound of each event time period—the time
period is assumed to start at the next smaller
time period "outer bound"—or zero if there is no
smaller entry. These time periods are used to
calculate the failure probabilities of the events
occurring at a particular "event time."
Since this card defines the outer bound of each
period, they are used as in this example:
Entries of 10, 50, and 100 would establish "event
times" of 5, 30, and 75 years. The probability of
the event occurring at 30 years would be
calculated by considering the failure rate over
the period 10 to 50 years. And so on...
299
-------
TYPE 22 CARD Distribution of Atmospheric Releases
Nl 22
N2
F(l) FAL Fraction of atmospheric releases which are
distriouted through the atmosphere over land
F(2) FLL Fraction of direct releases which go directly onto
land surfaces
F(3) FAW Fraction of direct releases which are distributed
through the atmosphere over water (considered for
ocean pathway uptake)
300
-------
TYPE 23 CARDS Event Characterizations (Part 1)
ONE CARD FOR EACH EVENT CONSIDERED - UP TO NEVSM EVENTS
Nl 23
N2 NEVTT(I) Event Type
1 = Atmospheric release (e.g. volcanos)
2 = Land Surface release ("Drilling Hits" canister)
3 = Release from drilling events not hitting
canister ("Drilling/No Hit")
4 = Aquifer release from non-drilling events
5 = Aquifer release from normal groundwater flow
F(l) EVNT(I) Event Identification Number
(taken from ADL report)
F(2) FHIT(I) Fraction of repository inventory in canisters
directly breached by failure event
F(3) FTANK(I) Fraction of repository inventory with which
groundwater flow can communicate
Default =1.0
For Type 3 and 4 events only
F(4) VTANK(I) Porosity volume of that portion of repository with
which groundwater flow can communicate
(cubic meters)
Default = VR entered on Type 52 card
For Type 3 and 4 events only
F(5) VDRILL(I) Volume of water removed from repository during a
drilling event (cubic meters)
Default = VTANK(I)
For Type 3 events only
A(l - 4) EDES(I,4) 16 character event identification.
301
-------
TYPE 24 CARDS
Event Characterizations (Part 2)
ONE CARD FOR EACH EVENT CONSIDERED - UP TO NEVSM EVENTS
Nl
N2
F(D
F(2)
F(3)
F(4)
F(5)
24
EVNT(I) Event Identification Number
(see Type 23 Card)
K1(I) Initial hydraulic conductivity in flow path
created by failure event (meters/year)
For Type 3 and 4 events only
KPRIM(I) Rate of change of hydraulic conductivity in flow
path created by failure event (meters/year
per year)
For Type 3 events only
PORS(I) Porosity in flow path created by failure event
For Type 3 and 4 events only
AKEA(I) Cross-sectional area of flow path created by
failure event (square meters)
A(l - 4) EDES(I,4) 16 character event identification.
**** NOTE 1: A Type 24 card for an event must appear somewhere
AFTER (not necessarily immediately after) the Type 23 card
for that event. This is an exception to the general rule
that standardized format cards may appear in any order.
302
-------
TYPE 25 CARDS
Event Failure Rate Data
ONE SET OF CARDS FOR EACH EVENT WHICH DOES NOT HAVE A TYPE 26 CARD
Nl 25
N2 Sequence number of card (up to six cards in a set)
F(l) EVNT(I) Event Identification Number
(See Type 23 Card)
F(2 - 6) FRATE(I) Failure rate of the event over the event time
period (events/year)
A(l - 4) EDES(I,4) 16 character event identification.
**** NOTE 1: Failure rates must be entered in order of increasing
event time period.' This is true regardless of the order in
whicn the event time periods are entered on the Type 20
cards.
**** NOTE 2: Where a failure rate is constant over one or more
time periods, it does not have to be entered repeatedly.
When the program reads a blank in an FRATE field, it will
assign the failure rate from the preceding field. Thus, if
the failure rate is constant over the entire time period
considered, it only needs to be entered in the first FRATE
field. (If it is desired to enter a zero rate after a
non-zero rate, providing any negative number will do this.)
**** NOTE 3: For events which are prevented by institutional
control for some time after disposal, the procedure
described in NOTE 2 may still be used. Although non-zero
failure rates may be input for event time periods during
institutional control, the program will subsequently set
these rates to zero for the period of institutional control
(TIC - entered on the Type 52 card).
**** NOTE 4: The set of failure rate cards for an event must
appear somewhere AFTER (not necessarily immediately after)
the Type 23 card for that event. This is an exception to
the general rule that standardized format cards may appear
in any order.
303
-------
TYPE 26 CARDS Initial Event Probability
ONE CARD FOR EACH EVENT WHICH DOES NOT HAVE A SET OF TYPE 25 CARDS
Nl 26
N2
F(l) EVNT(I) Event Identification Number
(See Type 23 Card)
F(2) PROB(I.l) Initial Probability of Event
For events which are assumed to start at
repository sealing (essentially design
failures). Event is assumed to occur at the
midpoint of the first event time period.
A(l - 4) EDES(I,4) 16 character event identification.
**** NOTE 1: If both a Type 26 card and a set of Type 25 cards
are entered for the same event, the Type 26 card will be
used and the Type 25 cards ignored.
**** NOTE 2: The initial probability card for an event must
appear somewhere AFTER (not necessarily immediately after)
tne Type 23 cara for that event. This is an exception to
the general rule that standardized format cards may appear
in any order.
304
-------
TYPE 30 CARDS
Radionuclide Data - Part 1
ONE TYPE 30 CARD FOR EACH RADIONUCLIDE - UP TO NRNM RADIONUCLIDES
Nl
N2
F(5)
F(6)
30
NRNTY(I) Radionuclide Type
1 = Simple Decay
2 = Daughter Product
F(l) RNID(I)
F(2)
F(3)
F(4)
0.693/
RNLD(I)
RNQO(I)
LR(D
Radionuclide Identification Number
(Formed from radionuclide atomic number and mass
number. For example, C-14 identification number
is 6.014, Pu-239's is 94.239, etc.)
Half-Life (years), which is immediately converted
to the decay constant: RNLD(I)
Initial Inventory at Repository Sealing (curies)
Leach rate (fraction per year), if different than
the overall waste form leach rate (WFLR - entered
on the Type 52 card). If no value entered, WFLR
is assumed.
RNDA(I) Retardation Factor in overlying aquifer
RNSOL(I) Solubility Limit on flow through repository
(curies/cubic meter)
A(l, 2) RNDSl(I) Eight character radionuclide identification
RNDS2(I)
305
-------
TYPE 31 CARDS
Radionuclide data - Part 2
ONE TYPE
Nl
N2
F(D
F(2)
F(3)
F(4)
F(5)
F(6)
****
31 CARD FOR EACH RADIONUCLIDE - UP TO NRNM RADIONUCLIDES
31
RNID(I) Radionuclide Identification Number
(see Type 30 card)
LAMS(I) Radionuclide-specific rate constant for transfer
of radionuclides from available to unavailable
soil (per year)
Default = GLMS entered on Type 60 card
RNKD(I) Distribution Coefficient in ocean sediments
(milliliters/gram)
RLMT(l.I) Release Limit in 40 CFR 191 for air releases
(curies)
RLMT(2,I) Release Limit in 40 CFR 191 for land surface
releases (curies)
RLMT(3,I) Release Limit in 40 CFR 191 for water releases
(curies)
, 2) Eight character radionuclide identification
**** NOTE 1: If the Release Limits for a radionuclide for all
three release modes are the same, only one entry in any one
of the tnree RLMT field needs to be made. The program will
assign this limit to all three categories.
**** NOTE 2: If it is desired that the curies released for a
radionuclide be calculated, rather than the "Release Ratio",
this can be accomplished by leaving all three RLMT fields
blank. The program will automatically assign RLMT values of
one, and will label the appropriate output "CURIES RELEASED"
rather than "RELEASE RATIOS".
NOTE 3: The Type 31 card for a radionuclide must appear
somewhere AFTER (not necessarily immediately after) the Type
30 card for that radionuclide. This is an exception to the
general rule that standardized format cards may appear in
any order.
306
-------
TYPE 32 CARDS
Radionuclide data - Part 3
ONE TYPE 32 CARD FOR EACH RADIONUCLIDE WHICH IS A DAUGHTER PRODUCT
UP TO NRNM RADIONUCLIDES
Nl
N2
F(D
F(2)
F(3)
F(2)
F(5)
2)
****
32
RNID(I) Radionuclide Identification Number
(see Type 30 card)
0.693/ Half-Life of Parent Radionuclide (years), which
RNLDl(I) is immediately converted to the decay constant:
RNLDl(I)
RNQOl(I) Initial Inventory of Parent Radionuclide (curies)
0.693/ Artificial Half-Life of Daughter Radionuclide
RNLDX(I) (years), which is immediately converted to the
decay constant: RNLDX(I)
RNQOX(I) Artificial Initial Inventory of Daughter
Radionuclide (curies)
Eight character radionuclide identification
**** NOTE 1: The "artificial" Half-Life and Inventory for
daughter radionuclides are for use in the groundwater
transport equations. These equations do not treat decay
chains, and the time-dependent inventories of daughter
products must be approximated as if they were simple-decay
radionuclides.
NOTE 2: The Type 32 card for a radionuclide must appear
somewhere AFTER (not necessarily immediately after) the Type
30 card for that radionuclide. This is an exception to the
general rule that standardized format cards may appear in
any order.
307
-------
TYPE 50 CARD Aquifer Flow System Data
Ml 50
N2
F(l) XA Distance along aquifer to "accessible environment"
outlet (meters)
F(2) XS Distance from top of repository to bottom of
overlying aquifer (meters)
F(3) XKA Permeability in aquifer pathway (meters/year)
F(4) XIA Gradient in aquifer pathway
F(5) PORA Effective Porosity in aquifer pathway
F(6) AQAREA Cross-sectional area of aquifer overlying the
repository (square meters) - (normally the
thickness of the aquifer times the widest
dimension of the repository floor area)
308
-------
TYPE 51 CARD Hydraulic Gradient Data
Nl 51
N2
****
Tnese parameters mathematically describe an exponential fit
of the hydraulic gradients due to the thermal buoyancy
effects of repository heat generation and an aquifer
interconnection (if any). As many as 10 sets of
coefficients may be entered, resulting in a sum of 10
exponentials plus a constant..
F(l) ALPH(I)
Hydraulic gradient equals the sum of all "I"
F(2) CVA(I)
CVA(I) * exp[-ALPH(I) * t ] terms plus CVC
F(3) CVC
309
-------
TYPE 52 CARD Leacn Rate, Canister Lifetime, and Other
Miscellaneous Data
Ml 52
N2
F(l) WFLR Leacn Rate of waste form (fraction per year)
NOTE: Different leach rates for specific
radionuclides may De entered on the Type 30
cards. If a non-zero value is entered there, it
will take precedence over this value.
F(2) CLIFE Canister Lifetime (years)
F(3) VR Porosity volume of the mined portion of the
repository (cubic meters) '
F(4) TIC Time over which institutional controls are assumed
to be effective in preventing intrusion by
drilling (years)
F(5) EXPECT Tne expected value for an event over the dose
commitment time period which determines whether
multiple occurrences of the same event are
considered. (Recommended input = 0.5)
310
-------
TYPE 53 CARD
Nl
N2
F(l) - TCLOS
F(2) VMIN
F(3) XHGH
F(4) XLUW
F(5) XILTH
Repository Closure and Flow Data
(Salt Repositories Only)
53
Time over which salt repository porosity volume
decreases from initial volume, VR, to minimum
porosity volume, VMIN (years)
Minimum repository volume (cubic meters)
Distance from top of overlying aquifer to
repository horizon (meters)
Distance from bottom of overlying aquifer to
repository horizon (meters)
Effective gradient created by pressure of
resealing salt on the water in the respository
after resaturation.
311
-------
TYPE 60 CARD Environmental Transfer Factors
Nl 60
N2
F(l) GLMS Rate constant for transfer of radionuclides from
available to unavailable soil (per year)
F(2) LAMR Rate constant for resuspension of radionuclides
from soil to air (per year)
F(3J LAMG Rate constant for deposition from air to ground
(per year)
F(4) LAMW Rate constant for deposition from air to ocean
(per year)
312
-------
TYPE 70 CARD Ocean Environmental Pathway Data
HI 70
N2
F(l) SI 10 Sedimentation coefficient for upper ocean
Equals 1.33E-7 (per year) when radionuclide
distribution coefficients are in milliliters/gram.
F(2) S2IO Sedimentation coefficient for lower ocean
Equals 2.55E-9 (per year) when radionuclide
distribution coefficients are in milliliters/gram.
F(3) TAU1 Transfer rate coefficient from upper to lower
ocean (per year)
F(4) TAU2 Transfer rate coefficient from lower to upper
ocean (per year)
313
-------
TYPE 96, 97, 98 or 99 CARDS Data separator cards
**** ONE of these cards must be used at the end of a data set to
indicate proper processing for subsequent problems (if
any). Subsequent runs will use the data entered for the
previous problem, but modified or expanded by the cards
entered after the data separator. After the data separator,
a new JOB CONTROL CARD must be entered, followed by the
appropriate number of TITLE CARDS (the NLINE parameter on
the new JOB CONTROL CARD), followed by new standardized
format data cards as appropriate.
Nl 96 DELETE OLD EVENT(S), CONSIDER NEW EVENT(S)
Indicates end of data for a particular problem. Tells
program that another problem will follow.
The next problem will neglect all event data entered
previously, and will only address event data entered
after this separator.
Nl 97 DELETE OLD RADIONUCLIDE(S), CONSIDER NEW
RADIONUCLIDE(S)
Indicates end of data for a particular problem. Tells
program tnat another problem will follow.
The next problem will neglect all radionuclide data
entered previously, and will only address radionuclide
data entered after this separator.
Nl 98 MODIFY OTHER DATA
Indicates end of data for a particular problem. Tells
program that another problem will follow.
Data entered on following cards will modify previous
data. ALL VALUES ON A NEW CARD MUST BE ENTERED, EVEN
IF ONLY A FEW ARE BEING CHANGED. If cards for a new
event or a new radionuclide are entered after this type
of a separator, this new event or radionuclide will be
ADDED to those considered previously.
Nl 99 END OF RUN
Indicates end of data for all problems.
Tells program tnat no additional problems will follow.
314
-------
Appendix G
SAMPLE INPUT AND OUTPUT FOR REPRISK
315
-------
Taole 6-1: REPRISK Input Cards for Sample Problem
3
1 1
1 0
PROGRAM = REPRISK JCL
DATASET = SALT
THIS
11
20
22
23 1
25 1
23 1
25 1
23 2
25 1
23 4
24
25 1
23 4
24
25 1
23 3
24
25 1
23 5
24
26
30 1
31
30 2
31
32
30 1
31
30 1
31
30 2
31
32
30 1
31
30 2
31
32
30 1
31
30 1
31
IS A RUN
10000.
100.
.15
74.0
74.0
73.0
73.0
40.1
40.1
71.0
71.0
71.0
75.0
75.0
75.0
40.2
40.2
40.2
11.0
11.0
11.0
94.238
94.238
94.239
94.239
94.239
94.240
94.240
94.242
94.242
95.241
95.241
95.241
95.243
95.243
93.237
93.237
93.237
55.135
55.135
55.137
55.137
. BASECASE
USING ADL
500.
.50
l.OE-3
4.0E-11
4.0E-3
l.OE-10
4.0E-6
2.0E-5
3.0E-3
31.50
2.0E-8
4.0E-3
3150.0
3.15E-3
2.0E-2
3.40E-3
1.0
89.
5.E-4
24400.
5.E-4
7950.
6760.
5.E-4
3.79E5
5.E-4
458.
5.E-4
13.2
7650.
5.E^
2.14E6
5.E-2
4.58E2
3.E6
2.1E-3
30.
2.1E-3
1 2 1 50 1 1
= IMSL.REPRISK REPOSITORY =
DATE 04/18/81
S FIRST ESTIMATES.
1000.
.35
2000.
5000.
.05
0.0
.016
0.0
6.E-5
3.15E-4
5.OOE-5
2.2E8
2.0E+3
3.3E7
2.E+3
1.7E6
4.9E7
2.E+3
1.7E5
2.0E+3
1.7E8
l.E+3
8.0E9
1.7E6
l.E+3
3.3E4
1.
1.7E8
2.2E4
2.0E+1
8.6E9
2.0E+1
l.E+5
0.1
3.2E+4
.2
l.OE-8
.06
0.1
0.1
4.0E+4
l.OE+4
1.OE+4
l.OE+4
l.OE+3
567-
4.0E+2
2.0E+3
2.0E+5
5.OE+4
4000.0
30000.0
0.5
500.0
100.
100.
100.
100.
100.
3.9E8
100.
100.
1.0E5
1.
1.
SALT
10000.
METEORITE
METEORITE
VOLCANO
VOLCANO
DRILLING/HIT
DRILLING/HIT
FAULTING
FAULTING
FAULTING
BRECCIA
BRECCIA
BRECCIA
DRILLING/NO HIT
DRILLING/NO HIT
DRILLING/NO HIT
ROUTINE RELEASE
ROUTINE RELEASE
ROUTINE RELEASE
1.7E-2 PU-238
PU-238
6.E-5 PU-239
PU-239
PU-239
2.2E-4 PU-240
PU-240
4.E-6 PU-242
PU-242
160.0 AM-241
AM-241
AM-241
10.0 AM-243
AM-243
7.E-7 NP-237
NP-237
NP-237
0.0 CS-135
CS-135
0.0 CS-137
CS-137
317
-------
Table G-l (continued): REPRISK Input Cards for Sample Problem
30 1 53.129 1.6E7 3.8E3 1. 0.0 I -129
I -129
2.E-5 TC- 99
TC- 99
3.0E-2 SN-126
SN-126
2.6E-6 ZR- 93
ZR- 93
0.0 SR- 90
SR- 90
0.0 C - 14
C - 14
1.2E5
31
30 1
31
30 1
31
30 1
31
30 1
31
30 1
31
50
51
51
51
52
53
60
70
99
53.129
43.099
43.099
50.126
50.126
40.093
40.093
38.090
38.090
6.014
6.014
1600.0
1.6E-3
3.1E-4
2.6E-4
l.OE-4
2.0E+2
5.0E-4
1.33E-7
1.2E-1
2.1E5
1.260
1.E5
4.5E-3
9.5E5
5.0E-4
28.8
9.5E-3
5730.
0.5
200.0
.132
.103
.283
100.0
2.0E+4
3.16E-4
2.5E-9
0.0
1.4E6
0.0
5.6E4
0.0
1.9E5
2.0E+3
6.0E+9
2.0E+0
2.8E4
0.0
31.5
0.1
2.0E6
1.3E+2
24.4
3.10E-2
9.0E+4
2.0E+5
8.0E+3
l.OE+4
8.0E+3
2.0E+4
0.01
100.0
l.OE+2
48.7
6.25E-4
1.
10.
100.
1.
1.
0.15
0.5
7.9
318
-------
PROGRAM = REPRISK JCL
DATASET = SALT.BASECASE
IMSL.REPRISK REPOSITORY = SALT
DATE 04/18/81
to
i—'
<-£>
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
THE (P)(C) RISK FOR THIS
THE (P)(C) RISK BY EVENT
EVENT
EVENT
EVENT
EVENT
EVENT
EVENT
EVENT
DOSE COMMITMENT PERIOD
IS:
74.0
73.0
40.1
71.0
75.0
40.2
11.0
THE (P)(C) RISK BY RADIONUCLIDE
METEORITE
VOLCANO
DRILLING/HIT
FAULTING
BRECCIA
DRILLING/NO HIT
ROUTINE RELEASE
IS:
PU-238
PU-239
PU-240
PU-242
AM-241
AM-243
NP-237
CS-135
CS-137
I -129
TC- 99
SN-126
ZR- 93
SR- 90
C - 14
IS 1.86E+02
3.40E-03
3.40E-02
4.52E+00
6.85E-03
9.59E-04
1.81E+02
0.0
2.54E-03
1.08E+00
1.06E+00
6.28E-03
7.93E+01
1.04E+02
1.90E-04
3.63E-02
9.76E-02
6.54E-04
3.13E-04
1.87E-02
1.89E-02
9.86E-02
5.36E-03
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
FOR SOMATIC
EFFECTS,
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
AND 2.45E+00
3.01E-05
3.01E-04
3.51E-02
4.50E-04
6.04E-05
2.41E+00
0.0
5.05E-06
3.01E-03
3.79E-03
2.28E-05
6.07E-01
1.82E+00
8.08E-07
6.42E-03
8.64E-03
3.51E-06
1.65E-05
1.80E-03
1.88E-03
2.94E-04
2.12E-04
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
FOR
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
GENETIC
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
EFFECTS
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
*****
&>
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Lttun cnirvi in me ruLLunmu IHDLC.O r\Lrr\Locii I o me ruLLuniMU umn. '
a
1. THE TOTAL NUMBER OF HEALTH EFFECTS FROM ONE SUCH EVENT INCURRED IN THIS DOSE COMMITMENT PERIOD. — '
2. THE RADIONUCLIDE CONTRIBUTING THE MOST HEALTH EFFECTS WITHIN THIS TOTAL.
3. THE PROBABILITY OF AT LEAST ONE EVENT OF THIS TYPE OCCURRING WITHIN THE TIME PERIOD REPRESENTED BY THIS EVENT TIME «p
ro
DOSE COMMITMENT PERIOD = 0 YEARS TO 10000 YEARS
50 YEARS
300 YEARS
EVENT TIMES
750 YEARS
1500 YEARS
SOMATIC HEALTH EFFECTS O
rl-
3500 YEARS
:^-
7500 YEARS m
a
******************************************************************************************************************** "^
EVENT
74.0
METEORITE
EVENT
73.0
VOLCANO
EVENT
40.1
DRILLING/HIT
EVENT
71.0
FAULTING
EVENT
75.0
BRECCIA
EVENT
11.0
ROUTINE RELEASE
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
*
1.13E+05
AM-241
4.00E-09
4.54E+05
AM-241
l.OOE-08
1.69E+02
AM-241
0.0
9.35E-K)!
SN-126
2.00E-06
3.23E+01
SN-126
0.0
0.0
l.OOE+00
4.74E+04
AM-241
1.60E-08
1.89E+05
AM-241
4.00E-08
1.17E+02
AM-241
8.00E-03
9.30E+01
SN-126
8.00E-06
3.16E+01
SN-126
0.0
0.0
0.0
2.65E+04
AM-241
2.00E-08
1.06E+U5
AM-241
5.00E-08
6.99E+01
AM-241
l.OOE-02
9.19E+01
SN-126
l.OOE-05
3.03E+01
SN-126
5.00E-06
0.0
0.0
1.20E+04
AM-241
4.00E-08
4.82E+04
AM-241
l.OOE-07
3.67E+01
AM-241
2.00E-02
8.98E+01
SN-126
2.00E-05
2.81E+01
SN-126
l.OOE-05
0.0
0.0
4.90E+03
PU-240
1.20E-07
1.96E+04
PU-240
3.00E-07
1.91E+01
PU-240
5.82E-02
2.45E+01
C - 14
6.00E-05
8.83E+00
C - 14
3.00E-05
0.0
0.0
2.93E+03
PU-239
2.00E-07
1.17E+04
PU-239
5.00E-07
1.10E+01
PU-239
9.52E-02
1.73E+01
C - 14
l.OOE-04
5.22E+00
C - 14
5.00E-05
0.0
0.0
70
m
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OO
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C
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FOR RELATIVELY LIKELY HUMAN INTRUSION EVENTS, MULTIPLE OCCURRENCES ARE ASSUMED. THE EVENT TIMES FOR EACH OCCURRENCE ARE EVENLY
SPACED THROUGHOUT THE PERIOD FROM LOSS OF INSTITUTIONAL CONTROLS ( 100 YEARS) TO THE END OF THE EVENT PERIOD ( 10000 YEARS).
FOR EACH CASE, THE CONSEQUENCES ARE SUMMED OVER THESE MULTIPLE OCCURRENCES.
(D
CD
IV)
o
o
3
EVENT
40.2
DRILLING/NO HIT
Co
12 CASES WERE RUN FOR DIFFERENT EXPECTED NUMBERS OF OCCURRENCES.
FROM 100 YEARS
TO 10000 YEARS
NUMBER OF
OCCURRENCES
159
166
173
180
187
194
201
208
215
222
229
236
PROBABILITY OF
THIS NUMBER
5.00E-03
1.65E-02
5.00E-02
9.00E-02
1.50E-01
1.90E-01
1.90E-01
1.50E-01
9.00E-02
5.00E-02
1.65E-02
5.00E-03
SOMATIC
HEALTH EFFECTS
GENETIC
HEALTH EFFECTS
1.45E+02
1.52E+02
1.58E+02
1.65E+02
1.71E+02
1.77E+02
1.84E+02
1.90E+02
1.97E+02
2.03E+02
2.09E+02
2.16E+02
1 .94E+00
2.02E+00
2.11E+00
2.19E+00
2.28E+00
2.36E+00
2.45E+00
2.53E+00
2.62E+00
2.71E+00
2.79E-KJO
2 .88E+00
CD
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PROBLEM COMPLETED
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L
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SOMATIC HEALTH EFFECTS FROM ALL EVENTS
PLOT OF LOGPROB*LOGCON LEGEND: A = 1 OBS, B = 2 OBS, ETC.
DOSE COMMITMENT TIME OF 0-10000YRS. 1
9:36 TUESDAY, JUNE 9, 1981
A A A AA
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A
A A
A A
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345
LOG OF HEALTH EFFECTS
-------
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*D.S. GOVERNMENT PRINTING OFFICE : 1983 0-381-085/4498
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