Modeling of Radionuclide 

Transport in Freshwater 

Systems Associated with 

Nuclear Power Plants

Office of Nuclear Regulatory Research

NUREG/CR-7231

Modeling of Radionuclide 

Transport in Freshwater 

Systems Associated with 

Nuclear Power Plants

Manuscript Completed: November 2016

Date Published: April 2017

Prepared by: S. B. Yabusaki, B. A. Napier,

W. A. Perkins, M. C. Richmond, C. L. Rakowski,

S. F. Snyder, and L. F. Hibler

Pacific Northwest National Laboratory

Richland, Washington 99352

Mark Fuhrmann, Project Manager

NRC Job Code V6366

Office of Nuclear Regulatory Research

NUREG/CR-7231

 

iii

ABSTRACT

The potential consequences of radionuclides that have been directly released into a surface 

water body, as happened in the 2011 Fukushima Daiichi nuclear power plant accident, are not 

well understood, especially for the lake and river settings where most U.S. nuclear power plant 

reactors are sited. Accordingly, hypothetical scoping analyses have been performed to better 

understand how radionuclide transport in freshwater systems might be affected by the 

interaction of radionuclide-specific decay and sorption with hydrologic and sediment conditions. 

Eight radionuclides, 137Cs, 134Cs, 131I, 90Sr, 3H, 106Ru, 125Sb, and 144Ce, were selected for these 

analyses based on a methodology that estimated the partitioning of the reactor core inventory to 

water as a function of reactor type, mass of uranium fuel, and fuel burnup. Transport 

simulations for each radionuclide were based on the release of a 10-day pulse of 1,000 m3 of 

water with 1 Bq of activity into small lake, small river, and large river settings. The small lake 

setting was based on a reservoir impounded by a dam on a river that provided a large water 

volume but limited transport, which led to high concentrations at early times. The small river 

setting examined relatively low flow and slow average velocity conditions, which resulted in less 

dilution (i.e., higher concentrations) and longer transit times for the 10-day radioactive release. 

The large river scenario examined conditions where relatively high flow resulted in lower 

concentrations but faster downriver transport. 

Bathymetric data and hydraulic parameters were adapted and modified from actual lake and 

river systems. Consistent with the scoping level of analysis, steady-state hydraulics were used 

with the rivers simulated in two dimensions (depth-averaged) and the lake in three dimensions. 

Modeled transport processes included advection, mixing/dispersion, decay, sediment transport, 

and sediment-radionuclide interaction (i.e., adsorption/desorption); modeled features included 

the impact of tributaries, dams, and impoundments.

v

FOREWORD

Over the years, the NRC has analyzed many hypothetical severe accidents involving releases 

of radionuclides. Most of these analyses assessed the impact of releases to the atmosphere 

because air-borne contaminants can be transported rapidly over a large area. Several studies 

(e.g., NUREG/CR–4251 and NUREG-0140) examined radionuclides carried in water, but these 

studies assumed that the molten core material breached the basemat of the reactor building and 

came into contact with soil and groundwater. Contaminants distributed in groundwater would 

move slowly due to groundwater flow rates and reactions with the soil. In this current study,

contaminated water is assumed to have been released directly to the water body, much like the 

observed release to the ocean during the Fukushima Daiichi accident. 

The Fukushima Daiichi nuclear reactor accident of March 2011 resulted in leakage of more than 

1,000 m3 of highly contaminated water directly into the Pacific Ocean. This type of direct 

leakage path had not been analyzed by the U.S. Nuclear Regulatory Commission (NRC). As a 

result, the Office of Nuclear Regulatory Research contracted with the staff at Pacific Northwest 

National Laboratory to produce this exploratory study entitled, Modeling of Radionuclide 

Transport in Freshwater Systems Associated with Nuclear Power Plants.

This report presents state-of-the-art hydrologic transport modeling results for leakage of 

waterborne radionuclides directly into a freshwater body. The study postulates releases to three 

types of freshwater settings typical of NPPs within the United States: a large river, a small river, 

and a small lake. Two- and three-dimensional modeling is used to explore the concentrations of 

radionuclides as they are transported through the three freshwater bodies. The approach is to 

determine how advection, dilution/dispersion, radioactive decay, and adsorption/desorption 

processes affect concentrations of each of the transported radionuclides under the hypothetical 

conditions in each freshwater setting. Although the study results do not apply to the Great 

Lakes or to estuary settings because of their different hydrological conditions, they do help 

define transport distributions and rates, effects of sediment-contaminant interactions, and the 

behavior of contaminants in rivers with and without dams. 

NRC’s interest is in the methodology and the overall insights provided on contaminant transport 

in the freshwater systems that were modeled. The eight radionuclides studied are associated 

with aqueous releases expected from damaged light water reactor fuel. Results are presented 

for a set of hypothetical locations as Bq/m3 based on the initial release of a 1 Bq source term. 

Because these results scale linearly, these fractional concentrations can be multiplied by any 

source term of interest. Results cannot be taken as representative of any particular nuclear 

power reactor facility as the modeling parameters and data are highly site specific. However, the 

observations of the movement of a relatively high concentration pulse of contaminants, the long 

distances it can be transported in rivers, and the possibility of long-term 

sediment/water/contaminant interactions are important general insights from this study. 

Accident scenarios capable of producing significant aqueous radionuclide source terms are 

expected to be very unlikely occurrences at any individual nuclear power plant location. 

Specifically, an accident resulting in core damage (a rare event) would need to occur in 

combination with the loss (or bypass) of the reactor containment and the existence of a leakage 

path for contaminated water to flow into a nearby water body. Reactor containment and 

potential leakage paths were not a subject of this study because they are highly scenario- and 

site-specific. It should be noted that a number of factors could mitigate aqueous releases such 

as water hold-up in plant systems or buildings, settling or plate-out of radionuclides, relative 
vi

elevation differences between in-plant leakage sources and nearby water bodies, and operator 

actions to reduce leakage rates or delay the timing of releases. Moreover, actions taken since 

the accident at Fukushima Dai-ichi by the NRC and the nuclear industry have enhanced safety 

and reduced both the likelihood and potential consequences of severe core damage events. 

Although a significant aqueous radionuclide release is expected to be a rare event, this project 

provides an improved understanding of the potential behavior of these releases and can better 

inform plans to control and minimize impact to public health and safety and the environment.

This report has been subject to external peer review by a panel of experts in the fields of reactor 

core inventories, flow and transport processes in open channels, and reactor accident 

consequences. Their comments as well as those from the many reviewers within the NRC 

improved the technical basis of this work.
vii

TABLE OF CONTENTS

ABSTRACT ................................................................................................................... iii

FOREWORD...................................................................................................................v

TABLE OF CONTENTS................................................................................................vii

LIST OF FIGURES.........................................................................................................ix

LIST OF TABLES ........................................................................................................xiii

EXECUTIVE SUMMARY ............................................................................................. xv

ACKNOWLEDGMENTS ............................................................................................ xvii

ABBREVIATIONS....................................................................................................... xix

1. INTRODUCTION ................................................................................................. 1-1

1.1 Background and Motivation...................................................................................... 1-1

1.1.1 Purpose ........................................................................................................ 1-2

1.1.2 Scope ........................................................................................................... 1-2

1.2 Approach.................................................................................................................. 1-2

1.2.1 Source Term................................................................................................. 1-2

1.2.2 Freshwater Settings...................................................................................... 1-3

1.2.3 Flow and Transport....................................................................................... 1-3

1.3 Report Sections........................................................................................................ 1-4

2. AQUEOUS SOURCE TERM ESTIMATION METHODOLOGY........................... 2-1

2.1 Introduction............................................................................................................... 2-1

2.2 Analysis of Historical Accidents................................................................................ 2-1

2.2.1 Three Mile Island Unit 2, 1979...................................................................... 2-1

2.2.2 Fukushima Daiichi, 2011 .............................................................................. 2-4

2.3 A Generalized Approach to Aqueous Source Term Development ........................... 2-6

2.3.1 Comparison of TMI Unit 2 and FD Waste Water.......................................... 2-8

2.4 Surface Water Source Term..................................................................................... 2-9

3. FRESHWATER SETTINGS ................................................................................ 3-1

3.1 Specifications for Hypothetical Freshwater Settings ................................................ 3-1

3.2 Examples of Release Pulses Transported in Rivers ................................................ 3-5

3.2.1 Long-Term Impacts of a Large Radionuclide Release ................................. 3-9

4. FLOW AND TRANSPORT MODELING.............................................................. 4-1

4.1 Mixing and Transport................................................................................................ 4-1

4.2 Theory ...................................................................................................................... 4-1

4.2.1 Sediment ...................................................................................................... 4-2

4.2.2 Dissolved Radionuclide ................................................................................ 4-3

4.2.3 Suspended Sediment-Sorbed Radionuclides............................................... 4-3

4.2.4 Bed Representation...................................................................................... 4-4

4.3 Simulators ................................................................................................................ 4-6

4.3.1 MASS2 ......................................................................................................... 4-6
viii

4.3.2 TETHYS .......................................................................................................4-6

4.4 Software History and Model Testing ........................................................................4-7

4.4.1 History ..........................................................................................................4-7

4.4.2 Testing and Applications ..............................................................................4-7

4.5 Modeling Approach ..................................................................................................4-8

4.5.1 Source Term.................................................................................................4-8

4.5.2 Lake/Reservoir .............................................................................................4-9

4.5.3 River Settings ...............................................................................................4-9

4.5.3.1 Extended Large River Configurations..........................................4-11

5. RADIONUCLIDE TRANSPORT MODELING RESULTS.................................... 5-1

5.1 Simulation Overview.................................................................................................5-1

5.1.1 Source Term.................................................................................................5-1

5.1.2 Sequence of Simulation Cases ....................................................................5-1

5.2 Modeling Results......................................................................................................5-1

5.2.1 Small Lake/Reservoir ...................................................................................5-1

5.2.1.1 One-Year Simulations....................................................................5-4

5.2.1.2 Sensitivity Test for Turbulent Mixing Coefficient............................5-7

5.2.2 Small Discharge River..................................................................................5-8

5.2.2.1 One-Year Simulations..................................................................5-12

5.2.3 Large Discharge River................................................................................5-18

5.2.3.1 One-Year Simulations with Extended Domain.............................5-21

5.2.3.2 Unimpounded and Impounded Large River Simulations .............5-24

5.2.3.3 Sensitivity Tests...........................................................................5-27

5.3 Discussion..............................................................................................................5-31

5.3.1 Mixing and Transport..................................................................................5-32

5.3.2 Sediment-Radionuclide Interactions...........................................................5-32

5.3.3 Fate of Contaminated Sediment.................................................................5-34

5.3.4 Scaling........................................................................................................5-34

6. CONCLUSIONS .................................................................................................. 6-1

6.1 Summary ..................................................................................................................6-1

6.1.1 Objectives.....................................................................................................6-1

6.1.2 Modeling Quality Assurance.........................................................................6-2

6.2 Conclusions from Model Results..............................................................................6-2

6.2.1 Transport ......................................................................................................6-3

6.2.2 Transit Times................................................................................................6-3

6.2.3 Sorption and Desorption...............................................................................6-3

6.3 Site-Specific Applications .........................................................................................6-4

7. REFERENCES .................................................................................................... 7-1

APPENDIX A – MODELING QUALITY ASSURANCE............................................... A-1

APPENDIX B – DETAILED FLOW AND TRANSPORT MODELING RESULTS....... B-1
ix

LIST OF FIGURES

2-1 Schematic Process for Estimating Radionuclide Releases to Surface Water from a 

Severe Reactor Accident.................................................................................................2-6

3-1 Reservoir/Lake Bathymetry Showing the Variable Water Depth .....................................3-3

3-2 An Example of a Section of the Small River Bathymetry.................................................3-4

3-3 Example of a Large River Section with Bathymetry.........................................................3-4

3-4 Observations of 131I Pulse as It Travels Downstream on the Columbia River ...............3-6

3-5 Ten Day Averaged Activity Concentrations of 90Sr at Three Dams along the Dnieper 

River: Kiev Reservoir, Zaporozhe Reservoir, and Kakhovka Reservoir ..........................3-7

3-6 Data from a Tracer Test on the Lower Missouri River.....................................................3-8

4-1 Sampling Locations for the Lake Simulation .................................................................4-10

4-2 Configurations Used for Large River Cases ..................................................................4-12

5-1 Simulated Near-Surface 137Cs Concentrations, Bq/m3 10 days, 20 days, and 30 

Days after Start of Release in the Lake Scenario............................................................5-2

5-2 Simulated 131I Activity Concentration History at the Near-Shore and Far-Shore 

Sample Locations in the Lake Scenario ..........................................................................5-3

5-3 Simulated 144Ce Activity Concentration History at the Near-Shore and Far-Shore 

Sample Locations in the Lake Scenario ..........................................................................5-3

5-4 Simulated 90Sr Activity Concentration History at the Near-Shore and Far-Shore 

Sample Locations in the Lake Scenario ..........................................................................5-3

5-5 Simulated 137Cs Activity Concentration History at the Near-Shore and Far-Shore 

Sample Locations in the Lake Scenario ..........................................................................5-4

5-6 Lake 134Cs Activity Over Time at Several Locations on the Same And Opposite 

Shore of the Release Location ........................................................................................5-5

5-7 Lake 137Cs Activity Over Time at Several Locations on the Same and Opposite 

Shore of the Release Location ........................................................................................5-5

5-8 Lake 131I Activity Over Time at Several Locations on the Same and Opposite Shore 

of the Release Location...................................................................................................5-5

5-9 Lake 90Sr Activity Over Time at Several Locations on the Same and Opposite Shore 

of the Release Location...................................................................................................5-6

5-10 Simulated Lake Aqueous-Only, Near-Surface 137Cs Concentrations, Bq/m3 30 Days, 

90 Days, 180 Days, and 360 Days after Start of Release from the Lake One-Year 

Simulation........................................................................................................................5-6

5-11 Comparison of Aqueous-Only 137Cs Activity Concentrations Over Time for the 

Original and Increased Mixing Coefficient Lake Simulations at Locations along the 

Same and Opposite Shore as the Release .....................................................................5-7

5-12 Simulated Lake Aqueous-Only, Near-Surface 137Cs Activity Concentrations, Bq/m3

30 Days, 90 Days, 180 Days, and 360 Days after Start of Release from the Lake 

Increased Mixing Coefficient Simulation..........................................................................5-8

5-13 Simulated Small River 137Cs Water Column Concentrations in the Aqueous-Only 

Simulation, Aqueous Phase in the Sediment-Inclusive Simulation, and Suspended 

Sediment-Sorbed Phase in the Sediment-Inclusive Simulation.......................................5-9
x

5-14 Simulated Small River Aqueous-Only 131I Activity Over Time at Several Locations 

Along the Same Shore as the Release And the Opposite Shore ..................................5-10

5-15 Simulated Small River Aqueous-Only 90Sr Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-10

5-16 Simulated Small River Aqueous-Only 137Cs Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-10

5-17 Simulated Small River Aqueous-Only 144Ce Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-11

5-18 Time Series Small River 144Ce Aqueous and Total Aqueous and Suspended Activity 

from the Sediment Simulation at Locations Along the Same Shore as the Release.....5-11

5-19 Small River Aqueous, Suspended Sediment-Sorbed, and Total 134Cs Activity Over 

Time at Several Downstream Locations on the Same and Opposite Shore of the 

Release Point ................................................................................................................5-13

5-20 Small River Aqueous, Suspended Sediment-Sorbed, and Total 137Cs Activity Over 

Time at Several Downstream Locations on the Same and Opposite Shore of the 

Release Point ................................................................................................................5-14

5-21 Small River Aqueous, Suspended Sediment-Sorbed, and Total 131I Activity Over 

Time at Several Downstream Locations on the Same and Opposite Shore of the

Release Point ................................................................................................................5-15

5-22 Small River Aqueous, Suspended Sediment-Sorbed, and Total 90Sr Activity Over 

Time at Several Downstream Locations on the Same and Opposite Shore of the 

Release Point ................................................................................................................5-16

5-23 Small River Bed Sediment-Sorbed 134Cs Activity Per Square Meter Over Time at 

Several Locations on the Same and Opposite Shore of the Release Location.............5-17

5-24 Small River Bed Sediment-Sorbed 137Cs Activity Over Time at Several Locations on 

the Same and Opposite Shore of the Release Location ...............................................5-17

5-25 Small River Bed Sediment-Sorbed 131I Activity Over Time at Several Locations on 

the Same and Opposite Shore of the Release Location ...............................................5-17

5-26 Small River Bed Sediment-Sorbed 90Sr Activity Over Time at Several Locations on 

the Same and Opposite Shore of the Release Location ...............................................5-18

5-27 Small River Bed Sediment-Sorbed 131I and 137Cs 20 Mi Downstream of the Release 

Compared with the Decay Expected Starting with the Maximum Concentration...........5-18

5-28 Simulated Large River 137Cs Concentrations in the Aqueous-Only Simulation, 

Aqueous Phase and Suspended Sediment Phase in the Sediment Simulation............5-19

5-29 Simulated Large River Aqueous-Only 131I Activity Over Time at Several Locations 

Along the Same Shoreas the Release and the Opposite Shore....................................5-20

5-30 Simulated Large River Aqueous-Only 90Sr Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-20

5-31 Simulated Large River Aqueous-Only 137Cs Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-20

5-32 Simulated Large River Aqueous-Only 144Ce Activity Over Time at Several Locations 

Along the Same Shore as the Release and the Opposite Shore...................................5-21

5-33 Time Series of Large River 144Ce Aqueous and Total Water Column Activity from

the Sediment Simulation Along the Same Shore As the Release .................................5-21

5-34 Near-Shore and Far-Shore 134Cs Concentration in the Large River Over One Year.....5-22

5-35 Near-Shore and Far-Shore 137Cs Concentration in the Large River for One Year ........5-23
xi

5-36 Near-Shore and Far-Shore 131I Concentration in the Large River for One Year............5-23

5-37 Near-Shore and Far-Shore 90Sr Concentration in the Large River for One Year ..........5-23

5-38 Aqueous Phase 134Cs Concentration Increases with Downstream Location.................5-24

5-39 Unimpounded and Impounded Lower River Comparison for 134Cs Total Water 

Column Concentrations at Lower River Locations ........................................................5-26

5-40 Unimpounded and Impounded Lower River Comparison for 137Cs Total Water 

Column Concentrations at Lower River Locations ........................................................5-26

5-41 Unimpounded and Impounded Lower River Comparison for 131I Total Water Column 

Concentrations at Lower River Locations......................................................................5-27

5-42 Unimpounded and Impounded Lower River Comparison for 90Sr Total Water 

Column Concentrations at Lower River Locations ........................................................5-27

5-43 Comparison of Decreased Release and Original Simulated Large River 137Cs Total 

Water Column Concentrations at 10 and 50 Mi from the Release ................................5-28

5-44 Comparison of Decreased Release and Original Simulated Large River 131I Total 

Water Column Concentrations at 10 and 50 Mi from the Release ................................5-28

5-45 Comparison of Increased Bed and Original Simulated 137Cs Total Activity 

Concentrations at 10 and 50 Mi from the Release ........................................................5-29

5-46 Comparison of Increased Bed and Original Simulated 137Cs Bed-Sorbed Activity 

Concentrations at 10 and 50 Mi from the Release ........................................................5-29

5-47 Comparison of Water Column Activity Concentration from the Original One-Year 

Large River and Increased Sediment Load Simulations................................................5-30

5-48 Comparison of Bed-Sorbed Activity from the Original one-Year Large River and 

Increased Sediment Load Simulation at 10 and 50 and 80 and 103 Mi Below the 

Release Location Are Shown ........................................................................................5-30

xiii

LIST OF TABLES

2-1 Measured Concentrations of Radionuclides in Various Locations of the TMI Unit 2 

Basement at Various Times ............................................................................................2-3

2-2 Concentrations of Radionuclides in Various Locations of the TMI Unit 2 Basement 

at Various Times Back-Decayed to March 28, 1979 .......................................................2-3

2-3 NRC Estimate of Radioactive Material Released to TMI Unit 2 Accident Waters ...........2-4

2-4 Derived Estimate of Radioactive Material Released to TMI Unit 2 Basement Waters ....2-4

2-5 Radionuclide Concentrations in FD Turbine Hall Basement Waters ...............................2-5

2-6 Estimated Release from the Fukushima Cable Pit Leak to the Pacific Ocean Based 

on Different Sources, and Extrapolated Total Release from Unit 2 Core to 

Basement Waters ............................................................................................................2-6

2-7 Fraction of Reactor Core Inventory Released to Water in the Basement at TMI.............2-7

2-8 Comparison of Fukushima Daiichi Aqueous Radionuclide Inventories Derived from 

TMI Release Fractions and Ocean Measurements .........................................................2-8

2-9 Comparison of Major Radionuclides in Accident-Generated Water at TMI Unit 2 and 

Fukushima .......................................................................................................................2-8

2-10 Estimates of Direct Release of Radionuclides to the Ocean from Fukushima ................2-9

3-1 Radionuclide Partition Coefficient and Half-Life Values ..................................................3-2

3-2 Travel time and velocity of solute in the Missouri River between Sioux City and Blair....3-8

4-1 Transport Simulation Approximate Domain Physical and Mesh Dimensions ..................4-9

4-2 Characteristics of the Extended Large River.................................................................4-12

5-1 Percent of Released Activity in the River Bed after 13.5 Days in the Small and 

Large Discharge River Settings.....................................................................................5-11

5-2 Monitoring Locations for the Extended Large River Simulations...................................5-25

xv

EXECUTIVE SUMMARY

The Fukushima Daiichi nuclear power plant accident in March 2011 highlighted a surface water 

contamination scenario not currently addressed in the NRC’s severe accident consequence 

analysis. The purpose of this study is to perform exploratory transport analyses of a direct 

release of radionuclides to surface water, similar to the Fukushima scenario. Transported

radionuclide activity is simulated in hypothetical river and lake systems typical of U.S. nuclear 

power plant sites. It must be emphasized that the types of scenarios discussed in this report are 

expected to be very rare events requiring a number of unlikely failures in engineered systems. 

It was assumed that these failures resulted in an accumulation of contaminated water in the 

structures of the nuclear power plant and that some of that water leaked to a freshwater body. 

This study has three principal tasks: 1) develop a radionuclide source term consistent with the 

Fukushima reactor type, uranium fuel mass, and fuel burnup status, along with the volume, rate, 

and duration of the March 2011 release; 2) design radionuclide release scenarios and 

specifications of processes, properties, and conditions for hypothetical freshwater settings

typical of U.S. nuclear power plant sites; and 3) simulate flow and the transport of radionuclides 

released into the hypothetical freshwater systems.

The selection of radionuclides to be included in the source term is based on the partitioning of 

the reactor core inventory to the cooling water in the Three Mile Island Unit 2 basement water. 

The eight radionuclides selected were 134Cs, 131I, 137Cs, 90Sr, 3H, 106Ru, 125Sb, and 

144Ce. Radionuclide-specific behavior is differentiated by half-life and sorption distribution 

coefficient, Kd. The source term volume and release rate were consistent with published

estimates of the release to the ocean from the Fukushima Daiichi nuclear power plant accident

in the aftermath of the March 11, 2011 earthquake and tsunami. For each of the selected 

radionuclides, a hypothetical 1 becquerel (Bq) activity source was associated with 1,000 m3 of 

water released over a 10-day period. 

Three hypothetical freshwater settings were addressed: 1) small lake, 2) small river, and 

3) large river. The lake setting, about 11 mi long and 0.62 mi wide, provided a large water 

volume (130,000 ac-ft) but limited transport. The small river setting examined relatively low flow 

[5,000 cubic feet per second (cfs)] and slow average velocity conditions, which resulted in less 

dilution (i.e., higher concentrations) and longer transit times for the 10-day radioactive release. 

The large river scenario examined conditions where a relatively high 100,000 cfs discharge 

(118,000 cfs with downstream tributary inflows) resulted in lower concentrations but faster 

downriver transport. Bathymetric data and hydraulic parameters were adapted and modified 

from actual lake and river systems. Consistent with the objective of a scoping level of analysis, 

steady-state discharge rates were used in all scenarios, with the rivers simulated in two 

dimensions (depth-averaged) and the lake in three dimensions.

The transport studies were driven by a shoreline release of the 8-radionuclide source term. 

Advection, mixing, and radioactive decay were simulated for all settings; radionuclide-sediment 

interaction and sediment transport processes were simulated in the small and large river 

settings for 50 mi downstream from the radionuclide release point. Simulations designed to 

capture the transport of the radionuclide release pulse through the three freshwater settings 

were used to explore the impact of radionuclide decay and partitioning to sediment. 

Subsequent transport simulations of the three freshwater settings were extended out to one 

year for the four most important radionuclides: 134Cs, 131I, 137Cs, and 90Sr. The large river 

setting was then lengthened from 50 mi to a dam 103 mi from the radionuclide release point. 
xvi

Downstream of this dam, two flow scenarios were examined for the next 190 river mi (for a total 

of 293 mi): 1) unimpounded free-flowing conditions and 2) impounded conditions with three 

intervening dams. 

Based on the modeling of the flow, specified source term, and radionuclide transport in the three

freshwater settings, the following important conclusions were made:

• Of the three hydrologic settings, the small lake scenario results in the highest radionuclide 

concentrations. Most of the lake volume available for dilution is not accessed at early times 

because transport is essentially limited to dispersion. As a result, radionuclide 

concentrations remain high. 

• In the river settings, the 10-day pulse of released activity remains largely intact for the entire 

length of the river, which for the extended large river model is 293 mi. Depending on the 

amount of activity in the release, radionuclide concentrations in the water could be high 

enough to require emergency measures for long distances downstream. Dams can slow the 

river transit considerably. In the extended large river simulation, first arrival of contaminants 

over a 190-mi reach took 4.4 days without dams and 14.2 days with three intervening dams. 

Over the 293-mi extent of the large river, transit of the full pulse, including the passage of 

the trailing end, took up to 50 days.

• Radionuclide sorption onto sediment is most significant in the presence of the pulse of 

released radionuclides. After the passage of the pulse, desorption from the bed sediments

becomes a longer-term, widespread source as the sorbed contaminants are driven to reequilibrate with the cleaner overlying water. The resulting water column concentrations are 

significantly lower than the pulse but may persist for extended time. 

• A key feature of the river transport model is the downstream persistence of higher 

concentrations along the near shore of the radionuclide release. There can be orders of 

magnitude differences in near-shore versus far-shore concentrations. In the case of the 

large river scenario, complete mixing across the river may not occur until 50 mi downstream. 

In the small river scenario, complete mixing occurs after 10 mi of transport. 

• Depending on the magnitude of radioactivity released, concentrations of radionuclides

sorbed to bed sediments, especially at low water stages, could have long-term impacts on

shoreline use. This could potentially be an issue along the entire length (up to 293 mi) of 

the analyzed river settings. 

• The simulated space- and time-dependent aqueous and sorbed activity concentrations in 

this study are based on a 1 Bq source term for each radionuclide in the 10-day release. The 

functionally linear transport and sediment-radionuclide interaction process models used in 

this study allow the simulated concentrations to be scaled for any magnitude of released 

activity simply by multiplying the presented radionuclide concentrations, which are per unit 

activity, by the desired radionuclide activity (Bq) in the source term. For example, increasing 

radionuclide activity in the source term by a factor of 3 results in activity concentrations 

3 times higher. 
xvii

ACKNOWLEDGMENTS

This project significantly benefitted from the comments, insights and discussions provided by 

the external Peer Review Panel: J. Van Ramsdell, Jr.; Forrest M. Holly, Jr.; and Tracy A. 

Ikenberry. 

This report underwent substantial internal review by NRC staff from the Office of Nuclear 

Regulatory Research (RES), the Office of Reactor Regulation (NRR), the Office of New 

Reactors (NRO), and the Office of Nuclear Security and Incident Response (NSIR); we thank all 

who contributed. Special thanks to Don Marksberry, Keith Compton, Mike Salay, Tom 

Nicholson, Meredith Carr, Tom Aird, Stephanie Bush-Goddard, Rebecca Tadesse, Don 

Palmrose, Trish Milligan, William Ott, Chuck Norton, and Steve LaVie. We thank Dana Powers 

and the members of the Advisory Committee on Reactor Safeguards subcommittee on

Radiation Protection and Nuclear Materials for their helpful comments. 

Massively parallel processing flow and transport simulations were performed using PNNL 

Institutional Computing at Pacific Northwest National Laboratory.

 xix 

ABBREVIATIONS

3H tritium

ac-ft acre-feet 

Ag Silver

Ba Barium

Bq Becquerel (one disintegration/second) 

BWR boiling water reactor

CDS central differencing

Ce Cerium

CFD computational fluid dynamics

cfs cubic feet per second

cm centimeter

Co Cobalt

Cs Cesium

DOE U.S. Department of Energy

EIS environmental impact statement

EPA U.S. Environmental Protection Agency

FD Fukushima Daiichi

FLEX Diverse and Flexible Mitigation Strategies

ft feet

GWd/MTU Gigawatt day per Metric Ton of Uranium

I Iodine

IAEA International Atomic Energy Agency

Kd Distribution or Partitioning Coefficient

kg kilogram

kgf kilogram-force

km kilometer

L Liter

La Lanthanum

m meter

mg milligram

mi mile or miles

mL milliliter

Mo Molybdenum

MPI Message Passing Interface

MTU Metric Tons of Uranium

MUSCL Monotonic Upstream-Centered Scheme for Conservation Laws

MWd/MTU Megawatt-day per Metric Ton of Uranium

NRC U.S. Nuclear Regulatory Commission
xx

NVSF normalized variable and space formulation

PBq Petabecquerel (1 × 1015 becquerel)

PNNL Pacific Northwest National Laboratory

PORV pressure-operated relief valve

PWR pressurized water reactor

RCS Reactor Coolant System

Ru Ruthenium

s second

SAC System Assessment Capability

Sb Antimony

SIMPLE Semi-Implicit Method for Pressure Linked Equations

Sr Strontium

Tc Technetium

Te Tellurium

TEPCO Tokyo Electric Power Company

TETHYS Transient Energy Transport HYdrodynamics Simulator

TMI Three Mile Island

UN United Nations

UNSCEAR United Nations Scientific Committee on the Effects of Atomic Radiation

USGS United States Geological Survey

μm micrometer or micron
1-1

1. INTRODUCTION

Historically, the surface water pathway for exposure to radioactive material from hypothetical 

nuclear reactor accidents has not received as much attention as the atmospheric pathway. The 

immediacy and unconstrained dispersal of an atmospheric release during a severe accident can 

lead to the potential for significant doses to exposed individuals (Gudiksen et al. 1989; 

Chernobyl Forum 2005). However, exposure from a radioactive release to surface water, while 

often considered to be smaller and less likely than an atmospheric release, may still have 

important consequences. 

1.1 Background and Motivation

The accident at the Fukushima Daiichi (FD) nuclear power plant in 2011 resulted in the 

accumulation of highly contaminated water in the reactor and turbine buildings during 

emergency cooling of the reactor fuel. Some of this water is known to have leaked into the 

ocean. The leak was discovered three weeks after the earthquake and tsunami, and was 

contained several days later. While the duration of the leak is not known, the source term could 

be estimated from the monitoring of radionuclide concentrations off the coast of Fukushima. 

Credible estimates ranged from 0.2 to 0.9 percent of the reactor core radionuclide inventory 

(UN 2014). 

The FD accident demonstrated that such an event could result in a substantial release of 

radioactivity directly into an adjacent surface water body. It highlighted a rare surface water 

contamination scenario that is not currently addressed in the U.S. Nuclear Regulatory 

Commission’s (NRC’s) severe accident consequence analysis. Most of the operating nuclear 

reactors in the United States are sited near freshwater bodies. This project is motivated by the 

need to assess a Fukushima-like scenario where contaminated water is directly released to 

freshwater settings. The basic conceptual model is one in which the released materials are 

transported in surface water from the point of release to locations where people and the 

environment are exposed via various pathways. The potential radiation doses to individuals that 

could result from a release of radioactive materials would be mitigated by federal, state, and 

local responses.

It is likely that the onset of an aqueous release from a severe power plant accident would be 

relatively slow. An unlikely series of failures of engineered systems would be needed for 

contaminated water to begin to accumulate in plant structures. However rare, the 1979 Three 

Mile Island (TMI) Unit 2 and 2011 FD accidents illustrate that such potential exists. Under these

conditions it would likely take several days to weeks to accumulate sufficient water for a direct 

release to a water body. Subsurface leakage is also possible. This type of release has been 

discussed by Niemczyk et al. (1981) and Oberlander et al. (1985); the impacts in this case 

would be relatively slow and less severe because of attenuation by radionuclide interactions 

with the soil. 

The methodology presented here does not address the events and processes leading up to the 

radionuclide release to the environment (e.g., mechanics of the accident, core meltdown, and 

breach of containment). Nor does it address the various mitigative strategies that would be 

used, such as emergency operating procedures, severe accident management guidelines, and 

Diverse and Flexible Mitigation Strategies (FLEX) (NEI 2015). It is expected that these 

strategies would preclude the accident or minimize the impact of a radionuclide release.
1-2

1.1.1 Purpose

Scoping analyses were performed to calculate the transport of radionuclides released from a 

hypothetical reactor accident into freshwater settings that are typical of U.S. nuclear power plant 

sites. These analyses were used to determine how advection, dilution/dispersion, radioactive 

decay, and sorption processes affect activity concentrations for each of the transported 

radionuclides under the specified conditions in each freshwater setting. Scoping analyses 

addressed the speed and distances of transport in the assumed scenarios, as well as the fate of 

dissolved and sediment-sorbed radionuclides in river water columns and beds.

1.1.2 Scope

The exploratory nature of this study is reflected in the small number of hypothetical freshwater 

settings considered, use of steady flow conditions, simple release scenario, and limited variation 

in sediment and transport conditions. However, this study differs from previous studies in that 

the simulations use a higher level of detail and the source term was informed by observations 

from actual nuclear power plant accidents: 

• multidimensional modeling was used to account for three-dimensional bathymetry, spatially 

varying flow fields, tributaries, dams and impoundments, transport of radionuclides and 

sediment, and sediment-radionuclide interactions;

• the aqueous radionuclide inventory in the release was estimated with a methodology based 

on reactor type, mass of uranium fuel, and fuel burnup, which was developed, in part, using

observations of aqueous partitioning of the reactor core inventory in the TMI contaminated 

building water;

• the volume, rate, and duration of the release were based on observations during the FD 

accident that included radioactivity measured in seawater near FD; and

• the release of radionuclides to surface water was not assumed to first pass through the 

subsurface environment as in earlier studies. Instead release was made consistent with 

observations of radioactivity entering the marine environment from FD.

1.2 Approach

The three principal tasks of this study included the following: 1) develop a radionuclide source 

term consistent with the FD reactor type, uranium fuel mass, and fuel burnup, along with the 

volume, rate, and duration of the March 2011 release; 2) design radionuclide release scenarios 

and specifications of processes, properties, and conditions for hypothetical freshwater settings

typical of U.S. nuclear power plant sites; and 3) simulate flow and the transport of radionuclides 

released into the hypothetical freshwater systems.

1.2.1 Source Term

The source term for the environmental transport modeling is a specified set of radionuclides that 

is associated with a liquid volume, release rate, and duration. A methodology to estimate the 

aqueous radionuclide inventories for severely damaged reactors is presented in this report.

The first step in the methodology is to determine the reactor core inventory as a function of 

reactor type (i.e., pressurized water reactor [PWR] or boiling water reactor [BWR]), amount of 

uranium fuel, and burnup (Ramsdell et al. 2001). This is followed by the determination of the 

potential aqueous radionuclide inventory (i.e., building water) following a severe nuclear power 

plant reactor accident. In this case, radionuclide measurements of contaminated water that 
1-3

accumulated in buildings in the aftermath of the 1979 TMI nuclear power plant accident provide 

a basis for partitioning individual radionuclides between the nuclear reactor core and the water 

phase. Attributes of the March 2011 FD reactor core and post-accident measurements of 

radionuclide concentrations in the building water were used to test and evaluate the 

methodology. 

The FD source term scenario assumes a direct release of a fraction of the estimated aqueous 

radionuclide inventory consistent with estimates of activity released into the marine system 

offshore from the FD nuclear power plant. The activity in the source term is assumed to be 

associated with a liquid volume and release period, which are consistent with the generation of 

contaminated water during emergency measures at TMI and FD. 

1.2.2 Freshwater Settings

For this exploratory analysis, hypothetical freshwater settings were limited to three of the most 

common surface water situations for operating nuclear power plants in the United States: small 

lake, small river, and large river. For the selection of the hypothetical lake setting, the most 

common situation was a reservoir impounded by a dam on a river. While the three selected 

freshwater settings account for the most common situations for nuclear power plants in the 

United States, they do not address the Great Lakes, estuaries, or coastal settings.

Bathymetric data and hydraulic parameters were adapted and modified from actual lake and 

river systems. Steady hypothetical water levels and discharge were used in all scenarios, with 

the lake simulated in three dimensions and the rivers in two dimensions (depth-averaged). The 

lake scenario examined a large water volume (i.e., large dilution potential) where limited 

transport leads to very high radionuclide concentrations until more of the lake volume 

participates in mixing. The small river scenario examined conditions where a relatively low flow 

rate minimizes dilution of the released radioactivity pulse. Conversely, the large river scenario 

examined conditions where a relatively high discharge results in higher dilution of the released 

pulse of radioactivity, but faster downriver transport. 

The initial small and large river domains addressed 50 mi of downstream transport from the 

source term release point. In subsequent analyses, the large river domain was extended from 

50 mi to a dam 103 mi from the radionuclide release point. This extension included the influx of 

2 tributaries that added 20 percent more flow to the large river. Downstream of this dam, two 

flow scenarios were examined for the next 190 river mi (for a total of 293 mi): 1) unimpounded 

free-flowing conditions and 2) impounded conditions with three intervening dams. 

1.2.3 Flow and Transport

The objective of the simplified and generic scoping analyses was to identify the transport 

consequences when a source term containing the predominant dose-contributing radionuclides 

was transported in lake and river settings. The analyses were based on a set of radionuclides, 

release volume, and duration developed for the FD source term scenario. 

The simulated space- and time-dependent aqueous and sorbed activity concentrations in this 

study were based on a 1 becquerel (Bq) activity source term for each radionuclide. The 

functionally linear transport and sediment-radionuclide interaction process models used in this 

study make it possible for others to scale the presented concentrations, which are per unit 

activity, for any magnitude of released activity. This can be accomplished simply by multiplying 

the simulated concentrations from this report by the desired radionuclide activity (Bq) in the 

source term. 
1-4

The initial modeling analyses addressed aqueous-only transport with radionuclide-specific 

decay using steady nonuniform flow fields for the three freshwater settings. The 

multidimensional simulations were designed to resolve spatial variations in the radioactive 

plume, such as the persistence of higher radionuclide concentrations along the same shore as 

the release. Bed and suspended sediment transport with radionuclide-sediment interactions 

were included in the subsequent river simulations to examine the behavior of radionuclides with 

different sorption distribution coefficients (i.e., Kds) in the context of the small and large river flow 

regimes. Sorption during the passage of the released radionuclide pulse followed by longerterm desorption from bed sediments was of particular interest. The extension of the large river 

modeling domain to a downstream dam 103 mi from the radionuclide release point incorporated

the impact of two tributaries and backwater effects on the distribution of aqueous and sorbed 

radionuclides. The final 190-mi extension downstream from this dam was modeled two different 

ways: as a free-flowing reach without impoundments and as a sequence of impoundments with 

intervening dams. These two different extended large river scenarios were used to compare the 

transport of radionuclides with and without the effect of dams and the wide, deep impoundments 

behind them. Of particular interest were 1) comparisons of large and small river mixing 

processes and their impact on near-shore versus far-shore concentration profiles with 

downstream distance, 2) transit times of the pulse of released radionuclide activity and their 

effect on the concentrations of short-lived radionuclides (e.g., 131I), and 3) radionuclide-specific 

bed sediment interactions and the corresponding impact on longer-term concentrations of 

radionuclides in the water column due to sorption and desorption.

Massively parallel processing was necessary to address the high-performance computing and 

large memory requirements for the multidimensional modeling of coupled flow with sediment 

and radionuclide transport and interaction. These processes were resolved in modeling 

domains represented by up to 2.4 million mesh cells and year-long simulations requiring over 

1 million time steps.

1.3 Report Sections

The report continues with Section 2, Aqueous Source Term Estimation Methodology, which 

describes the procedure for calculating the aqueous radionuclide inventory, the fraction 

released, and the volume and duration of the release. Section 3, Freshwater Settings, 

describes the small lake, small river, and large river systems as well as the hydraulic modeling 

approach and radionuclide-specific properties. Section 4, Flow and Transport Modeling, 

describes the processes, governing equations, and simulators used to model the scenarios, and 

the results of the flow and non-radionuclide transport modeling. Section 5, Radionuclide 

Transport Modeling Results, describes the results of the simulated transport of radionuclide 

activity. Section 6, Conclusions, summarizes the approach and provides an overview of the 

findings. Finally, Section 7 is a list of references.
2-1

2. AQUEOUS SOURCE TERM ESTIMATION METHODOLOGY

2.1 Introduction

The generation of large volumes of highly contaminated waste water is common to both the

Three Mile Island TMI and FD accidents. This section outlines a methodology used to estimate 

aqueous concentrations of radionuclides in accidents with severe fuel damage. This could be 

useful when measurements for only a limited set of radionuclides are reported. For example,

early in the FD accident, obtaining wastewater data was difficult for radionuclides other than 131I, 

134Cs, and 137Cs. The method detailed in this section enables estimates for other potentially 

important radionuclides in the aqueous phase, which was necessary for this project to 

determine concentrations for radionuclides that are difficult to analyze or require longer time for 

analysis. 

2.2 Analysis of Historical Accidents

This methodology develops a relationship between the reactor core inventory and the 

concentrations of radionuclides in an accident-generated water release as a function of the 

age/condition of the reactor fuel. The 1979 TMI and 2011 FD accidents provided information 

useful in developing aqueous source terms for hypothetical waterborne release scenarios. The 

accident at TMI Unit 2 in 1979 resulted in a large amount of radioactive water accumulating in 

the basement of the reactor building and in adjacent buildings, although no release of this 

material to the environment occurred. The accident at FD also resulted in accumulations of 

contaminated water in the basements of the reactor buildings, adjacent buildings, and the 

tunnels between them; some of this water was accidentally released into the Pacific Ocean. 

2.2.1 Three Mile Island Unit 2, 1979

The TMI Unit 2 had been operating about three months when the series of events that led to the 

accident began at 0400 on March 28, 1979. Reactor Building basement water sources included 

the reactor coolant system, spray system, air coolers, and inleakage of river water. The 

description of the sources in the next paragraphs is adapted from McIsaac and Keefer (1984).

When a pressure-operated relief valve (PORV) opened, reactor coolant began to escape from 

the Reactor Cooling System (RCS). The lost coolant flowed to the Reactor Coolant Drain Tank 

located in the basement. As a consequence of rapid pressurization, the rupture disk on this 

tank soon burst and coolant escaped to the basement floor. Coolant continued to escape to the 

Reactor Building basement via this pathway until the PORV block valve was closed. Additional 

coolant, in the form of steam and water, and hydrogen gas escaped through the PORV when 

the block valve was intermittently opened to regulate RCS pressure. An estimated 1 × 106 L of 

reactor coolant was released to the basement via this pathway during the first three days 

following the onset of the accident. 

In addition to the 1 × 106 L of RCS water released during the accident, an average of 29.4 L/h 

flowed through the PORV block valve for more than two years following the accident. This 

leakage contributed 6.74 × 105 L of RCS water to the basement water volume. Thus the total 

volume of RCS water that escaped to the basement was approximately 1.67 × 106 L, which is 

about 69 percent of the total volume of water released to the basement as of September 23, 

1981.
2-2

A pressure spike that occurred as a result of a hydrogen burn in containment on the day of the 

accident activated the Reactor Building spray system, which remained on for almost 6 minutes. 

During that time, the system discharged an estimated 6.43 × 104 L of chemically treated water, 

containing boron and sodium hydroxide, into the Reactor Building. Most of this water would 

have eventually drained to the basement.

Further increases in the basement water level after the accident are attributed to leakage from 

the river water cooling system of the Reactor Building air cooling assembly. The leakage is 

suspected to have been from a relief valve on the assembly cooling coils. Based on back 

projections of water level and reconstruction of events associated with water inventory, an 

estimated 6.81 × 105 L of river water was released to the basement from this source before it 

was secured. The river water from this source represents about 28 percent of the maximum 

basement water inventory prior to September 1981. Thus, in this accident, over 1,000 tons of 

water accumulated within the first three days, and continuing in-plant and external sources more 

than doubled that within three years.

Measurements were made of the concentrations of radioactive contaminants in the water in the 

TMI Unit 2 basement at various times. These are summarized in McIsaac and Keefer (1984); 

Table 2-1 reproduces their summary. Table 2-2 shows a back-calculation of these results to the 

date of the accident, March 28, 1979. These back-calculations have not been adjusted for the 

slowly increasing volume of water. The radionuclides listed are those reported by McIsaac and 

Keefer (1984); they represent those most likely to be found (3H, 137Cs, 90Sr), a good surrogate 

for short-lived 131I (129I), and the major refractory fission products (106Ru, 125Sb, 144Ce). 

Various estimates of the amount of radioactive material immediately released to the water in the 

lower levels of the TMI containment are available. An estimate was made by the NRC for the 

environmental impact statement (EIS) related to decontamination and decommissioning of the 

reactor (NRC 1981) using an average of measured concentrations and an estimated water 

volume. This estimate is presented in Table 2-3. An estimate of the total release to basement 

waters may also be made using the data of McIsaac and Keefer (1984) as described in 

Section 2.2 of this report; this estimate is presented in Table 2-4. These two estimates are 

reasonably similar.

Particle size distributions of the sediment solids were determined by analyzing 500X 

photomicrographs of the material filtered from the samples following ultrasonic treatment 

(McIsaac and Keefer 1984). Measurements were made in 2-μm intervals, and did not include 

particles under 1 μm. By number, about 12 percent of the particles collected from the sump 

were larger than 10 μm. About 39 percent of the sump particles were in the 1- to 3-μm size 

range. On a population basis, the mean particle size measured in the sump samples was 

6.2 μm. In another sample from the floor, the particle size distribution measured was found to 

contain very few particles larger than 10 μm. The mean particle size on a volume basis was 

measured to be about 20 μm, and on a population basis it was about 4 μm. A total of 65 

percent of the particles in this sediment sample exhibited sizes between 1.5 and 3 μm, and only 

1.5 percent were found to be larger than 10 μm. These very small particles would be easily 

transported by surface water.
2-3

Table 2-1. Measured Concentrations of Radionuclides in Various Locations of the TMI Unit 2 Basemen

(Bq/mL)

Nuclide 8/28/79 11/15/79 5/14/81 9/24/81 6/23/82 6/23/82 1/11/83 1/11/83 1/11/83 

3H 3.81E+04 3.85E+04 2.23E+04 2.17E+04 -- -- -- -- -- 

90Sr 1.04E+05 8.51E+04 1.92E+05 1.78E+05 2.58E+05 2.15E+05 9.21E+04 8.73E+04 1.28E+05 

106Ru 2.59E+02 1.15E+02 -- -- <1.3E+03 9.62E+01 <5.8E+02 <1.4E+03 <3.5E+02 

125Sb 5.55E+02 8.51E+02 1.11E+03 <7.4E+02 <1.1E+02 9.62E+02 <2.6E+02 <7.4E+02 <1.8E+02 

129I 5.11E-01 -- 1.59E-01 7.40E-01 <2E-4 -- 4.00E-02 4.11E-02 1.51E-02 

134Cs 1.48E+06 1.19E+06 7.10E+05 5.99E+06 5.18E+05 5.18E+05 3.63E+04 2.48E+04 2.44E+04 

137Cs 6.51E+06 5.99E+06 5.29E+06 5.07E+06 5.59E+06 5.88E+06 4.44E+05 3.04E+05 3.06E+05 

144Ce 2.33E+02 3.22E+01 -- <1.3E+03 -- -- <1.6E+02 <4.4E+02 <1.1E+02 

Source: McIsaac and Keefer 1984

Table 2-2 Concentrations of Radionuclides in Various Locations of the TMI Unit 2 Basement at Variou

Decayed to March 28, 1979 (Bq/mL)

Nuclide 8/28/79 11/15/79 5/14/81 9/24/81 6/23/82 6/23/82 1/11/83 1/11/83 1/11/83 

3H 3.90E+04 3.99E+04 2.52E+04 2.50E+04 

90Sr 1.05E+05 8.64E+04 2.03E+05 1.89E+05 2.79E+05 2.32E+05 1.01E+05 9.58E+04 1.40E+05 

106Ru 3.45E+02 1.78E+02 (a) 8.93E+02 (a) (a) (a) 

125Sb 6.16E+02 9.98E+02 1.89E+03 (a) (a) 2.17E+03 (a) (a) (a) 

129I 5.11E-01 1.59E-01 7.40E-01 (a) 4.00E-02 4.11E-02 1.51E-02 

134Cs 1.70E+06 1.47E+06 1.45E+06 1.39E+07 1.54E+06 1.54E+06 1.30E+05 8.87E+04 8.74E+04 

137Cs 6.58E+06 6.08E+06 5.56E+06 5.37E+06 6.02E+06 6.34E+06 4.84E+05 3.32E+05 3.33E+05 

144Ce 3.39E+02 5.67E+01 (a) (a) (a) (a) 

(a) less than values not back-decayed
2-4

Table 2-3. NRC Estimate of Radioactive Material Released to TMI Unit 2 Accident Waters

Nuclide

Inventory (Bq)

As Reported 

9/30/1980

Back-decayed 

to 3/28/1979

3H 9.3E+13 1.0E+14

137Cs 1.6E+16 1.6E+16

134Cs 2.4E+15 4.1E+15

90Sr 2.6E+14 2.7E+14

89Sr 7.0E+12 1.3E+16

Others 2.8E+12 --

Source: NRC 1981

Table 2-4. Derived Estimate of Radioactive Material Released to TMI Unit 2 Basement 

Waters

Nuclide

TMI Core 

Inventory, 

8/28/1979 (Bq)

Release 

Fraction

TMI Core Inventory 

Back-Decayed to 

3/28/1979 (Bq)

Estimated 

Release to 

Basement (Bq)

3H 1.4E+14 0.57 1.4E+14 7.9E+13

90Sr 2.8E+16 0.017 2.9E+16 4.9E+14

106Ru 9.0E+16 0.00004 1.2E+17 4.8E+12

125Sb 1.9E+15 0.003 2.1E+15 6.2E+12

129I 7.2E+09 0.14 7.2E+09 1.1E+09

131I 4.8E+12 0.2 2.5E+18 5.1E+17

134Cs 6.9E+15 0.42 7.9E+15 3.3E+15

137Cs 3.1E+16 0.41 3.1E+16 1.3E+16

144Ce 6.0E+17 0.00001 8.7E+17 8.7E+12

Based on release fraction information in McIsaac and Keefer 1984

2.2.2 Fukushima Daiichi, 2011

The tsunami at FD resulted in flooding of the lower levels of the reactor buildings with sea water. 

Loss of groundwater control systems allowed the influx of groundwater. The highly 

contaminated water in the lower levels of the Fukushima reactor buildings resulted from 

emergency attempts to cool the reactors and fuel storage pools allowing the contaminated water 

to accumulate in basement areas. Much of this injected water subsequently drained into the 

turbine building basements and other structures. Measurements made of radionuclides in 

standing water in the basements of the turbine buildings are shown in Table 2-5 (TEPCO 

2011a). These measurements indicated that the highest concentrations existed in the 

basement of Unit 2.
2-5

Table 2-5. Radionuclide Concentrations in FD Turbine Hall Basement Waters

Nuclide

Concentration of Radioactivity (Bq/mL)

Unit 1 Unit 2 Unit 3 Unit 4

Sampled on 

March 26, 2011

Sampled on 

March 26, 2011

Sampled on 

March 26, 2011

Sampled on 

March 24, 2011

56Co N.D. 1.60E+05 N.D. N.D.

58Co N.D. N.D. N.D. 2.70E-01

60Co N.D. N.D. 2.70E+02 N.D.

99Mo N.D. N.D. N.D. 1.00E+00

99mTc N.D. 8.70E+04 2.20E+03 6.50E-01

106Ru N.D. N.D. N.D. 3.30E+00

108mAg N.D. 2.50E+05 N.D. N.D.

129Te N.D. N.D. N.D. 2.60E+01

129mTe N.D. N.D. N.D. 1.30E+01

132Te N.D. N.D. N.D. 1.40E+01

131I 1.50E+05 1.30E+07 3.20E+05 3.60E+02

132I N.D. N.D. N.D. 1.30E+01

134I N.D. N.D. N.D. N.D.

134Cs 1.20E+05 2.30E+06 5.50E+04 3.10E+01

136Cs 1.10E+04 2.50E+05 6.50E+03 3.70E+00

137Cs 1.30E+05 2.30E+06 5.60E+04 3.20E+01

140Ba N.D. 4.90E+05 1.90E+04 N.D.

140La N.D. 1.90E+05 3.10E+03 7.40E-01

N.D. = Not Detected

Some of this turbine hall basement water appears to have leaked into the ocean by way of a 

utility tunnel (cable storage pit) or its gravel base mat. Water measured in, and just outside, the 

tunnel, had concentrations of 131I at 5.2 × 106 Bq/mL, 134Cs at 1.9 × 106 Bq/mL, and 137Cs at 

1.9 × 106 Bq/mL (TEPCO 2011b). This water had radionuclide concentrations about one-half 

that of the water in the Unit 2 turbine hall basement; it may have been diluted with groundwater 

or mixed with water from one of the other nearby reactors. The leak was discovered on April 2, 

2011 and successfully stopped on April 5, 2011. It is not known how long after the March 11, 

2011 accident that the leak began before being found. Contaminated water leaking through a 

20-cm crack in the concrete wall and falling directly into the seawater was observed. The 

observed leak had a flow roughly equivalent to several garden hoses. Initial analyses by 

TEPCO indicated that perhaps 520 m3 of water containing a combined total of about 4.7 PBq of 

131I, 134Cs, and 137Cs escaped (TEPCO 2012). Later evaluations by others based on ocean 

dispersion estimates resulted in radionuclide release estimates about four times higher 

(Kawamura et al. 2011; Tsumune et al. 2012; Estournel et al. 2012; Buesseler 2013; Miyazawa 

et al. 2013), although the uncertainties are large and the estimate could be even higher 

(Charette 2013). 

Using the sampling results from the basement of Unit 2 (the most likely source of the leak), the 

ratios of other radionuclides to cesium and iodine derived from Table 2-5 may be used to 

estimate the composite release from FD to the ocean. Isotopes of strontium and technetium 

were not initially measured; Bailly du Bois et al. (2012) indicates that the isotopic ratios 

(90Sr/137Cs) and (99Tc/137Cs) were around 0.02 and 0.01 respectively. These ratios differ 

significantly from the initial ratios in the fuel because of different vapor pressures and 

solubilities. Using this information and concentration ratios derived from Table 2-5 with the 

release estimates of Kawamura et al. (2011), Tsumune et al. (2012), Estournel et al. (2012), 

and Miyazawa et al. (2013), the total release to the ocean from the Fukushima leak may be 

estimated as shown in Table 2-6. The United Nations Scientific Committee on the Effects of 
2-6

Atomic Radiation (UNSCEAR) in its 2013 Report to the General Assembly (UN 2014) also 

evaluated the direct release to the ocean and concluded that about 3 to 6 PBq of 137Cs and 10

to 20 PBq of 131I were released. The magnitude of the strontium estimate generated in this way 

is corroborated by Buesseler (2013) and Casacuberta et al. (2013). The estimate of the total 

release to the basement in Table 2-6 is based upon the measurements of Estournel et al. 

(2012) multiplied by a factor accounting for the ratio of the amount of water in the basement 

(10,000 m3) to that released (520 m3) and a factor of two for the apparent dilution seen in the 

cable pit. 

Table 2-6. Estimated Release from the Fukushima Cable Pit Leak to the Pacific Ocean 

(Pbq) Based on Different Sources, and Extrapolated Total Release from Unit 2 

Core to Basement Waters

Nuclide

Release to Pacific Ocean Estimated 

Inventory in 

Basement 

TEPCO 2012 Waters

Kawamura et 

al. 2011

Tsumune et 

al. 2012

Estournel et 

al. 2012

56Co 0.065 0.278 0.250 0.285 11.0

99mTc 0.035 0.151 0.136 0.155 5.96

108mAg 0.102 0.435 0.391 0.446 17.2

90Sr/90Y 0.019 0.080 0.072 0.082 3.15

99Tc 0.009 0.040 0.036 0.041 1.58

131I 2.810 11.0 11.00 12.3 473

134Cs 0.936 4.00 3.50 4.10 158

136Cs 0.102 0.435 0.391 0.446 17.2

137Cs 0.936 4.00 3.60 4.10 158

140Ba 0.199 0.852 0.767 0.873 33.6

140La 0.077 0.330 0.297 0.339 13.0

2.3 A Generalized Approach to Aqueous Source Term Development 

A generalized approach to estimating the aqueous source term from a reactor accident can be 

developed based on the experience gained during the events at TMI and FD. This calculation is 

needed to estimate concentrations of radionuclides in the leaked water because at FD only a 

limited number of radionuclides were initially reported. The approach is based upon release of 

radionuclides from the reactor to waters collected in the building substructures, followed by a 

loss of some fraction of that water to the environment. A simplified schematic of such a process 

is given in Figure 2-1. The evaluation includes consideration of the total amount of radioactive 

material in the reactor at the time of the accident, the fractional release of that material to the 

confines of the reactor buildings, dilution in waters derived from the accident and the responses 

to it, and subsequent leakage from the reactor complex to the aquatic environment.

Figure 2-1. Schematic Process for Estimating Radionuclide Releases to Surface Water 

From a Severe Reactor Accident.
2-7

The evaluation procedure first requires an estimate of reactor core radionuclide contents. As 

reactors operate, energy is liberated by the fission of fuel nuclei, reducing the amount of fuel 

and increasing the content of fission products. A common measure of fuel usage is termed 

“burnup” and is reported in units of megawatt-days per metric ton of uranium fuel (MWd/t). The 

reactors at FD were BWRs that had been running for many months on reloaded fuel elements, 

and thus had an average high burnup. The reactor at TMI was a PWR that had only been 

operating for three months, and thus had a low fuel burnup. Reactor type, size, and operating 

history all have an influence on the total amount of radioactive material available for a release. 

Previous research for the NRC resulted in tabulations of reactor fuel inventories for various fuel 

burnup levels in units of Bq per metric ton of uranium (Ramsdell et al. 2001). The Ramsdell et 

al. (2001) reference provides values for BWRs and PWRs for a range of burnup from 22 to 

75 gigawatt days per metric ton of uranium fuel (GWd/MTU). These are summarized in 

Appendix A.

The next step in the evaluation procedure requires information about the transfer of radioactive 

material from the reactor to the confines of the reactor complex. After the TMI accident, 

extensive post-accident analyses were conducted and it was determined that large fractions of 

some radionuclides were released into the water that spilled into the lower levels of the reactor 

and turbine building basements. The total release fraction of various materials from the core to 

the water was determined by McIsaac and Keefer (1984). Their estimates of the fraction of 

materials in the water are given in Table 2-7. Similar fractions of radionuclides released are 

seen at FD; the UNSCEAR 2013 Report to the General Assembly (UN 2014) notes that “several 

tens of per cent of the inventories of the more volatile elements (i.e., hydrogen/tritium, iodine 

and cesium) in the cores of the three damaged reactors have been found ... in stagnant water, 

mainly in the basements of the turbine and reactor buildings but also in surrounding areas. 

Less volatile elements (e.g., strontium, barium and lanthanum) were also found but at levels that 

were between about one and ten percent of those for the more volatile elements in terms of 

their relative inventories.” While these FD release fractions have yet to be refined, the 

preliminary results indicate that the use of similar release fractions in severe reactor accidents 

has merit.

Table 2-7. Fraction of Reactor Core Inventory Released to Water in the Basement at TMI

Material Fraction Material Fraction

3H 0.57 Pu 0.000006

90Sr 0.017 Cr 0.005

106Ru 0.00004 Fe 0.01

125Sb 0.003 Ni 0.008

129I 0.14 Zr 0.000004

131I 0.2 Ag 0.002

134Cs 0.42 Cd 0.003

137Cs 0.41 In 0.009

144Ce 0.00001 Sn 0.0007

U 0.000008 Gd 0.001

Source: McIsaac and Keefer 1984

The 94 MTU of fuel in Unit 2 at FD had a burnup of about 35 GWd/MTU, based on the ratio of 

134Cs to 137Cs of about 1.0 (Pretzsch et al. 2011). Using the TMI-derived release fractions, 

94 MTU in the core, and an interpolated core inventory from Ramsdell et al. (2001), the total 

inventory released to the FD Unit 2 building water may be estimated as shown in Table 2-8. 

Comparing this estimate with that derived in Table 2-6, it may be seen that the two agree to well 
2-8

within a factor of 2. Thus, the methodology was able to provide estimates that compared 

reasonably well with the only available independent measurements of an aqueous radionuclide 

inventory from a severe nuclear power plant reactor accident. An assumed release fraction to 

the environment from the basement completes the assessment.

Table 2-8. Comparison of Fukushima Daiichi Aqueous Radionuclide Inventories Derived 

from TMI Release Fractions and Ocean Measurements

Nuclide

TMI 

Release 

Percentage

FD Core Inventory 

(PBq from 94 MTU 

at 35 MWd/MTU)

PBq Estimated in 

FD Basement 

Using Release 

Fractions

PBq Estimated in FD 

Basement Using

Ocean Release

Ratio of 

Ocean / 

Fractions 

Methods

90Sr 1.7 305 5.19 3.15 0.61

131I 20 2,040 408 473 1.16

134Cs 42 431 181 158 0.87

137Cs 41 391 160 158 0.98

2.3.1 Comparison of TMI Unit 2 and FD Waste Water 

The estimates derived in this report using the methods of Section 2.2 for masses of radioactive 

material in accident-generated water in the basement of TMI Unit 2 and FD Unit 2 are given in 

Table 2-9. There are significant differences in the events at TMI Unit 2 and FD. The initiating 

event at FD (i.e., the tsunami) introduced a large amount of seawater to the lower levels of the 

reactor complex, and the inleakage of groundwater and input of cooling water both continued at 

relatively high rates; thus, the amount of water at FD was larger. Beyond the differences of 

reactor type (i.e., BWR at FD and PWR at TMI Unit 2), additional differences existed in the 

radionuclide inventories in the reactors just prior to the accident. TMI Unit 2 had been running 

only a few months and the fuel burnup ranged from about 900 to 6,000 MWd/MTU (Schnitzler 

and Briggs 1985), averaging about 2,500 MWd/MTU. This is about one-tenth the burnup of the 

FD Unit 2 fuel (Pretzsch et al. 2011). 

The levels of fuel damage caused by the accidents at TMI Unit 2 and FD Unit 2 appear similar. 

The amounts of uranium dioxide fuel were approximately the same (about 94 metric tons in 

each reactor). The differences in fuel burnup account for most of the difference in the releases 

to basement water seen in Table 2-9 between TMI Unit 2 and Fukushima. The concentrations 

of shorter-lived radionuclides (e.g., 131I) in fuel are determined more by power level than burnup, 

and should be similar. 

Table 2-9. Comparison of Major Radionuclides in Accident-Generated Water at TMI

Unit 2 and FD

Nuclide

TMI Fukushima Ratio

(PBq) (PBq) Fukushima/TMI

3H 0.079 0.95 12

90Sr 0.49 5.2 10.6

106Ru 0.0048 0.047 9.7

125Sb 0.0062 0.074 11.9

131I 510 410 0.8

134Cs 3.3 180 54.5

137Cs 13 160 12.5

144Ce 0.0087 0.030 3.4
2-9

The concentrations of long-lived radionuclides (3H, 90Sr, 137Cs) in fuel are determined mostly by 

burnup, and ought to differ by about the ratio of burnups (i.e., one order of magnitude). 

Intermediate-lived radionuclides (144Ce) should be in between. This is the behavior noted in 

Table 2-9. The only radionuclide concentration not immediately obvious is 134Cs, which is 

produced both directly as a fission product and via neutron capture from nonradioactive 133Cs, 

which is a common fission product. As a result, 134Cs increases at a rate greater than a simple 

burnup ratio.

An independent assessment of the amounts of water, 131I, and 137Cs in the lower levels of FD 

Units 1, 2, and 3 was recently published (Hidaka and Ishikawa 2014). The estimate of 131I 

normalized to March 11, 2011 in water beneath Unit 2 is 1,700 PBq, which may be decayed to 

April 1, 2011 of the cable pit leak to 280 PBq. The estimate for 137Cs is 99 PBq. These are both 

within 50 percent of their respective values in Table 2-8 derived using the methods of 

Section 2.2, and also are similar to the results in Table 2-6 derived from ocean measurements. 

Substantial uncertainty still exists regarding the actual amounts of radioactivity released from 

the reactors during the accidents, but the various approximation techniques produce similar 

results.

2.4 Surface Water Source Term

Because the reactor and turbine buildings are robust and partially subterranean, it is unlikely 

that all of the water could escape the buildings to surface water even in the severest of 

accidents. As noted above, the release rate of water seen leaking directly to the ocean during 

the FD accident was the rough equivalent of several garden hoses. Thus, a fractional release of 

that material must be hypothesized.

Evaluations based on ocean dispersion estimates resulted in radionuclide release estimates 

shown in Table 2-10 (Kawamura et al. 2011; Tsumune et al. 2012; Estournel et al. 2012; the UN 

(2014) estimate is an expert summarization of these references) for the direct release (not 

including fallout from the atmospheric releases), although the uncertainties are large and the 

estimate could be even higher (Charette et al. (2013) indicate 11 to 16 PBq of 134Cs; Bailly du 

Bois et al. (2012) estimate 12 to 41 PBq of 137Cs – although these estimates are somewhat 

confounded by an atmospheric component). The values in Table 2-10 represent about 

2.5 percent of the entire amount available in the water in the FD buildings (Section 2.3); those of 

Charette et al. (2013) and Bailly du Bois et al. (2012) represent from 11 to 25 percent.

The leak at FD was relatively small and may have been undetected for several days. It took 

almost 3 days to contain the leak from the time of discovery. It appears that about 2.5 percent of 

the available aqueous radionuclide inventory was released. Equivalently, the activity in the 

released water was about 0.3 percent of their aggregate activity in the reactor core inventory. 

Table 2-10. Estimates of Direct Release of Radionuclides to the Ocean from Fukushima 

(PBq)

Nuclide

Release to Pacific Ocean

TEPCO 

2012

Kawamura et 

al. 2011

Tsumune et 

al. 2012

Estournel et 

al. 2012

UN

2014

131I 6.8 11 11 12.3 9 – 18

134Cs 1.2 4.0 3.5 4.1 3 – 6

137Cs 1.2 4.0 3.6 4.1 3 – 6
2-10

In addition to a fractional release, a period of time over which the release occurs is also required 

for the specification of the source term. The primary direct leak was discovered on April 2, 2011 

and successfully stopped on April 5, 2011. It is not known how long after the March 11 accident 

the leak began before being found; however, the amount of radioactive material released into 

the ocean was estimated for TEPCO (2012) by the Central Research Institute of Electric Power 

Industry based on the monitoring data of radioactivity concentration of materials in the seawater 

near the north/south water discharge channels at the power station. This analysis found that 

the largest releases began about March 26, 2011. This would indicate that the major releases

occurred over a period of approximately 11 to 12 days. For the initial scoping analysis, a 10-day 

radionuclide release duration is assumed.

To transport the radioactive material from the reactor buildings to the adjacent surface water 

body, there must be a water volume associated with the release. Initial TEPCO analyses 

suggested that the major leak at FD to the ocean in March and April 2011 consisted of about 

520 metric tons (m3) of water (TEPCO 2012); subsequent analyses indicated that the 

radionuclide release could have been up to 4 times greater, which could indicate that larger 

amounts of water were involved (i.e., up to 2,000 m3). The water in the FD buildings resulted 

from not only reactor coolant and injected water but also the residuals from the tsunami and 

groundwater inleakage. Estimates of the quantity of water that accumulated in the buildings 

associated with Units 1, 2, and 3 ranged up to 55,000 m3 in the months following the accident 

(Hidaka and Ishikawa 2014). The total amount of water in the TMI Unit 2 basements was about 

1,000 m3 in the first three days (McIsaac and Keefer 1984) from the reactor coolant system via 

the open PORV and Reactor Building spray system, after which most water accumulation was

slowed or stopped. This provides a reasonable lower bound to the amount of water that could 

be released to the environment. For the initial scoping analysis, it is assumed that the 

radionuclide release be associated with 1,000 m3 of water. 

In summary, the methodology to develop an aqueous radionuclide source term for 

environmental release was demonstrated for the 2011 FD reactor accident. The first step was 

to determine the reactor core inventory based on the reactor type (single BWR), mass of 

uranium fuel (94 metric tons), and fuel burnup (35 GWd/MTU) using the approach of Ramsdell 

et al. (2001). Then, the aqueous radionuclide inventory (i.e., concentrations in building water) 

was calculated using the reactor core inventory and the partitioning of radionuclides to water 

observed following the 1979 TMI nuclear power plant accident. For the FD event, the aqueous 

radionuclide inventory comprised eight radionuclides: 3H, 90Sr, 106Ru, 125Sb, 131I, 134Cs, 137Cs, 

and 144Ce. A direct release of 2.5 percent of the predicted aqueous radionuclide inventory 

(~0.3 percent of the reactor core inventory) was shown to be consistent with activity estimates in 

the marine system offshore from the FD nuclear power plant in the wake of the March 11, 2011 

earthquake and tsunami. Finally, the hypothetical source term was associated with 1,000 m3 of 

water released over a 10-day period, which was intended to account for the generation of 

contaminated water during emergency measures in a severe reactor accident. 
3-1

3. FRESHWATER SETTINGS 

This section describes the physical hydrologic settings and radionuclide characteristics used in 

the fate and transport calculations for the scoping analysis. The prototype lake and river model 

environments will receive radionuclides via the liquid release described in the previous section. 

The attributes of these freshwater settings are informed by characteristics of existing nuclear 

power plant sites to simulate reasonably representative conditions. Processes controlling the 

transport and mobility of the target radionuclides in the lake and river environments include 

hydrodynamics, transport of dissolved constituents (i.e., advection and mixing), sediment 

transport, reactions with bed and suspended sediments, transport of dissolved and sedimentsorbed radionuclides, and radioactive decay. This scoping analysis uses three freshwater data 

sets (i.e., small lake, small river, and large river) that include bathymetry, hydrologic conditions, 

sediment conditions, and radionuclide transport properties. 

The scope of this study is the examination of freshwater settings and conditions controlling the 

aqueous transport of radionuclides from a severe reactor accident scenario. Of the operating 

nuclear power plant reactors in the United States, 83 are associated with freshwater bodies.1 

Of the reactors sited near freshwater bodies, 51 are sited near largely free-flowing sections of 

rivers and 32 are sited near lakes or reservoirs—including the 12 associated with the Great 

Lakes. Most of the lakes or reservoirs proximate to reactor sites are artificial impoundments on 

rivers controlled by dam operations. Large rivers (annual average flow greater than 50,000 cfs) 

with nuclear reactors include the Mississippi River (e.g., Grand Gulf Nuclear Station), the 

Columbia River (e.g., Columbia Generating Station), and the Missouri River (e.g., Callaway 

Nuclear Power Plant). Reactors using recirculating (as opposed to once-through) cooling water 

systems minimize water use, allowing them to be sited on river sections with small discharges 

(annual average flow less than 10,000 cfs) such as the Schuylkill River (i.e., Limerick 

Generating Station), Colorado River (i.e., South Texas Project), Rock River (i.e., Byron Nuclear 

Generating Station), and Savannah River (i.e., Vogtle Electric Generating Plant). 

3.1 Specifications for Hypothetical Freshwater Settings

This study uses three hypothetical freshwater settings for a severe reactor accident radionuclide 

release. All three cases use the same 10-day radionuclide activity release. Consequently, 

differences in radionuclide concentrations and exposure are dictated by the transport and 

transformation conditions for each modeled setting and the radionuclide-specific distribution 

coefficients (Kd) and half-lives (Table 3-1). One lake/reservoir setting was considered; however, 

as most reactors are sited near rivers, two river settings were considered corresponding to small 

and large discharges that include free-flowing reaches. 

Lake/Reservoir. The lake setting was intended to examine conditions where the potentially 

large volume of water available to dilute the radionuclide release was offset by less dynamic flow 

conditions, which limited transport to primarily mixing rather than advection. The selected lake 

setting was an impoundment behind a dam with a small nominal 100 cfs flow. The lake was 

modeled to be about 6,000 ac with an approximate volume of 130,000 ac-ft; measuring about 1.2 

mi (2 km) at its widest and about 11 mi (17.7 km) long. Volumetrically, the modeled lake system 

is over 3 orders of magnitude smaller than Lake Erie, the smallest of the Great Lakes. 

 1 http://www.nrc.gov/info-finder/reactor/
3-2

Table 3-1. Radionuclide Partition Coefficient (Kd) and Half-Life Values

Nuclide

Kd

(L/kg)

Half-life

(years)

3H NA 12.32

90Sr 2.3E+2 28.79

106Ru 1.1E+4 1.02

125Sb 5.5E+2 2.75

131I 5.9E+1 0.022

134Cs 1.6E+3 2.07

137Cs 1.6E+3 30.17

144Ce 4.2E+4 0.78

Small Discharge River. The small discharge river setting was intended to be used to examine 

conditions where lower volumetric flow rates limit dilution and lead to relatively slower transport. 

In this case, the river setting was modeled with a nominal 5,000 cfs discharge and 50 mi of 

downstream transport from the shoreline release point. 

Large Discharge River. The large discharge river setting was intended to be used to examine 

conditions where higher volumetric flow rates result in faster transport and generally lower 

radionuclide concentrations. In this case, the river setting was modeled with a nominal 

100,000 cfs discharge for 50 mi of downstream transport from the shoreline release point. 

Bathymetry is the primary data required to represent the shape of the river and lake bottoms in 

the specification of the model geometry. Typically, multiple data sources are integrated into a 

single bathymetric surface. The extents of the simulated domain are defined, and then the 

bathymetric surface is used to create the computational mesh for the hydrodynamic and 

transport modeling. 

The lake/reservoir setting was based on an impoundment behind a dam. The modeled 

lake/reservoir width was approximately 2,000 to 6000 ft wide with variable water depths and a 

maximum depth of 85 ft. The small river was given a pool/riffle configuration. The large river 

settings addressed free-flowing and impounded scenarios, including tributaries. All data sets 

were modified from actual geometries to better suit the hypothetical and scoping nature of these 

hydrodynamic and transport analyses (Figure 3-1, Figure 3-2, and Figure 3-3). 

The fate of a radionuclide in a water body can sometimes depend on its interaction with other 

constituents, including sediment or biota. In this work, radionuclide interaction with sediment or 

biota was not considered in the lake setting. Sediment interaction was considered in the river 

settings, but biota was not. Suspended sediment characteristics in rivers and lakes can vary 

widely depending on location and geologic characteristics of the watersheds in the river basin. 

Deposition of contaminated sediments can affect the magnitude and timing of downstream 

radionuclide concentrations and lead to longer-term dose consequences. If more study is 

warranted, the attenuation and chronic source associated with sediment-radionuclide interaction 

and deposition are candidates for further exploration. Future work looking at long-term (i.e., 

years) transport processes in an actual river with annual hydrographs and flood/drought cycles 

may need to include bedload transport, both erosion and deposition, and a multi-layer sediment 

bed, especially in alluvial rivers.
3-3

Figure 3-1. Reservoir/Lake Bathymetry Showing the Variable Water Depth. The inset 

shows an example of a typical computational mesh (horizontal layer) used 

for three-dimensional (3D) hydrodynamics and transport modeling.
3-4

Figure 3-2. An Example of a Section of the Small River Bathymetry. A typical 

computational mesh is also shown overlaid on the bathymetry. Elevation 

units are feet.

Figure 3-3. Example of a Large River Section with Bathymetry. Also shown is the 

computational mesh for a 2-D depth-averaged model. Each mesh cell is 

approximately 10 m on a side. Depth units are feet. 
3-5

3.2 Examples of Release Pulses Transported in Rivers

The intent for modeling the transport of a hypothetical pulse of radionuclides released into 

riverine settings is to better understand the collective and systematic impact of processes, 

properties, and conditions on downstream radionuclide concentrations. As the radionuclide 

pulse moves downstream, lateral mixing eventually leads to fully mixed conditions across the 

channel cross-section, whereas longitudinal mixing tends to dissipate peak concentrations by 

spreading out the length of the pulse. A key outcome is determining the timing of downstream 

arrivals and the extent of radionuclide activity attenuation from dilution, sorption, and decay 

processes. The transport of instantaneous and pulse releases in rivers has been observed in 

dye and tracer experiments and in many inadvertent releases of materials into rivers. Several 

examples are discussed below, focusing on radionuclide releases and dye tests.

Releases of 131I occasionally took place from the Hanford plutonium production reactors to the 

Columbia River, when a fuel element failed. Nelson et al. (1966) measured 131I concentrations 

at various locations downstream of the Hanford D Reactor following several releases. Timedependent concentration plots of the downstream arrival of the releases show substantial 

attenuation of peak concentrations and spreading of the pulse during transport through 

impoundments behind dams. For the Columbia River, the 131I concentration was reduced by 

about a factor of 8 over approximately 250 mi. The time histories of observed 131I

concentrations at downstream locations (Figure 3-4) show the transport of a distinct 

concentration peak as a result of the relatively instantaneous nature of the release. In contrast, 

a controlled radionuclide release with constant concentration over a period of several days (e.g., 

the source term used in this study) would result in the transport of a concentration pulse 

resembling a square wave at downstream locations. Spreading from longitudinal mixing tends 

to smooth out the front and trailing edges of the square wave pulse. Nelson et al. (1966) 

calculated time of travel from the D Reactor to a site about 200 mi downstream to vary from 

about 9.5 days during average flow (102,000 cfs) to about 2.3 days under very high-flow 

conditions (627,000 cfs); or 21.1 and 87.0 mi/day, respectively. 

In 1996, a flood on the Pripyat River Floodplain in the area of Chernobyl inundated 

contaminated soils, releasing 90Sr to the water. This contaminant flowed downstream through 

the Dnieper River system and was sampled at several locations (IAEA 2006). This pulse of 90Sr 

took more than 6 months to flow about 560 mi and concentrations were reduced by a factor of 

three (Figure 3-5). The very slow travel time is because of the large size of the reservoirs in the 

system, especially the Kakhovka reservoir which has a volume of 13 million ac-ft. 

Tests using Rhodamine BA dye on the lower reaches of the Missouri River were conducted in 

1966 by the United States Geological Survey (USGS 1969). For the section of the river 

illustrated in Figure 3-6, the dye was injected into the river at Sioux City and detected at three 

locations over a total distance of about 84 mi. Tests conducted in October and December 

resulted in significantly different transit times and concentrations for the peak arrivals of dye at 

the same downstream sampling locations (i.e., Decatur, Blair, and Omaha, Nebraska). For the 

December test, peak arrival concentrations in Omaha, Nebraska doubled and travel time 

increased by 40 percent. Similar data are available for a number of river systems.

The Missouri River study also provided a set of tables of travel times and water velocities 

between different sampling points. Table 3-2 extracts a small example of those data for the 

distance of 84 mi between Sioux City and Blair, illustrating that as discharge varies so too will 

travel times and velocities of dissolved chemicals. 
3-6

Figure 3-4. Observations of 131I Pulse as It Travels Downstream on the Columbia River 

(Nelson et al. 1966).
3-7

Figure 3-5. Ten Day Averaged Activity Concentrations (blue diamonds) of 90Sr at Three 

Dams along the Dnieper River: (a) Kiev Reservoir, (b) Zaporozhe Reservoir, 

and (c) Kakhovka Reservoir (IAEA 2006). Triangles represent simulated 

concentrations.
3-8

Figure 3-6. Data from a Tracer Test on the Lower Missouri River. Tracer was injected at 

Sioux City and sampled downstream at Decatur, Blair and Omaha. Graphs 

showing the arrival concentration profiles at the three locations for tests in 

October and December 1966 (USGS 1969).

Table 3-2. Travel Time and Velocity of Solute in the Missouri River between Sioux City 

and Blair (USGS 1969).

Discharge (CFS) Time (hours) Velocity (MPH)

10,000 44.0 1.90

20,000 33.0 2.52

50,000 22.7 3.68

100,000 17.0 4.90
3-9

Other studies on several rivers using dyes showed similar behavior on stretches of the Missouri 

River (Yotsukura et al. 1970), the Ohio River (Wiley 1997), and the Potomac River (Taylor et al. 

1985). In addition to determinations of contaminant travel time, these studies allow analysis of 

longitudinal dispersion. Other tracer tests have provided transit rates that include: 3.1 mi/day for 

70 mi of the upper Ohio River (Wiley 1997), 5.5 mi/day for the Potomac from Cumberland to 

Point of Rocks (Taylor et al. 1985), 5.6 mi/day for the upper Hudson River (above Troy, NY) 

(Caplow et al. 2004) and 55.9 mi/day for a 298 mi stretch of the lower Mississippi (USGS, 

1976). These travel time examples vary depending on discharge rates, channel geometries,

and the operations of dams.

In summary, travel times of contaminants downstream depend on the discharge and velocity of 

the river, which can vary substantially in time and space (e.g., effect of tributaries, dams, and 

reservoirs). Water column concentrations are generally reduced by dilution, dispersion, decay, 

and sediment interaction, yet coherent pulses of dissolved contaminants with relatively high 

concentrations have been observed hundreds of miles from their sources. 

3.2.1 Long-Term Impacts of a Large Radionuclide Release

A large release of radionuclides to a small river (25 to 200 cfs) occurred in the early 1950s 

(Napier 2014). Beginning in 1948, the Soviet Union initiated a program for production of nuclear 

materials for a weapons program. The first facility for production of plutonium was constructed 

in the central portion of the country east of the southern Ural Mountains, about halfway between 

the major industrial cities of Ekaterinburg and Chelyabinsk. The facility, now known as the 

Mayak Production Association, and its associated town, now known as Ozersk, were built to 

irradiate uranium in reactors, separate the resulting plutonium in reprocessing plants, and 

prepare plutonium metal in the metallurgical plant. The rush to production, coupled with 

inexperience in handling radioactive materials, led to large radiation exposures, not only to the 

workers in the facilities, but also to the surrounding public. Designed disposals of low- and 

intermediate-level liquid radioactive wastes, and accidental releases via cooling water from tank 

farms of high-level liquid radioactive wastes, into the small Techa River caused significant 

contamination and exposures to residents of numerous small riverside villages downstream of 

the site. Discovery of the magnitude of the aquatic contamination in late 1951 caused revisions 

to the waste handling regimes, but not before about 100 PBq (3 million Ci) of fission product 

radionuclides (with large contributions of 90Sr and 137Cs) were released – about 3 times the 

estimated release from the FD accident presented in Section 2.2.2, but of a different 

radionuclide mix. Although use of the Techa River was prohibited following discovery of the 

magnitude of the releases, residents up to 150 mi downstream received chronic bone doses of 

up to 2 Sv (200 rem) because they were ignoring the prohibition on river shoreline use. Over 50 

years later, the dose rate in the river sediments was still sufficiently high above background that 

villages remained evacuated. 

The low flow and small profile of the Techa River minimized dilution and maximized 

sorption. Sorption of radionuclides to sediments along the shoreline and in the river bed during 

the passage of these releases resulted in a distributed radioactive source with long-term 

consequences. In this case, the primary pathway for exposure involved uncontrolled access to 

the river shoreline. The sediment-sorbed activity was immobile and subject to decay and 

desorption into the water column. However, the radionuclides were sufficiently long-lived (e.g., 

137Cs and 90Sr) and strongly sorbed to create a chronic exposure scenario that required access 

restrictions long after the passage of the radionuclide releases in the water column.

 

4-1

4. FLOW AND TRANSPORT MODELING 

This section describes the processes, governing equations, and simulators used to model the 

scenarios, the modeling approach, and the results of the flow and non-radionuclide transport 

modeling. The various scenarios were modeled using simulators (Section 4.3) that solve the 

governing equations of mass, momentum, and transported scalar conservation. For brevity, the 

details of mass and momentum simulation will be omitted. Detailed descriptions can be found in 

citations mentioned in the model descriptions below. In this work, the fate and transport of 

sediment and radioactive species is described, for which some details require discussion.

4.1 Mixing and Transport

When a contaminant is introduced into a flowing river it first experiences mixing due to its 

buoyancy and initial momentum forming into a “cloud” of concentration. After the initial 

discharge, the contaminant undergoes several mechanisms of mixing and transport, detailed 

here with increasing magnitude: molecular diffusion, turbulent diffusion, advective dispersion,

and advection. Due to the high turbulence in even the most quiescent flow, turbulent diffusion is 

far larger than molecular diffusion, though it is modeled in much the same way with mass flux 

proportional to the concentration gradient by a mixing coefficient. Advective dispersion is 

caused by the cross-channel variation in velocity and turbulent diffusion, spreading the cloud out 

in the longitudinal, or stream-wise, direction. In general, the largest mechanism of contaminant 

transport is advection, or the movement due to the downstream velocity of the water in which 

the contaminant cloud resides (Fischer et al. 1979, Rutherford 1994, Martin et al. 2012). 

In natural rivers, where depth is generally much smaller than width, and width is much smaller 

than length, vertical diffusion occurs the most quickly, with concentrations rapidly becoming 

vertically well-mixed by the turbulent diffusion. Complete transverse mixing occurs next, with 

turbulent diffusion causing the contaminant to be mixed across the cross section of the river as 

a function of the distance across and the turbulence of the flow. Once the contaminant is wellmixed in both the vertical and transverse directions, the continued turbulent mixing across the 

cross section causes the contaminant to “sample” different velocities (e.g., higher in the middle, 

lower near the shore), stretching the cloud along the direction of flow (i.e., the longitudinal 

direction). While all this is occurring, the mass of the water and the contaminant are being 

advected, or moved downstream by the flow of the water. The magnitude of both the turbulent 

diffusion and advective dispersion can be affected by the shape of the bed; the bends in the 

river; and the presence of zones of low velocity, typically found near the shore. The 

contaminant can also experience other mechanisms that affect its concentration and transport

(e.g., chemical or radioactive decay, sorption, or precipitation).

4.2 Theory

This section briefly summarizes the theory behind the fate and transport simulations performed

in this work. As with the hydrodynamic modeling, details can be found in the model citations. 

The governing equation for transport of a scalar φ (amount of transported constituent per unit 

volume) in the water column is 

∂

∂t ⌡⌠

V

φdV+ ⌡⌠

S

φv⋅ndS = ⌡⌠

S

ε

φ

∇φ⋅ndS + ⌡⌠

V

qφdV (4-1)
4-2

where V is volume; S is surface area; v is the fluid velocity vector with components ui

; n is the 

surface area outward-directed unit normal; qφ is a source term; and ε

φ is the turbulent mixing 

coefficient of φ. 

The source term of Equation (4-1) represents processes that increase or decrease constituent 

mass or activity in the water column. This includes sediment erosion and deposition, decay of 

aqueous and sediment-sorbed radionuclides, erosion and deposition of sediment-sorbed 

radionuclides, and direct sorption to the bed sediment. The mathematical representation of the 

important source term components is described below for the different scalar types. The 

representation of suspended and bed sediment and radionuclide interaction with sediment was 

used in the river settings only (i.e., sediment interaction was not considered in the lake setting). 

4.2.1 Sediment

When the fate and transport of suspended sediment is modeled by Equation (4-1), the 

contribution to the source term consists of rates of erosion from and deposition to the bed. The 

source term contribution from net deposition is represented as 

qφsed= E−D (4-2)

where qφsed

has dimensions of mass per unit bed area per time. E is the erosion rate, given for 

example by (Partheniades 1962):

E =

















 τ

b

τ

e

−1 E

o

;if τ

b

>τ

e

0;if τ

b

≤τ

e

(4-3)

where τ

bis the bed shear computed from the hydrodynamic state, Eo is the erodibility 

coefficient, and the critical erosion shear stress, τ

e

, represents the shear at which erosion is 

initiated. The erosion rate computed using Equation (4-3) is limited by the availability of 

sediment in the bed. In this work, the sediment was assumed to be non-cohesive and only 

deposition was considered, as reflected in the adoption of zero erodibility (E

o = 0). 

D is the sediment deposition rate, given for example by (Krone 1962) 

D =



















1− 

τ

b

τ

d

wφsed;if τ

b

<τd

0;if τ

b

≥τd

(4-4)

where φsed is the volumetric sediment concentration, w is the particle settling velocity, and τ

dis 

the critical deposition shear stress. The parameters w, τ

e

, and τ

d

, are sediment-specific 

properties. Their values will vary depending on the sediment particle size, chemical 

composition of the sediment, and other local conditions. Consequently, they are usually 
4-3

determined by calibration guided by reported values from the literature. Although a plethora of 

alternative formulations for erosion and deposition are available (see for example García 2008), 

the formulations adopted herein are appropriate and demonstrative for establishing the 

methodology of the scoping study.

4.2.2 Dissolved Radionuclide

The dissolved radionuclide (or aqueous phase) is affected by decay, sorption to and desorption 

from suspended sediment, and direct sorption to and desorption from the bed surface 

(radionuclide interaction with biota is not considered in this work). The source term in 

Equation (4-1) is represented as 

qφ = − λ

φφ + Kφ 

  K  d

φ

φsedφ−φpart+ ρsedD50 (1−p)K

φ 

  K  d

φ

φ−φbed (4-5)

The first term describes radioactive decay, where λ

φ is the decay rate (1/T), which is computed 

from the half-life, t

φ1/2

, as 

λ = ln2

t

φ1/2

(4-6)

The second term on the right-hand side of Equation (4-5) represents the exchange with the 

suspended particulate phase of φ. Kd

φ

is a partitioning coefficient specific to the scalar φ and 

sediment size and type (Onishi and Thompson 1984). The value of Kd

φ

is the ratio of 

particulate to dissolved contaminant when they are in equilibrium 

Kd

φ

=

φpart

φsedφ (4-7)

where φpart is the volumetric concentration of particulate or sorbed radionuclide and φsed is the 

volumetric concentration of suspended sediment. The magnitude of the exchange is governed 

by the dissolved/particulate imbalance and the rate K

φ at which contaminant is exchanged 

between phases, which has dimensions of 1/T.

The third term on the right-hand side of Equation (4-5) similarly represents the exchange of 

dissolved contaminant within the water column with any particulate contaminant on the bed 

surface. φbed is the bed concentration of φ and p is the bed porosity. The exchange is 

assumed to be limited to the surface of the bed, or the mass of sediment occupying a thickness 

of one sediment grain diameter, D50, at the top of the bed.

4.2.3 Suspended Sediment-Sorbed Radionuclides

When suspended sediment-sorbed radionuclides (or particulate phase) are simulated, the 

source term for Equation (4-1) includes the loss of mass due to sediment deposition and 

interaction with the aqueous phase. The source term takes the form 
4-4

qφpart= −λ

φφpart− Kφ 

  K  d

φ

φsedφ−φpart + 













φbedE− 

Dφpart

φsed

(4-8)

The first term on the right-hand side of Equation (4-8) represents decay, as in Equation (4-5). 

The second term represents exchange with the dissolved phase and corresponds to the second 

term of Equation (4-5). The third term represents the particulate mass deposited to or eroded 

from the bed, as described above. 

4.2.4 Bed Representation

This section describes the representation of sediment and sorbed radionuclides in the river bed 

in Modular Aquatic Simulation System in 2 Dimensions (MASS2) (Section 4.3.2). MASS2 can 

represent multiple sediment size fractions and multiple bed layers, but for this work bed 

sediment was represented with a single sediment size fraction in a single well-mixed layer with 

a specified, spatially and temporally constant porosity, p, and a variable layer depth, dbed. The 

bed sediment is stored as mass per unit bed area, Msed. The depth of the bed is computed as 

dbed= 

Msed

ρb

(4-9)

where ρb is the bed bulk density, 

ρb

=ρs (1−p)

and ρs

is the sediment solids (or particle) density.

At the end of a simulation time step, Δt, the deposition rates computed during the suspended 

sediment transport solution are added to the bed mass 

Msed = ( ) Msed

old

+Δt (D−E)h1h2 

where h1

h2 is the plan-view surface area of the cell. This is an approximate time integration of 

the source term in Equation (4-2).

Transported scalar quantities are also accounted for in the bed, both in a dissolved phase within 

the bed pore water and particulate phase(s) sorbed to bed sediments. Dissolved scalar 

quantities are stored as mass per unit bed area, M

φpore

. When necessary, a pore concentration 

is computed as 

φpore= 

M

φpore

pdbed
4-5

Particulate scalar quantities are also stored as mass per unit bed area, M

φbed

. The ratio of 

scalar to sediment mass is necessary 

φbed= 

M

φbed

Msed

At the end of the time step, all other direct exchange with the water column is accounted for. 

This takes two forms. First, any particulate contaminant eroded or deposited with sediment is 

subtracted or added to the current particulate mass 

M

φbed

= 

  M

φ 

bed old

+Δt











Dφ  part

φsed

−φbedE h1h2

which is a time integration of the third term of Equation (4-8). Second, any exchange of 

particulate contaminant on the bed surface with the water column is accounted for 

M

φbed

= 

  M

φ 

bed old

+Δt



  ρ  s

D50 (1−n)K

φ 

  K  b

φ

φ−φbed h1h2,

which is a time integration of the third term of Equation (4-5). The exchange is assumed to be 

limited to the surface of the bed, or the mass of sediment occupying a thickness of one 

sediment grain width, D50, at the top of the bed.

Those scalar quantities that decay in the water column also decay in the bed. This decay is 

accounted for at the end of each time step, after any exchange with the water column has been 

considered. The masses of dissolved scalar quantities are decayed using 

M

φpore

= 

  M

φ 

pore old

exp ( ) −λ

φ

Δt (4-10)

Similarly, each particulate phase is decayed using 

M

φbed

= 

  M

φ 

bed old

exp ( ) −λ

φ

Δt (4-11)

Radionuclides sorbed to bed sediments are assumed to be instantaneously in equilibrium with 

their dissolved counterparts in the bed pore water 

φpore= 

φbed

Kd

φ

This is enforced at the end of each computational time step after the fluxes described above are 

considered. 
4-6

4.3 Simulators

Two simulators, MASS2 and Transient Energy Transport HYdrodynamics Simulator (TETHYS), 

are used to model the various scenarios in this scoping study. Both models solve the 

momentum and scalar transport equations discretized using the finite-volume method (Ferziger 

and Perić 2002; Versteeg and Malalasekera 2007). 

4.3.1 MASS2

MASS2 is a two-dimensional, depth-averaged hydrodynamic and transport model (Perkins and 

Richmond 2004a, 2004b). The model simulates time-varying distributions of depth-averaged 

velocities, water surface elevations, suspended sediment, and water-quality constituents. 

MASS2 is applicable to a wide variety of environmental analyses of rivers and estuaries where 

vertical variations in the water column are negligible or unimportant.

MASS2 uses a boundary-fitted, orthogonal, curvilinear computational mesh. A key feature is 

the use of multiple computational mesh blocks. Multiple blocks allow MASS2 to be applied to 

complex domains. Blocks can be connected to each other with cells having a one-to-one or 

one-to-many correspondence. This allows the use of a high-density mesh where detailed 

results are needed and coarser meshes elsewhere. MASS2 is designed for execution on 

desktop to massively parallel processing computing architectures. The source code is written in 

standard Fortran 90 using the Message Passing Interface (MPI) (MPI Forum 2009) and the 

Global Array toolkit (Nieplocha et al. 1996, 2006) for interprocess communication, and the 

Portable, Extensible, Toolkit for Scientific Computation (PETSc) (Balay et al. 2014) for the 

solution of linear equation systems. 

The code can simulate a wide variety of hydrodynamic conditions, including supercritical flow 

and hydraulic jumps. MASS2 can also be used to simulate advection, mixing, decay, sediment 

transport, and sediment-contaminant interaction. Any number of conservative or decaying 

scalar quantities (e.g., salinity or radionuclides) may be simulated simultaneously with 

hydrodynamics or using precomputed hydrodynamics. In addition, MASS2 has the ability to 

simulate water-quality parameters (e.g., total dissolved gas, temperature, and suspended 

sediment). Advective fluxes are computed using deferred correction (Ferziger and Perić 2002) 

with the choice of several high-resolution schemes (e.g., central differencing [CDS], secondorder upwind, and the monotonic upstream-centered scheme for conservation laws [MUSCL]). 

These are implemented using the normalized variable and space formulation (NVSF) of Darwish 

and Moukalled (1994). The equations of mass, momentum, and species conservation are 

discretized using the finite-volume method (Patankar 1980) and solved using iterative solution 

procedures. The coupling of the momentum and mass conservation (continuity) equations is 

achieved using a variation of the Semi-Implicit Method for Pressure Linked Equations (SIMPLE)

algorithm (Patankar 1980) extended to shallow-water flows. 

The small river and large river settings were simulated using the MASS2 simulator.

4.3.2 TETHYS

The TETHYS (Yang et al. 2013; Richmond et al. 2013) simulator solves the governing 

equations of mass, momentum, and scalar conservation on an unstructured mesh. The finitevolume method (Ferziger and Perić 2002) is used to discretize the governing equations on a 

computational mesh consisting of arbitrarily shaped three-dimensional cells (e.g., hexahedral

and tetrahedral). A co-located storage scheme is used where all computed variables are 
4-7

defined at the centroid of each mesh cell. Advective fluxes are computed using deferred 

correction (Ferziger and Perić 2002) with the choice of several high-resolution schemes such as 

CDS, second-order upwind, and MUSCL. These are implemented using the NVSF of Darwish 

and Moukalled (1994) modified for unstructured meshes (Darwish and Moukalled 2003). 

Coupling between the pressure and velocity fields is done using the iterative SIMPLE algorithm 

(Patankar 1980) modified for co-located variables on unstructured meshes using Rhie-Chow 

interpolation (Ferziger and Perić 2002). Discretizing the governing equations and implementing 

the SIMPLE algorithm results in systems of linear algebraic equations that are solved using 

iterative methods available in PETSc (Balay et al. 2014). TETHYS is designed for execution on 

desktop to massively parallel processing computing architectures. The source code is written in 

C++ and uses the MPI (MPI Forum 2009) and the Global Array toolkit (Nieplocha et al. 1996, 

2006) for its parallel interprocess communication and PETSc (Balay et al. 2014) for linear 

system solution.

The lake setting was simulated using the TETHYS simulator.

4.4 Software History and Model Testing

The process models and simulators applied in this work have been developed, enhanced, and 

maintained by the Pacific Northwest National Laboratory (PNNL) for many years. They are a 

part of a longer history of sediment and radionuclide transport modeling in surface water 

systems at PNNL going back to the 1970s. As part of the Hanford Environmental Dose 

Reconstruction Project (Walters et al. 1996), an unsteady flow and transport model including 

radioactive decay, was used to simulate the transport of radionuclides (24Na, 32P, 65Zn, 76As, and 

239Np) released to the Columbia River from the operation of reactors at the Hanford Site. The 

model was applied to the river from Priest Rapids Dam to the vicinity of Portland, Oregon, from 

January 1950 through January 1971. Model validation was accomplished by comparing 

computed water depths and 51Cr concentrations to historical river monitoring data. 

4.4.1 History

The MASS2 simulator was initially developed in 1997 to model fully coupled hydrodynamics, 

water temperature, and dissolved gas transport in open rivers and reservoirs (Richmond et al.

1999). Since that time, additional transport processes have been added and a parallel version of 

the code was developed. The TETHYS simulator is a newer computational fluid dynamics 

(CFD) code that PNNL developed to address the need to simulate fully 3D flows based on 

solutions of the Navier-Stokes equations (Richmond et al. 2013). Development of TETHYS 

began in 2006 and is currently continuing with the addition of new capabilities to simulate 

coupled geochemistry, multiphase flow (e.g., water, air, and oil) phenomena, and enhanced 

river-reservoir simulations where non-hydrostatic density stratification effects are important.

4.4.2 Testing and Applications

The documentation for MASS2 (Perkins and Richmond 2004a, 2004b) present several cases 

that are used to regularly test the code as part of the code configuration management. In 

addition, MASS2 has been extensively validated against observed field data in river and 

reservoir systems as part of several applications on the Columbia River and Snake River 

systems. These studies include simulating water temperature and dissolved gas transport 

(Richmond et al. 2000), time-varying salmon habitat (Hanrahan and Richmond 2008), stranding 

caused by discharge fluctuations (Perkins et al. 2004), and radionuclide transport (Kincaid et al. 

2000). Validation simulations are typified by Richmond et al. (1999) and Niehus et al. (2014) 
4-8

who demonstrated model fidelity for spatial and temporal distributions of simulated quantities for 

a number of river-reservoir systems. Furthermore, water surface elevations and velocities 

compared favorably with measured tailwater elevations at dams using velocities measured with

an acoustic doppler current profiler (Niehus et al. 2014). Simulated and observed time-varying 

water temperature and total dissolved gas also compared favorably over a wide range of 

locations. For radionuclide transport, the MASS2 code was used as the river transport simulator 

in the System Assessment Capability project for the U.S. Department of Energy Hanford Site 

(Kincaid et al. 2000). The simulated contaminant concentrations from the MASS2 model were

compared to measurements for two separate time periods: 1964 to 1966, when radionuclides 

were directly discharged to the river from once-through cooled plutonium production reactors 

and 1992 to 1996, when contaminants entered the river from groundwater sources and 

upstream inputs. The results of these comparisons showed reasonable agreement with the 

available field data.

TETHYS is currently being applied to simulate flow and transport across a wide range of spatial 

and temporal scales. Basic test cases for steady and unsteady flows in 3D and two-dimensional 

(2D) geometries are described by Richmond et al. (2013). In addition to surface water systems, 

the fundamental CFD formulation of TETHYS allows it to be used to simulate flow and transport 

in explicit pore-scale geometries consisting of individual sediment grains for DOE Office of 

Science applications (Oostrom et al. 2016; Scheibe et al. 2015; Yang et al. 2015). At the scales 

of meters to tens of kilometers, density stratified flows in Dworshak and Lower Granite 

Reservoirs on the Snake and Clearwater Rivers are being simulated to help understand the 

relationships between water temperatures and migration behavior of salmon (Bellgraph et al. 

2009).

Verification tests using surface water geometries and conditions similar to two of the freshwater 

scenarios were designed to test MASS2 and TETHYS against analytical solutions for 

radionuclide transport and decay. Comparisons were generally excellent and are summarized in 

Appendix A, Sections A.1 and A.2. 

4.5 Modeling Approach

4.5.1 Source Term

The source term release volume (1,000 m3), rate (100 m3/d), and duration (10 d) described in 

Section 2 are used for all simulations of the freshwater settings and scenarios in this report. 

For each freshwater setting, the source term is released into a single internal grid cell along the 

shore. For each radionuclide, the 10-day source term is associated with the release of 1 Bq 

(unit) of activity. In absolute terms, 1 Bq is an extremely minute amount of activity; e.g., over 

15 orders of magnitude smaller than the estimated release to surface water for the 2011 FD

accident. There are two principal advantages for this radionuclide source term implementation. 

First, using the same activity release allows a common basis for comparing transport behaviors 

of different radionuclides at specific times and locations. In this case, differences in simulated 

activity concentrations are a direct consequence of the sorption and decay parameterizations 

that are radionuclide-specific. But second, and more importantly, the unit activity release allows 

the space- and time-dependent aqueous and sorbed activity concentrations presented in this 

report to be scaled for any 10-day activity release simply by multiplying by the desired source 

activity (Bq). This is because of the functionally linear transport and sediment-radionuclide 

interaction process models used in this study. For example, increasing radionuclide activity in 

the source term by a factor of 3 results in activity concentrations 3 times higher. 
4-9

4.5.2 Lake/Reservoir

The geometry of the lake model domain was adapted from bathymetric data for a large river

impoundment. Physical extent and mesh dimensions of the lake setting are summarized in 

Table 4-1. The interior of the model domain was discretized using a surface triangular mesh 

with a resolution of about 100 ft. This was extruded down to the bottom elevation at 1 ft 

intervals, forming a 3D prism-celled mesh. An inlet boundary was defined at the northwest 

corner of the domain. At this boundary, a constant discharge of 100 cfs was imposed. The 

outlet was defined at the southwest end. Hydrodynamics were simulated with a “rigid lid,” i.e., 

the top boundary was a slip wall. All other boundaries were nonslip walls.

Table 4-1. Transport Simulation Approximate Domain Physical and Mesh Dimensions

Dimension

Freshwater Settings

Units Lake Large River Small River

Length mi 11 60 60

Nominal Width ft 3,300 1,800 650

Average Depth ft 24 15 7

Discharge cfs 100 100,000 5,000

Maximum Velocity ft/s 13 26

Mesh Cells 1.4M 714K 2.4M

Mesh Resolution ft 105 30 14

Vertical Mesh Resolution 1.0 N/A N/A

Transit time hr N/A 17 25

Transport simulations for an actual lake could include the representation of several transport 

mechanisms (e.g., wind, wave action, thermal buoyancy, and sorption to and desorption from 

sediment and biota). The data required to represent these mechanisms are very site-specific. 

Consequently, for this scoping study, these mechanisms were lumped into a single constant 

turbulent mixing coefficient. A value of 0.04 m2/s was chosen. This is a measured value for 

Lake Huron (Fischer et al. 1979) and within the range measured by Peeters et al. (1996) in 

smaller lakes. The initial lake case was simulated for 30 days total: 10 days during the release 

and for 20 days afterward. Simulation output was sampled at discrete locations near the release 

site and along the shore at a radius of 0.5 and 1.0 mi from the release point (Figure 4-1). 

Subsequent lake simulations that were extended to one year, were based on the same boundary 

conditions, parameters, and sampling locations; however, a coarser mesh with 400 ft horizontal 

resolution and 3 ft vertical resolution was necessary to maintain turnaround times. 

4.5.3 River Settings

It was assumed that the hypothetical river cases in this work were well-mixed vertically. This 

assumption has been reasonable for past water quality and transport modeling in these settings. 

Consequently, the river cases were simulated as 2D depth-averaged flow and transport with 

MASS2. 

Structured curvilinear meshes were prepared for about 60 mi in each river setting to model 

50 mi of transport downstream from the point of release (this distance was later extended for the 

large river, see below). The approximate resolutions used are shown in Table 4-1. 

Steady-state hydrodynamics were simulated first. Discharge was imposed as the upstream 

boundary condition. An appropriate stage was imposed as the downstream boundary condition. 

The most important parameters for the hydrodynamic simulations were channel roughness and 
4-10

Figure 4-1. Sampling Locations for the Lake Simulation. Circles represent 0.5 and 

1.0 mi radii centered about release point for radionuclides.

turbulent eddy viscosity. Normally, these are determined through calibration. In the large river 

case, these values were available from a previous calibration: turbulent eddy viscosity (both 

transverse and longitudinal) was 0.0186 m2/s and Manning’s roughness coefficient varied from 

0.027 to 0.038. Because no calibrated values for turbulent eddy viscosity and roughness were 

available for the small river, some reasonable values were chosen: 0.06 m2/s for turbulent eddy 

viscosity and 0.027 for Manning’s roughness coefficient, which are within the range of observed 

values presented by Fischer et al. (1979) for eddy viscosity and Chow (1959) for Manning’s 

roughness. 

Table 4-1 summarizes the physical dimensions of the river cases and some hydrodynamic 

results. Both river cases had islands and some braiding of the main channel. The small river 

was dominated by pool and riffle sequences: deeper, slower stretches (around 3 ft/s) alternated 

with short, shallow, faster stretches (some small areas with velocities higher than 20 ft/s). The 

small river required a much higher resolution mesh in order to adequately resolve narrowed 

channel and high velocity areas. In contrast to the small river, the large river had a mostly 

consistent flow regime throughout the domain. While the flow velocity did vary spatially in the 

large river, there were no areas of supercritical flow. 

Transport simulations were performed using the steady-state velocity field from the 

hydrodynamic simulation. A constant sediment concentration of 3.75 mg/L was imposed at the 

upstream boundary, based on a representative value as mentioned earlier. A radionuclide 

injection point was chosen along a shore a few miles below the upstream boundary. The 

injection was made into a single cell, an area approximately 10 m by 10 m. The 10-day, 

1,000 m3 source term described in Section 2 was released from the shore in both river settings. 

Simulation output was saved at hourly intervals and later sampled at discrete locations near the 

release point and along the near and opposite shores. The simulation was started 2 days 

before the beginning of the 10-day release, which allowed the sediment transport to become 

steady state in the upper portions of the models. A 30-second computational time step was 

used for all of the river transport cases.
4-11

An important parameter for the transport simulations was the turbulent mixing coefficient. As 

with the hydrodynamic parameters, the turbulent mixing coefficient is usually determined 

through calibration and validation. In this case, an isotropic turbulent mixing coefficient, 

0.186 m2/s, validated for previous water-quality simulations in these settings, was chosen for all 

the river transport simulations. This value is near the lower end of some observed values in 

several rivers listed by Fischer et al. (1979). A second-order accurate advection scheme was 

used for all simulations: MUSCL for the large river and second-order upwind for the small river 

(as described by Darwish and Moukalled 1994). 

The initial set of simulations continued for 3.5 days after the end of the 10-day release, which 

was enough time, in both rivers, for the principal pulse of released radionuclides to pass the 

50-mi downstream sampling locations. Two transport simulations were performed for each river 

setting: one without sediment interaction (aqueous-only) and one with sediment transport and 

sediment-radionuclide interaction. All simulations account for radioactive decay under the 

assumption that radionuclides decay only after release into the freshwater systems (i.e., the 

specified source term activity is at release, not prior to release). 

Sediment transport in the river scoping analyses was based on models and parameters from a 

previous assessment of similar river settings. For the small and large river settings, a 3.75 mg/L 

suspended sediment concentration was used with the following sediment properties:

• Median particle diameter between a fine sand and silt (d50): 0.003 cm 

• Solids density: 2,650 kg/m3

• Settling velocity: 0.000010 m/s 

• Erodibility: 0.0 

• Critical shear for erosion: 0.0073 kgf/m2

• Critical shear for deposition: 0.0073 kgf/m2

The modeling specification of the bed and suspended sediment is important for estimating 

radionuclide adsorption/desorption processes and their role in fate and transport. Consistent 

with the scoping nature of these analyses, the simulation of sediment fate and transport for the 

river settings of this study was kept simple. A single bed layer of sediment was uniformly 

initialized to a thickness of 0.1 ft (0.03048 m) with a porosity of 0.4. Simulated suspended 

sediment load was affected by local deposition, but the bed was not allowed to erode (i.e., 

erodibility was set to zero), in order to maintain a small bed layer throughout the river domains. 

This ensured that bed sediments would be available for interaction with dissolved radionuclides 

in the water column. 

Partitioning coefficient (Kd) values from the literature are used to describe the radionuclide

interaction with bed and suspended sediment particles (Table 3-1). Sorption and desorption 

between the bed and water column is governed by a rate that is driven by the deviation from 

equilibrated conditions defined by the radionuclide-specifc Kds. The rate applies to the surface 

layer of the bed to a depth of one sediment grain diameter. The maximum (i.e., intrinsic) 

sorption/desorption rate in this study was 1.16 × 10-5 s-1, which was used in previous work in 

these settings. Radionuclide exchange with organic matter is not considered in this scoping 

analysis, again, for simplicity. 

4.5.3.1 Extended Large River Configurations

To examine the effects of 1) radionuclide-sediment interactions, 2) tributaries, and 3) 

impoundments over longer distances and durations, the original 2D large river domain was 
4-12

extended to a dam 103 mi from the release point. This extension included two small tributaries 

that added a total of 18,000 cfs to the 100,000 cfs discharge. From this dam, two different 

configurations were simulated out to 293 mi from the release point: 1) unimpounded freeflowing river and 2) impounded river with three intervening dams (Figure 4-2)

Figure 4-2. Configurations Used for Large River Cases. The lower river section was run 

both as a free-flowing river and as a series of impoundments. 

The bathymetry of the large river was adapted for unimpounded and impounded river scenarios. 

Characteristics of the river segments are given in Table 4-2. The numbering of the lower 

segments (e.g., Lower Imp. 1) is from upstream to downstream, and the lowest section (i.e., 

Lower Impoundment 4) does not terminate at a dam.

Eddy viscosity and turbulent mixing coefficient were the same as the original, 50-mi-long large 

river simulations. 

Table 4-2. Characteristics of the Extended Large River

Dimension Units

Common

Section

Lower River Scenarios

Unimpounded Impounded

Upper Lower

Lower 

Imp. 1

Lower 

Imp. 2

Lower 

Imp. 3

Lower 

Imp. 4

Length mi 103 190 77 23 45 45

Average depth ft 19.7 9.5 35.5 30.7 33.3 18.0

Discharge cfs 118,000 118,000 118,000 118,000 118,000 118,000

Susp sediment kg/m3 3.75E-3 3.34E-3 3.34E-3 2.61E-3 2.57E-3 2.44E-3

Mesh cells 784,800 439,383 99,430 62,281 155,916 114,985

Mesh resolution ft 188 158 189 104 94 121

Transit time hr 111 106 203 30 66 41

It should be noted that the average velocity for the unimpounded river segments is much larger 

than the impounded segments. The total travel time for the lower river was 106 hours for the 

unimpounded river, but 340 hours when simulated as a series of impoundments. 
5-1

5. RADIONUCLIDE TRANSPORT MODELING RESULTS

5.1 Simulation Overview

5.1.1 Source Term

For all freshwater settings and scenarios in this study, aqueous and sorbed concentrations are 

simulated in space and time based on the release of 1 Bq of activity for each radionuclide (3H, 

90Sr, 106Ru, 125Sb, 131I, 134Cs, 137Cs, 144Ce) with 1,000 m3 of water over 10 days. These 

concentrations are reported in units of Bq/m3 but could also be interpreted to be concentrations 

per Bq of activity released in the 10-day source term. For the linear partial differential equations 

and functions underlying the process models used in this study, this interpretation allows the 

reported radionuclide concentrations to be scaled for any activity release simply by multiplying 

by the intended activity release. For example, a 1 terabecquerel (TBq) 137Cs release would 

result in concentrations 1012 times the reported 137Cs concentrations. The scaling is valid when 

the advection, diffusion, decay and partitioning functions have linear dependence. 

5.1.2 Sequence of Simulation Cases

Steady-state hydrodynamics are simulated first and saved. The resulting flow field is then used 

in radionuclide transport simulations using the source term described above. The base case for 

each of the three hydrologic settings is an aqueous-only simulation (i.e., without radionuclidesediment interactions) focusing on the transport of each of the eight radionuclides in the 10-day 

release pulse. The base case targeted short-term simulations. In the lake setting, a 30-day 

period was simulated. In the river settings, the simulation period was 13.5 days (enough time 

for the primary pulse of released radionuclides to exit the domain). 

A second set of analyses focused on continuing the lake and coupled radionuclide-sediment 

interaction river simulations out to one year. To ease the computational requirements for these 

simulations, the release was limited to the four radionuclides that represent the principal 

contributors to dose: 131I, 134Cs, 137Cs, and 90Sr. For the small and large river settings, water 

column activity concentrations were simulated with and without sediment-radionuclide 

interactions to identify the impact of sorption/desorption processes on the water column activity 

concentrations. 

The third set of analyses examined the effect of impoundments on radionuclide transport by 

extending the one-year, large river simulation out to a total of 293 mi. In this case, the last 

190 mi were modeled in two different configurations: 1) free-flowing unimpounded river and

2) impounded river with three intervening dams. 

The complete results including 3H, 106Ru, 125Sb, and 144Ce in the initial base case simulations 

can be found in the Appendix B. In the case of the small and large river settings, the 13.5-day

simulations were also used to examine the inclusion of radionuclide-sediment interactions. In all 

simulations, radionuclides decay according to the half-lives listed in Table 3-1.

5.2 Modeling Results

5.2.1 Small Lake/Reservoir

Unlike the advection-dominated river cases, radionuclide movement in the small lake setting is 

dispersion-dominated, which is a much slower process than advection. Figure 5-1 shows the 
5-2

progress of the 137Cs plume over the short-term simulation period (30 days). Because advection 

is minimal, the plume spreads from the release point in a nearly circular manner until it reaches 

the far shore, after which it can only spread toward the ends of the lake domain. Figure 5-2 to 

Figure 5-5 show relative concentration time series for 131I, 144Ce, 90Sr, and 137Cs, respectively, at 

the selected sample locations (Figure 4-1). These four radionuclides are shown because they 

are considered to represent a range of decay behavior. Figures B-1 through B-8 in Appendix B 

show similar figures for the eight radionuclides considered. Concentrations remain very high, 

compared to the river cases, near the release point over the entire simulation period. At the end 

of the 30-day simulation (20 days after the end of the radionuclide release), concentrations are 

still rising at all locations, except the release point and 1 mile upstream on the near shore. 

(a) (b)

(c)

Figure 5-1. Simulated Near-Surface 137Cs Concentrations, Bq/m3 (a) 10 days, (b) 20 days, 

and (c) 30 Days after Start of Release in the Lake Scenario. The black 

markers indicate sample locations.
5-3

Figure 5-2. Simulated 131I Activity Concentration History at the Near-Shore (left) and FarShore (right) Sample Locations in the Lake Scenario.

Figure 5-3. Simulated 144Ce Activity Concentration History at the Near-Shore (left) and 

Far-Shore (right) Sample Locations in the Lake Scenario.

Figure 5-4. Simulated 90Sr Activity Concentration History at the Near-Shore (left) and FarShore (right) Sample Locations in the Lake Scenario.
5-4

Figure 5-5. Simulated 137Cs Activity Concentration History at the Near-Shore (left) and 

Far-Shore (right) Sample Locations in the Lake Scenario.

5.2.1.1 One-Year Simulations

For the lake simulations that were extended to one year, there were no changes in the lake 

boundary conditions and parameters. However, there were changes to the mesh resolution. 

Simulation of the four radionuclides, 134Cs, 137Cs, 131I, and 90Sr, for a full year with the original 

lake mesh resolution would have been computationally prohibitive. Consequently, a coarser 

mesh was developed. As with the original 100 ft resolution mesh, the interior of the lake 

shoreline was triangulated, but this time with a 400 ft horizontal resolution mesh. This triangular 

mesh was extruded in 3 ft vertical steps (versus 1 ft originally). 

Figure 5-6 through Figure 5-9 show the simulated activities for the four radionuclides 

considered. Shorter half-lives result in earlier peaks at the seven monitoring locations. 

However, for a given radionuclide, the order of the peak occurrences at these locations is 

consistent. The earliest concentration peaks were at the 0.5-mi upstream and downstream 

locations on the near-shore. The latest peaks were at the far and near-shore locations 1 mi 

downstream with the latest peak (137Cs and 90Sr) at 69 days. 131I activity decreases much 

quicker than the other radionuclides due to its short half-life. Even though it was small, 

advection had a marked effect on radionuclide transport. Concentrations at upstream locations 

were lower by 2 to 4 orders of magnitude than at the downstream locations. 

Figure 5-10 shows plan views of the activity plume at several times during the simulated year. 

Even though it is small, advection has a significant effect on the overall movement of the plume. 

The plume extends about 1 mi upstream at most. The downstream edge of the plume reached 

the lake outlet by 90 days. Afterward, advection pushed the plume out without any additional 

upstream movement. 
5-5

 

Figure 5-6. Lake 134Cs Activity Over Time at Several Locations on the Same (left) And 

Opposite (right) Shore of the Release Location.

 

Figure 5-7. Lake 137Cs Activity Over Time at Several Locations on the Same (left) and 

Opposite (right) Shore of the Release Location.

 

Figure 5-8. Lake 131I Activity Over Time at Several Locations on the Same (left) and 

Opposite (right) Shore of the Release Location.
5-6

 

Figure 5-9. Lake 90Sr Activity Over Time at Several Locations on the Same (left) and 

Opposite (right) Shore of the Release Location.

(a) (b)

(c) (d)

Figure 5-10. Simulated Lake Aqueous-Only, Near-Surface 137Cs Concentrations, Bq/m3 (a) 

30 Days, (b) 90 Days, (c) 180 Days, and (d) 360 Days after Start of Release 

from the Lake One-Year Simulation. The black markers indicate sample 

locations.
5-7

5.2.1.2 Sensitivity Test for Turbulent Mixing Coefficient

The key parameter for the lake transport simulation was the turbulent mixing coefficient. The 

value chosen was in the range measured by Peeters et al. (1996) in smaller lakes, but near the 

minimum. The one-year lake simulation for 137Cs was repeated with a turbulent mixing 

coefficient 5 times higher (0.2 m2/s). This was near the upper end of the measurements made 

by Peeters et al. (1996). 

Simulated time-dependent activity using the increased turbulent mixing coefficient is compared 

to the original simulation in Figure 5-11. With a higher mixing coefficient, concentrations at the 

sampling locations peak sooner and decrease much slower. The enhanced mixing peaks are 

higher than the original peaks for the upstream locations and lower than the original peaks for 

the downstream locations. This can be seen by comparing the simulated spatial activity 

distributions from the increased mixing coefficient simulation in Figure 5-12 with the original 

simulation results in Figure 5-10.

Figure 5-11. Comparison of Aqueous-Only 137Cs Activity Concentrations Over Time for 

the Original and Increased Mixing Coefficient Lake Simulations at Locations 

along the Same (left) and Opposite (right) Shore as the Release.
5-8

(a) (b)

(c) (d)

Figure 5-12. Simulated Lake Aqueous-Only, Near-Surface 137Cs Activity Concentrations, 

Bq/m3 (a) 30 Days, (b) 90 Days, (c) 180 Days, and (d) 360 Days after Start of 

Release From the Lake Increased Mixing Coefficient Simulation. The black 

markers indicate sample locations. Compare to Figure 5-10.

5.2.2 Small Discharge River

For a given radionuclide, the lower flow rate in the small river setting (5,000 cfs vs 100,000 cfs

in the large river setting) results in water column concentrations ~20 times higher than in the 

large river simulations due to less dilution. In contrast to the large river, the activity plume in the 

small river setting mixes laterally quickly (Figure 5-13). Figure 5-14 to Figure 5-17 compare time 

series of 131I, 90Sr, 137Cs, and 144Ce activities, respectively, from the aqueous-only simulations. 

Note that in the interest of brevity, these four radionuclides are shown because they are 

considered to represent a range of sorption behavior. Similar figures for the eight radionuclides 

considered are shown in Figures B-14 through B-21 in Appendix B. The “average” line in those 

figures indicates what the concentration would be assuming complete mixing using the 

radionuclide release rate and river flow rate. The small river near-shore and far-shore

concentrations converge to the fully mixed average concentration within 10 mi of the release. 

This is not only because of the smaller width and lower velocity of the small river case, but also 

from the additional mechanical mixing that occurs in the small river’s pool and riffle nature.
5-9

Aqueous water column activity concentrations from the sediment-inclusive simulations were 

only slightly lower than the respective aqueous-only simulations, except for 106Ru and 144Ce, 

which had the highest sediment sorption distribution coefficients (Kds). Figure 5-18 compares 

the aqueous 144Ce activity concentrations from the sediment-inclusive simulation to the 

aqueous-only simulation. Table 5-1 shows percent of released radionuclide activity remaining in 

the sediment bed 13.5 days after the start of the release for the entire model domains of both 

the small and large discharge river settings. The sediment retained substantial portions of 106Ru 

and 144Ce, lesser fractions of the Cs isotopes, and very little of the other radionuclides. 

Retention is based, in part, on the sediment sorption distribution coefficient, Kd, given in 

Table 3-1. Larger fractions of the released activity were left in the small river bed than in the 

large river simulation (Table 5-1). This is because the small river had significantly higher 

aqueous concentrations and longer contact time with the bed (i.e., lower average velocity), 

which resulted in much more activity sorbed to the bed sediments. Consequently, the postpulse water column concentrations from bed desorption in the small river are commensurately 

higher.

 

Figure 5-13. Simulated Small River 137Cs Water Column Concentrations (Bq/m3) in the 

Aqueous-Only Simulation (top), Aqueous Phase in the Sediment-Inclusive 

Simulation (middle), and Suspended Sediment-Sorbed Phase in the 

Sediment-Inclusive Simulation (bottom). Flow is from right to left. 

Downstream blue-colored areas are inundated but not directly connected to 

the channel. The figures extend approximately 10 mi below the release 

location. Black markers indicate sample locations 2 and 10 mi downstream.
5-10

Figure 5-14. Simulated Small River Aqueous-Only 131I Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

Figure 5-15. Simulated Small River Aqueous-Only 90Sr Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

Figure 5-16. Simulated Small River Aqueous-Only 137Cs Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).
5-11

Figure 5-17. Simulated Small River Aqueous-Only 144Ce Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

Figure 5-18. Time Series Small River 144Ce Aqueous (left) and Total Aqueous and 

Suspended (right) Activity From the Sediment Simulation at Locations 

Along the Same Shore as the Release. Compare with the results of the 

aqueous-only simulation (Figure 5-17).

Table 5-1. Percent of Released Activity in the River Bed after 13.5 Days in the Small and 

Large Discharge River Settings

Species

Large River Small River

% of Release % of Release

3H 0 0

90Sr 0.28 1.4

106Ru 12 46

125Sb 0.66 3.2

131I 0.04 0.17

134Cs 1.9 8.9

137Cs 1.9 9.0

144Ce 36 86
5-12

5.2.2.1 One-Year Simulations

To identify longer-term behaviors, the small discharge river simulations were extended in 

duration to one year. No changes were made in mesh, boundary conditions, or simulation 

parameters. 

Figure 5-19 to Figure 5-22 show one-year time histories of water column activity for 134Cs, 137Cs, 131I, and 90Sr, respectively. Dissolved activities (aqueous phase) are in the top plot of each 

figure, the activities sorbed on the suspended sediment in the water column are in the middle 

plots, and the total of the two is shown in the bottom plots. During the passage of the pulse of 

released radionuclides, there was a large sorption of activity to the bed sediments. After the 

passage of the pulse of released radionuclides, the bed sediment-sorbed activity is slowly 

desorbed resulting in slightly elevated concentrations in the aqueous phase. Figure B-22 to 

Figure B-28, in Appendix B, show similar plots for the seven radionuclides considered for this 

case (tritium is assumed to not sorb). In general, there is a simple extension of the post-pulse 

radionuclide desorption from the bed sediments in the previous short duration simulations. The 

slowly decreasing post-pulse concentrations are controlled by the decay rate (i.e., half-life) and 

the radionuclide partitioning between the water column and the (bed) sediment (i.e., Kd). In 

particular, the 131I activity concentrations rapidly decrease over the 45 half-lives in the one-year 

simulation. It also has the lowest Kd of the four simulated radionuclides, which means a smaller 

fraction is associated with the bed sediments. To a much lesser degree, the 2-year half-life for 

134Cs, results in a slightly faster rate of removal from the water column compared to 137Cs. 

Equilibrium is not reached in the post-pulse partitioning of radionuclides between the bed 

sediment and overlying water column (i.e., desorption is rate-limited). This means a parcel of 

water traveling downstream progressively accumulates more activity as it passes over 

continuously desorbing bed sediments. So while aqueous radionuclide concentrations at any 

given location are decreasing with time, the longitudinal distribution of water column

concentrations at any instant of time is increasing with downstream distance. Figure 5-23 to 

Figure 5-26 show the time-dependent bed sediment-sorbed activity concentration for 134Cs, 137Cs, 131I, and 90Sr, respectively. Figure B-29 to Figure B-35, in Appendix B, show bed

sediment-sorbed concentrations for the seven radionuclides considered for this case. 

For 131I, both water column (Figure 5-21, top) and bed (Figure 5-25), concentrations decrease

quickly after passage of the release pulse. This is primarily due to decay. Figure 5-27 compares 

the history of 131I and 134Cs bed concentrations, the two shortest lived radionuclides. Blue lines 

have been added to the plots to show rates of decay. The reduction of bed 131I can be almost 

entirely explained by decay, whereas 134Cs activity falls at a much greater rate than its decay, 

indicating desorption plays a greater role. 
5-13

Figure 5-19. Small River Aqueous (top), Suspended Sediment-Sorbed (middle), and Total 

(bottom) 134Cs Activity Over Time at Several Downstream Locations on the 

Same (left) and Opposite (right) Shore of the Release Point.
5-14

Figure 5-20. Small River Aqueous (top), Suspended Sediment-Sorbed (middle), and Total 

(bottom) 137Cs Activity Over Time at Several Downstream Locations on the 

Same (left) and Opposite (right) Shore of the Release Point.
5-15

Figure 5-21. Small River Aqueous (top), Suspended Sediment-Sorbed (middle), and Total 

(bottom) 131I Activity Over Time at Several Downstream Locations on the 

Same (left) and Opposite (right) Shore of the Release Point.
5-16

Figure 5-22. Small River Aqueous (top), Suspended Sediment-Sorbed (middle), and 

Total (bottom) 90Sr Activity Over Time at Several Downstream Locations on 

the Same (left) and Opposite (right) Shore of the Release Point.
5-17

Figure 5-23. Small River Bed Sediment-Sorbed 134Cs Activity Per Square Meter Over 

Time at Several Locations on the Same (left) and Opposite (right) Shore of 

the Release Location.

 

Figure 5-24. Small River Bed Sediment-Sorbed 137Cs Activity Over Time at Several 

Locations on the Same (left) and Opposite (right) Shore of the Release 

Location.

 

Figure 5-25. Small River Bed Sediment-Sorbed 131I Activity Over Time at Several 

Locations on the Same (left) and Opposite (right) Shore of the Release 

Location.
5-18

 

Figure 5-26. Small River Bed Sediment-Sorbed 90Sr Activity Over Time at Several 

Locations on the Same (left) and Opposite (right) Shore of the Release 

Location.

Figure 5-27. Small River Bed Sediment-Sorbed 131I (left) and 137Cs (right) 20 Mi 

Downstream of the Release Compared with the Decay Expected Starting 

with the Maximum Concentration.

5.2.3 Large Discharge River

In the large river base case simulations, the activity plume hugs the shore on which the release 

was made (Figure 5-28). There are orders of magnitude differences between the near-shore 

and far-shore concentrations for 10 mi downstream from the release point. Differences are still 

discernible 50 mi downstream from the release point. 

Figure 5-29 to Figure 5-32 compare the 14-day time series of 131I, 90Sr, 137Cs, and 144Ce 

activities, respectively, from the aqueous-only simulations for near-shore and far-shore 

locations. Note that in the interest of brevity, these four radionuclides are shown because they 

are considered to represent a range of sorption and decay behavior. Figure B-44 to 

Figure B-51, in Appendix B, are similar figures for the eight radionuclides considered. The 

“average” line in those figures indicates what the activity concentration would be assuming 

complete mixing using the radionuclide release rate and river flow rate. The average is higher 

than any curves in the far-shore plots because it is an average of concentrations across the 

width of the river. As with the small river, concentrations in the pulse of released radionuclides

flow downstream with very little dilution with distance. After the release is stopped,

concentrations decrease rapidly and this profile of a rapid increase followed by near constant 
5-19

concentrations and then a rapid decrease is maintained for miles. After the 10-day pulse passes 

through the system, aqueous concentrations decrease rapidly to a plateau ~3 orders of 

magnitude lower than peak concentrations followed by slower decline. These low, slowly

diminishing radionuclide concentrations in the water column are the result of later arrivals from 

slower moving transport pathways. 

When radionuclide-sediment interactions were included in the simulations, water column 

concentrations for most of the radionuclides were slightly lower than the aqueous-only base 

case simulation (c.f., the top two graphics in Figure 5-28). For the radionuclides with high 

affinity to sediment (i.e., high Kd values), 106Ru and 144Ce, water column concentrations were 

noticeably reduced downstream. In the coupled sediment and radionuclide transport simulation 

with 144Ce, the downstream aqueous and total (aqueous plus suspended sediment-sorbed)

water column 144Ce activity concentrations (Figure 5-33) were noticeably lower than the 144Ce 

activity concentrations in the aqueous-only base case simulation (Figure 5-32). This indicates 

significant 144Ce sorption to the bed sediments. Figure B-52 to Figure B-58, in Appendix B, 

contain sets of 14-day plots showing aqueous concentrations, sorbed concentrations, and the 

aqueous plus suspended sediment-sorbed concentrations for each of the seven radionuclides 

considered (tritium is not included in these sorption cases). 

 

Figure 5-28. Simulated Large River 137Cs Concentrations (Bq/m3) in the Aqueous-Only 

Simulation (top), Aqueous Phase (middle) and Suspended Sediment Phase 

(bottom) in the Sediment Simulation. Flow is from left to right. The figures 

extend approximately 10 mi below the release location. Black markers 

indicate sample locations.
5-20

 

Figure 5-29. Simulated Large River Aqueous-Only 131I Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

 

Figure 5-30. Simulated Large River Aqueous-Only 90Sr Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

 

Figure 5-31. Simulated Large River Aqueous-Only 137Cs Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).
5-21

 

Figure 5-32. Simulated Large River Aqueous-Only 144Ce Activity Over Time at Several 

Locations Along the Same Shore as the Release (left) and the Opposite 

Shore (right).

Figure 5-33. Time Series of Large River 144Ce Aqueous (left) and Total Water Column 

(aqueous + sorbed to suspended sediment) (right) Activity from the 

Sediment Simulation Along the Same Shore as the Release. Compare with 

the results of the aqueous-only simulation (Figure 5-32).

5.2.3.1 One-Year Simulations with Extended Domain

To identify longer-term behaviors over longer distances, the MASS2 large river domains were 

extended 103 mi downstream from the release point, terminating at a dam. Simulations were 

lengthened to one year. The extended reach included 3,000 and 15,000 cfs contributions from 

two tributaries. Other than the extended mesh and tributary flows, no changes were made in 

the influent boundary conditions or parameters. The specification was summarized earlier in

Table 4-2. Results are provided for the four radionuclides with the highest dose consequences: 

131I, 134Cs, 137Cs, and 90Sr.

In these extended large river simulations, there are consistent patterns of concentration 

variation with time (Figure 5-34 to Figure 5-37, showing combined aqueous and suspended 

sediment activity concentrations in the water column) that are an extension of the previously 

identified behaviors: persistence of differences between near-shore and far-shore

concentrations over 50 mi downstream and post-pulse concentrations that are non-zero but 

orders of magnitude lower than the 10-day pulse concentrations. The extended simulations 

also show 1) the slowing and spreading of the transported pulse when it encounters the lowervelocity impounded section, 2) the effect of tributaries on near-shore concentrations, 3) the 
5-22

considerable effect of 45 half-lives of decay on the 131I activity concentrations, and 4) the long 

tails of residual activity as radionuclides that partitioned to bed sediments during the passage of 

the 10-day pulse slowly desorb. These tails are a longer-term desorption effect with modelpredicted concentrations orders of magnitude lower than the peak concentrations in the pulse of 

released radionuclides that slowly decrease over time. However, radionuclide activity

concentrations increase slightly with distance downstream. This behavior is driven by 

disequilibrium between the radionuclide activity sorbed to the bed sediment, which was loaded

during the passage of the radionuclide release pulse, and the radionuclide activity in the postpulse water column, which is now much less contaminated. This leads to desorption from the 

contaminated bed sediments along the impacted length of the river. For the balance of the oneyear simulation, the desorption rate was sufficiently low that the bed sediments and overlying 

water column never equilibrated. Consequently, a parcel of water traveling downstream 

progressively accumulates more activity as it passes over continuously desorbing bed 

sediments. So while aqueous radionuclide concentrations at any given location are decreasing 

with time, the tendency is for aqueous concentrations to increase with downstream distance at 

any given time (e.g., Figure 5-34). 

The difference between near-shore and far-shore concentrations is highly dependent on 

proximity to the release location and the distance from release. The 2-mi far-shore sampling 

point has very low concentrations and the 10-mi far-shore point has peak pulse concentrations 

5 orders of magnitudes less than the release location and very low concentrations in the water 

column post-pulse.

The 80-mi near-shore monitoring point has a consistent, but different shape than the other 

concentration curves. The 80-mi point is downstream of the large tributary and is subject to 

dilution from the tributary (Figure 5-38). 

 

Figure 5-34. Near-Shore (left) and Far-Shore (right) 134Cs Concentration in the Large 

River Over One Year.
5-23

 

Figure 5-35. Near-Shore (left) and Far-Shore (right) 137Cs Concentration in the Large 

River for One Year.

 

Figure 5-36. Near-Shore (left) and Far-Shore (right) 131I Concentration in the Large River 

for One Year.

Figure 5-37. Near-Shore (left) and Far-Shore (right) 90Sr Concentration in the Large River 

for One Year.
5-24

Figure 5-38. Aqueous Phase 134Cs Concentration Increases with Downstream Location. 

This is from Day 138 after the end of the release period. 

5.2.3.2 Unimpounded and Impounded Large River Simulations

The output concentrations at mile 103 (downstream dam boundary) of the One-Year Extended 

Domain Large River simulations in the previous section were considered to be well mixed and 

then used as inputs to the two “lower river” configurations: free-flowing river and a river with a 

series of impoundments behind three intervening dams. The impoundment runs were done to 

assess the impact of dams on transported concentrations through space and time.

Plots of concentration as a function of time (relative to the start of the release) were created at 

various distances downstream from the release point. The lower river runs had monitoring 

locations from 104 to 293 mi from the release point. Table 5-2 details all of the sampling points.
5-25

Table 5-2. Monitoring Locations for the Extended Large River Simulations

Miles 

Downstream Location

0 Release

2 Right and Left Banks

10 Right and Left Banks

20 Right and Left Banks

30 Right and Left Banks

40 Right and Left Banks

50 Right and Left Banks

80 Right and Left Banks

103 Above Dam 1

104 Below Dam 1

180 Dam 2

203 Dam 3

248 Dam 4

293 End

5.2.3.2.1. Unimpounded River

The unimpounded river model setting examines flow and contaminant transport assuming there 

are no dams below Dam 1, resulting in free flow from mile 104 to mile 293. Comparison of 

results for the impounded and unimpounded systems are shown in Figure 5-39 to Figure 5-42

for 134Cs, 137Cs, 131I, and 90Sr, respectively. The unimpounded river setting results in rapid travel 

as indicated by the narrowness of the release pulse in time-dependent plots at the monitoring 

locations (Figure 5-39 to Figure 5-42). There is also a general clustering of the arrival times of 

the pulse at different monitoring locations indicating short transit times. Similar to the previous 

results for the shorter 50-mi long river domain, there is a drop of several orders of magnitude in 

concentrations after the release pulse passes through. The post-pulse concentrations are 

controlled by the aqueous phase radionuclide concentration in the pulse, decay rate and 

sediment distribution coefficient. For example, the 131I post-pulse activity concentrations in 

Figure 5-41 are dominated by rapid decay as a result of the 8-day half-life. At a given location 

over time, the other three radionuclides have long tails of slowly decreasing concentrations as 

desorption from the bed sediments is the principal longer-term source. As in the previous large 

river configurations, the post-pulse concentrations increase with downstream distance. This is 

principally because the desorption rate is sufficiently low that disequilibrium is maintained 

between the bed sediments and overlying water column. This allows a parcel of water traveling 

downstream to progressively accumulate desorbed activity. 

5.2.3.2.2. Impounded River

In comparison to the unimpounded river, the results for the lower river with a series of 

impoundments are impacted by the deeper and wider wetted perimeter, which slows the 

average velocity of water flowing downstream, increases the contact time with the release 

pulse, and provides considerably more bed sediments for the radionuclides to interact with. 

This leads to a pattern of slower travel for the release pulse and increased concentrations for 

the desorption tail that increases with downstream distance (Figure 5-39 to Figure 5-42). Both 
5-26

the impounded and unimpounded lower river configurations initially had a uniform 0.1 ft layer of 

sediment across the bottom. 

The graphics shown here compare the modeled impounded to unimpounded concentrations 

over time at similar monitoring points starting at 104 miles from the release point. As expected, 

the 104-mile location (just below the upstream dam) was very similar between the impounded 

and unimpounded cases (the first 180 days are plotted to better show the differences in pulse 

shape). The first pool in the impounded configuration is the largest and has an average velocity 

that is less than half that of the other pools. The effect of the slower velocity is seen in the large 

temporal offset of the release pulse breakthroughs between the 104 and 180 mi monitoring 

locations, and the dilation in the duration of the pulses. 

Figure 5-39. Unimpounded (left) and Impounded (right) Lower River Comparison for 

134Cs Total Water Column Concentrations at Lower River Locations.

Figure 5-40. Unimpounded (left) and Impounded (right) Lower River Comparison for 

137Cs Total Water Column Concentrations at Lower River Locations.
5-27

Figure 5-41. Unimpounded (left) and Impounded (right) Lower River Comparison for 131I

Total Water Column Concentrations at Lower River Locations.

Figure 5-42. Unimpounded (left) and Impounded (right) Lower River Comparison for 90Sr

Total Water Column Concentrations at Lower River Locations.

5.2.3.3 Sensitivity Tests

The extended large river setting was used to conduct three sensitivity tests. The first sensitivity 

test addressed the linear scaling of simulated activity concentrations relative to the activity 

release. The second sensitivity test addressed the effect of a larger bed depth. The third 

sensitivity test addressed the effect of a larger suspended sediment load. 

5.2.3.3.1. Reduced Activity Release

Simulated concentrations of a tracer scale linearly with tracer mass input. For example, 

concentrations simulated with a unit mass of input will be reduced by 50 percent if the input 

mass is reduced by 50 percent. This linearity holds even if the tracer decays. In the river 

settings, sorption to and desorption from suspended and bed sediments should also be linear. 

This test was carried out to verify that. In this case, the fate of 137Cs and 131I was simulated for 

90 days, but the activity in the 10-day release was reduced by 3 orders of magnitude from the 

original simulations. Figure 5-43 and Figure 5-44 compare simulated concentrations of 137Cs

and 131I, respectively, with those from the original simulation at two locations. As expected, the 

reduced concentration is 3 orders of magnitude less than that of the base case.
5-28

 

Figure 5-43. Comparison of Decreased Release and Original Simulated Large River 

137Cs Total Water Column Concentrations at 10 (left) and 50 (right) Mi from

the Release.

 

Figure 5-44. Comparison of Decreased Release and Original Simulated Large River 131I

Total Water Column Concentrations at 10 (left) and 50 (right) Mi from the 

Release.

5.2.3.3.2. Increased Bed Depth

The sorption to and desorption from the bed was shown to be very significant in the river 

settings simulations. A key parameter for that process is the bed depth. The original depth was 

arbitrarily chosen to be 0.1 ft. For this test, the uniform bed depth was increased to 0.2 ft to see 

how much of an effect such a change would have. The fate of 137Cs and 131I was simulated for 

one year, using the original release levels. Figure 5-45 and Figure 5-46 compare simulated 

water column and bed sediment-sorbed concentrations of 137Cs with those from the original 

simulation at two locations. Increasing the bed depth by a factor of two results in a 4 percent 

increase in the amount of radionuclide sorbed to the bed sediments during the passage of the 

pulse of released radionuclides. Consequently, there is negligible impact on the aqueous pulse 

concentrations. Post-pulse water column concentrations, however, are about half of the base 

case. This is because a similar amount of bed-sorbed radionuclide is now associated with twice 

as much bed volume, which halves the bed concentration and the desorption rate. 
5-29

 

Figure 5-45. Comparison of Increased Bed and Original Simulated 137Cs Total Activity 

Concentrations at 10 (left) and 50 (right) Mi from the Release.

 

Figure 5-46. Comparison of Increased Bed and Original Simulated 137Cs Bed-Sorbed

Activity Concentrations at 10 (left) and 50 (right) Mi from the Release.

5.2.3.3.3. Increased Sediment Load

While typical for the two river settings, the suspended sediment load, 3.75 mg/l, is lower than 

many alluvial rivers. A one-year simulation of 137Cs was carried out with the extended large 

river setting but with a suspended sediment load of 100 mg/l. 

The increased sediment load had little effect on overall activities at locations above the dam. 

Concentrations of suspended sediment-sorbed radionuclide in the water column were increased 

by about 2 orders of magnitude (Figure 5-47, top). This, however, had very little effect on the 

total water column activity concentration (Figure 5-47, bottom) since the suspended sedimentsorbed concentrations were still about 2 orders of magnitude lower than the aqueous phase. In 

the dam forebay, 103 mi from the release, residual bed activity was noticeably higher. This 

indicates increased deposition of suspended sediment, with its sorbed activity, in the dam 

forebay as the release pulse passed (Figure 5-48). This leads to a small but noticeable 

increase in the longer-term post-pulse total radionuclide concentration in the water column in 

the forebay of the dam. 
5-30

 

Figure 5-47. Comparison of Water Column Activity Concentration from the Original OneYear Large River and Increased Sediment Load Simulations. Suspended 

sediment-sorbed phase (top) and total water column (bottom) 137Cs activity 

concentrations at 10 and 50 (left) and 80 and 103 (right) mi from the release 

location are shown.

 

Figure 5-48. Comparison of Bed-Sorbed Activity from the Original One-Year Large River 

and Increased Sediment Load Simulation at 10 and 50 (left) and 80 and 103 

(right) Mi Below the Release Location Are Shown.
5-31

5.3 Discussion

Of the three hypothetical hydrologic settings, the small lake scenario results in the highest 

radionuclide concentrations from the release of the radionuclide source term. Most of the large 

volume of water available for dilution is not accessed at early times because transport is 

essentially limited to dispersion, which is a relatively slow process. This allows high 

concentrations to persist well beyond the 10-day release period. Short-term peak 134Cs and 

137Cs concentrations 0.5 mi from the release point on the near shore are at least 17 times higher 

than any downstream river sampling location. Far-shore lake concentrations are comparable to 

the peak river concentrations. Peak 131I concentrations are also high for all sampling locations 

before decay significantly attenuates concentrations after 5 months. The small, seemingly 

negligible 100 cfs discharge has an important effect as the three locations with the highest 

concentration peaks are all downstream. The latest peak concentration arrivals occur at the two 

1.0 mi downstream locations on the near-shore and far-shore. A sensitivity analysis with a 

turbulent mixing coefficient 5 times higher results in earlier peak concentrations that 

subsequently decrease at a much slower rate. The lake modeled is 11 mi long and 0.62 mi 

wide with an average depth of 24 ft; results would not be applicable to a large lake (e.g., one of

the Great Lakes). 

Model results show that while dilution occurs as the pulse of released radionuclides becomes 

fully mixed in both the large and small river settings, the concentration pulse is transported 

downstream largely intact with little dispersive attenuation of peak concentrations for the entire 

length of the river (up to 293 mi). The exceptions are for radionuclides with 1) short half-lives 

relative to the transit time (e.g., 131I) and 2) high distribution coefficients (e.g., 144Ce). After the 

passage of the pulse, aqueous concentrations plateau ~3 orders of magnitude lower than the

peak pulse concentrations. These results will vary depending on characteristics of the river 

system (e.g., channel braiding or the number and size of tributaries), decay, and the sediment 

interactions with the radionuclide.

The lower river velocities in the impoundments behind the dams have the effect of lengthening 

the duration of the release pulse passing a given location. In the extended large river 

simulation, transit time over a 190-mi reach took 4.4 days without dams and 14.2 days with 

three intervening dams for the same flow rate. 131I concentrations are sensitive to these 

differences in transit times because of the 8-day half-life, which results in higher downstream 

concentrations for the unimpounded scenario. This suggests that dams could be used to 

control water releases with the intent of providing more time for 131I to decay.

Radionuclide sorption is most significant during the passage of the pulse of released 

radionuclides, effectively loading radionuclide activity onto the bed sediments. After the 

passage of the pulse, the significant decrease in water column concentrations favors desorption 

from the bed sediments, which becomes the principal source of activity in the water column and 

an important control on the duration and magnitude of post-pulse concentrations. The modeling 

indicates that post-pulse desorption will occur for the balance of the one-year simulation period 

along the entire length of the impacted riverbed. Over time, desorption decreases bed

sediment-sorbed concentrations. One less obvious consequence of continuous desorption 

along the entire impacted length of the river is that radionuclide water column concentrations 

increase with downstream distance. In this case, water traveling downstream progressively 

accumulates radionuclide activity as it passes over desorbing bed sediments. This effect would 

continue as long as nonequlibrium desorption conditions persist.
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5.3.1 Mixing and Transport

As shown in Figure 5-28, a key feature of the river transport is the downstream persistence of 

higher concentrations along the near-shore of the radionuclide release. There can be orders of 

magnitude differences in near-shore versus far-shore concentrations. In the case of the large 

river scenario, higher near-shore concentrations occur as far as 100 mi downstream, although 

most transverse mixing takes place in the first 50 mi. In the small river scenario, complete 

mixing across the channel occurs after 10 mi of transport. Tributaries in the extended large river 

scenario also impact shoreline concentrations by providing flows of uncontaminated water to the 

shore from which they entered the river. Longitudinal mixing increases with distance 

downstream, spreading the pulse along the axis of the river as it is transported downstream.

This effect is amplified when the pulse enters dammed impoundments where velocities are 

slower (Figures 5-39 to 5-42). Pulse durations increased by a factor of 2 to 3 during 

downstream transport, depending on the modeled scenario.

The small river scenario has a flow rate (5,000 cfs) that is 20 times smaller than the large river 

scenario (100,000 cfs). The principal consequence of this difference in flow rates is that there 

will be 20 times less dilution when the initial release pulse is fully mixed from bank to bank. 

Thus, concentrations will be commensurately higher in the small river scenario. The small river 

also has a lower average velocity, which increases the residence time. These conditions, high 

radionuclide concentrations and longer residence times, contribute to higher amounts of 

radionuclides sorbed to sediment. Sorption to bed sediments is therefore higher in 1) the small 

than the large river and 2) the impounded than the unimpounded lower river. 

5.3.2 Sediment-Radionuclide Interactions

In the model, the partitioning of radionuclide activity between aqueous and sediment-sorbed 

phases is based on a Kd model in which the equilibrium radionuclide concentration on the 

sediment is linearly proportional (based on Kd) to the aqueous concentration with no limit on the 

sorption capacity of the sediment. While sorption/desorption is instantaneous within the 

porewater of the sediment bed, the model uses a rate to control the sorption/desorption 

between the bed sediments and the water column. The highest rate will occur when the ratio of 

sediment-sorbed concentrations to aqueous water column concentrations differs the most from 

the Kd; conversely, the lowest rate will be zero when the ratio equals the Kd, which means that 

the sediment-sorbed and water column radionuclide concentrations are in equilibrium. In the 

model, the radionuclide-specific Kds are from the literature and the sorption/desorption rate was 

developed for use in a previous sediment and radionuclide transport modeling application for a 

large river. 

While sorption is an important process leading to elevated radionuclide concentrations in the 

bed sediment that could have longer-term effects, its impact on lowering aqueous 

concentrations in the release pulse is generally relatively small. High Kds result in significant 

fractions of 144Ce and 106Ru sorbed to bed sediments, but the radionuclides expected to have 

the highest aqueous concentrations (i.e., 134Cs, 131I, 137Cs, and 90Sr in descending order) are 

only slightly lower in the water column than corresponding cases without sorption. For example, 

aqueous 134Cs concentrations in the small river are 9 percent lower with adsorption than if no 

adsorption is included; 131I is 0.34 percent lower. As a result, concentrations of sorbed 

radionuclides in the sediment bed are relatively constant along the length of the river; with 

slightly higher concentrations in areas of low velocity (e.g., dam embayments). After the 

passage of the pulse of released radionuclides, the bed sediment-sorbed radionuclide 

concentrations, which reflect loading during the pulse passage, are far from equilibrium with the 
5-33

“cleaner” overlying aqueous radionuclide water column concentrations. This disequilibrium 

drives rate-limited desorption from the bed to the water column. Desorption from the bed 

sediments becomes a longer-term, widespread source, albeit with significantly lower water 

column concentrations than during the pulse. 

For the balance of the one-year simulation after the passage of the release pulse, equilibrium is 

not reached in the partitioning of radionuclides between the bed sediment and overlying water 

column (i.e., desorption is rate-limited). As a result, radionuclides are continuously desorbing 

from the bed sediments along the entire downstream length of the river. This means a parcel of 

water traveling downstream progressively accumulates more activity as it passes over

continuously desorbing bed sediments. So while aqueous radionuclide concentrations at any 

given location are decreasing with time, the tendency, as shown in Figure 5-40, is for aqueous 

concentrations to increase with downstream distance at any given time.

An important objective of this exploratory study is to provide information that can be used to 

decide whether further studies are needed to address the modeled radionuclide transport

processes in more detail. Since each radionuclide was modeled under the same conditions with 

the same 1 Bq source term, radionuclide-specific behavior is differentiated only through the 

impact of decay and Kd. Consequently, the radionuclide transport scoping calculations can be 

viewed as a sensitivity analysis for a range of partitioning (including no sorption) and decay 

behavior. The general conclusion is that a fraction of the radionuclide activity in the 10-day 

pulse release will partition to the bed sediments and this will result in a chronic, distributed 

source to the water column via desorption. What is less certain is the magnitude of this effect. 

Thus, it is important to recognize the limitations of the sorption modeling approach used in this 

study. 

Radionuclides partition to mineral and biological surfaces as a function of many factors including 

the availability, morphology, chemical composition, and charge of sorption sites, as well as the 

presence of competing, inhibiting, or complexing ions that alter reactivity with those sorption 

sites. The conditions controlling partitioning and rates are typically very site-specific with 

variation in space and time. For the 30-second temporal resolution in the model, sorption and 

desorption reaction rates are an appropriate consideration; however, these rates are not 

necessarily symmetric or fully reversible. For example, 137Cs/134Cs deposited in lakes from 

weapons test fallout and the Chernobyl accident were retained more strongly on sediment over 

periods on the scale of hundreds of days, reducing the desorption rate (Smith et al. 2000; Smith 

and Comans 1996). This effect may depend on how the contaminant was deposited. 

Experimental sorption/desorption studies of Cs on suspended river sediment indicated that 

retention increased by a factor of up to 16 when adsorption contact times were increased from 

0.5 to 120 hours (Ciffroy et al. 2001). Enhanced retention of 137Cs (but not 90Sr) as the 

sediment/contaminant interaction ages is also observed in the Dnieper River system (IAEA 

2006).

As a scoping study targeting generic freshwater settings, the sorption modeling does not 

consider these conditions. Instead, the modeling relies on literature values for radionuclide 

distribution coefficients (Kds) that linearly relate aqueous and sediment-sorbed concentrations. 

The rate of partitioning is based on a maximum rate developed for a previous study that is 

scaled by the deviation of aqueous and sorbed radionuclide concentrations from equilibrium, 

which is defined by the Kd. 

Over time Cs may become fixed to the sediment, essentially making it unavailable to the water 

column under normal chemical conditions. With the variability of Kd and the desorption rate, as 
5-34

well as possible dependence on the source term, the chronic concentrations of radionuclides in 

the aqueous phase presented in this section must be considered estimates with substantial 

uncertainty. In particular, if the desorption rate of Cs decreases substantially over a time scale 

of days to months, the aqueous concentrations will be correspondingly lower. This could result 

in substantial reductions of the chronic concentrations of Cs radionuclides in the water column.

5.3.3 Fate of Contaminated Sediment

While the long-term fate of contaminated sediment is beyond the scope of this study, it should 

be mentioned briefly that there are several processes that impact the distribution of 

contaminated sediment. Over time, clean sediment is naturally supplied as it moves 

downstream from uncontaminated areas. This clean material can be deposited over

contaminated layers of sediment, inhibiting interaction of contaminants with the water column. 

This is especially the case where flow rates are decreased (e.g., in dam forebays where 

sediment tends to accumulate). While the burial of contaminated sediment can potentially 

reduce the transport of contaminants, periodic high-flow events can scour that sediment from 

the bed, rapidly mixing it with clean sediment and redistributing it further downstream. If 

flooding occurs, the contaminated sediment may be deposited outside the normal course of the 

river. 

5.3.4 Scaling

The space- and time-dependent aqueous and sorbed radionuclide concentrations scale linearly 

with their source term magnitude. This scaling applies to the transport and sedimentradionuclide interaction process models used in this study. The scaling is valid when the decay 

and partitioning functions are linearly dependent on concentrations. The scaling property allows 

quick estimates for releases that are smaller or larger than the modeled source term. 
6-1

6. CONCLUSIONS

6.1 Summary

6.1.1 Objectives

This scoping study explores the potential behavior of contaminated water released directly to a 

freshwater body in a scenario similar to the 2011 Fukushima Daiichi (FD) accident, in which 

some contaminated building water leaked directly into the sea. The FD accident highlighted a 

scenario not currently addressed in the NRC’s severe accident consequence analysis. Very 

large volumes of contaminated water were generated by emergency measures to cool the 

reactors and spent fuel pools. UNSCEAR (UN 2014) estimated that between late March and 

April 2011,15 to 30 PBq of 131I, 134Cs, and 137Cs (many other radionuclides were present but not 

reported) were released into the ocean due to this accidental release.

A number of U.S. nuclear power plants are located on or very near lakes or rivers. In these 

settings, although highly unlikely, a FD-like release scenario could result in immediate impacts 

on freshwater bodies as well as longer lasting consequences. This study provides a scoping 

level assessment of the contaminant behavior resulting from a reactor accident in which 

contaminated water is generated and some of it is lost to a freshwater body. A key objective is 

to understand how advection, dilution/dispersion, decay, and sorption processes control the 

distribution of radionuclides in the context of freshwater settings and conditions. 

The approach in this study differed from previous studies in the following ways:

• multidimensional surface water modeling was used to account for the 3D bathymetry and 

spatially varying flow fields; 

• radionuclide sorption and desorption was addressed in the context of bed and suspended 

sediment in the model; 

• a method was developed to calculate the aqueous radionuclide inventory from 1) an 

estimation of the reactor core inventory as a function of reactor type, metric tons of uranium 

fuel, and fuel burnup, and 2) the aqueous partitioning of the reactor core inventory based on 

measurements of radionuclide concentrations in building water from Three Mile Island Unit 

2;

• an estimate of the fraction of the aqueous radionuclide inventory released from the FD 

nuclear power plant was shown to be consistent with estimates of the 2011 surface water 

release of radioactivity to the marine environment; and

• the source term for the radionuclide transport analyses was released directly to surface 

water bodies without transport through intervening subsurface media, which is consistent 

with the 2011 environmental monitoring of radioactivity from the FD nuclear power plant.

The scoping nature of the source term, freshwater settings, and conditions are primarily in the 

simplifying assumptions:

• limited number of surface water settings (i.e., three) to represent U.S. nuclear power plant 

sites (e.g., no marine or Great Lake settings);

• steady flow conditions;

• single sediment grain size with no erosion of bed sediments;
6-2

• single Kd for each radionuclide to describe sediment sorption and desorption with a single 

sorption/desorption rate;

• no wind or thermal stratification for the lake scenario; and

• four radionuclides (131I, 134Cs, 137Cs, 90Sr) to represent the inventory for the extended 

duration and extended river length simulations.

6.1.2 Modeling Quality Assurance

Each modeling component of this study has been tested and assessed for accuracy using 

observations, mass balance calculations, analytical solutions, or benchmarking. This includes 

1) comparing the estimated aqueous radionuclide inventory against the Fukushima building 

water composition; 2) comparing the release fraction of the aqueous radionuclide inventory 

against estimates based on monitored radionuclide concentrations in the marine waters off the 

coast from FD, and 3) comparing the simulated river and lake radionuclide concentrations 

against analytical transport solutions. The latter are described in Appendix A.

6.2 Conclusions from Model Results

In the case of direct release to a water body, depending on the source term, the pulse of 

contaminated water can have very high concentrations of radionuclides. In free-flowing river 

reaches, the first arrival of a release to a downstream exposure location may occur after a few 

hours of transport, especially along the near shore of the release. The radionuclide 

concentrations in the release pulse will be diluted by several orders of magnitude once it is well 

mixed with river or lake water. Further mixing in the lake or transport downstream may lower 

peak concentrations; however, depending on the source term concentrations could still be 

sufficiently high to require emergency actions. In lakes, this condition could persist for some 

time. 

As discussed in Section 5, a contaminant pulse released into a river system can move 

downstream as a relatively coherent pulse potentially for hundreds of miles. After the 10-day 

release of radionuclides attained a fully mixed concentration over the river cross-section, the 

steady flow conditions assumed in these scoping studies were able to transport the pulse intact 

for 293 mi despite longitudinal mixing and other attenuation processes. Consequently, it is 

important to recognize that monitoring and emergency actions may be needed for significant

distances downstream. 

Flow through many river systems is heavily regulated by dams. The principal effects of the 

impoundments behind dams are to 1) slow downriver transport of released radionuclides, 

2) increase residence time, 3) increase bed sediment surface area available for sorption, and 

4) increase deposition of suspended sediments with sorbed radionuclides. The transport of a 

radionuclide release pulse through a river system with impoundments may take many days if 

not months for large systems. This will influence the amount of time that monitoring and 

emergency actions may be needed. It also presents an opportunity to regulate flow to help 

minimize impacts. 

Following passage of the release pulse in river systems, contaminant concentrations will 

decrease sharply. However, residual radionuclide activity retained on bed sediments will desorb 

at a slow rate, resulting in water concentrations that still may degrade water quality. In effect, 

these bed sediments become a distributed source of radionuclides in the river that will persist 

long after the initial release event. The modeling results presented in Section 5 depict the 
6-3

transport of a unit activity release of radionuclides over 10 days followed by longer-term 

desorption of residual radioactivity from bed sediments into the overlying water column. 

6.2.1 Transport

• Of the three hydrologic settings, the lake scenario results in the highest radionuclide 

concentrations. Most of the lake volume available for dilution is not accessed at early times 

because transport is essentially limited to dispersion. As a result, radionuclide 

concentrations remain high, likely for extended times. 

• Once the release is fully mixed over the river cross-section, dilution from the ratio of river 

flow to volumetric release rate is 1 × 105 for the small river and 2 × 106 for the large river.

• In the river settings considered, the 10-day pulse of released activity remains largely intact 

for the entire length of the river, which for the extended large river model is 293 mi. 

• A key feature of the river transport is the downstream persistence of higher concentrations 

along the near shore of the radionuclide release. There can be orders of magnitude 

differences in near-shore versus far-shore concentrations. In the case of the large river,

transverse mixing is mostly complete after 50 mi of downstream transport. In the small river 

scenario, complete mixing across the channel occurs after 10 mi of transport.

• For the sediment-radionuclide interaction and transport process models used in this study, 

the simulated aqueous and sorbed radionuclide concentrations scale linearly with source 

term to three significant figures. This scaling property allows quick conversion of the 

presented concentrations, which are per Bq in the 10-day release, simply by multiplying by 

the desired source term radionuclide activity. 

6.2.2 Transit Times

• Transit times for free-flowing river reaches can be quite fast. For a point 50 mi downstream 

from the source term release point, radionuclides first arrived after 17 hours for the large 

river and 25 hours for the small river. However, different river stages and different reaches 

could result in much slower or faster transport times. 

• Dams can slow the transit time considerably. In the extended large river simulation, transit 

time over a 190-mi reach took 4.4 days without dams and 14.2 days with three intervening 

dams. 

6.2.3 Sorption and Desorption

• Radionuclide sorption is most significant during the passage of the pulse of released activity 

due to the difference in concentration between the water column and the sediment bed,

which drives adsorption to the bed sediment. 

• After the passage of the pulse of released activity, desorption from the bed sediments 

becomes a longer-term, widespread source of radionuclides to the water column, albeit with 

significantly lower water column concentrations than the pulse. 

• Sorption to suspended sediment accounts for a negligible fraction of the released 

radionuclides. While this is due, in part, to the relatively low 3.75 mg/L suspended sediment

load in the baseline specification of the river scenarios, a 100 mg/L suspended sediment 

load sensitivity case did not alter this finding.

• Sorption to bed sediments is higher in 1) the small than the large river and 2) the impounded 

than the unimpounded lower river. In the small river, significantly higher water column 
6-4

concentrations during the passage of the release pulse (due to less dilution) result in 

commensurately higher bed-sorbed concentrations. The impoundments behind the dams 

are wide and deep, providing a larger wetted surface area (i.e., more bed sediment) for 

sorption. In both cases, sorption is enhanced by comparatively longer residence times.

• Sorption onto bed sediments has only a small effect in lowering dissolved concentrations of

137Cs, 134Cs, 90Sr, and 131I in the pulse of released radionuclides. For example, aqueous 

134Cs and 137Cs concentrations in the small river are 9 percent lower with adsorption than the 

aqueous-only case (no adsorption); 131I is 0.34 percent lower. However, depending on the 

magnitude of activity released and radionuclide sorption properties, water column 

concentrations driven by longer-term post-pulse desorption from bed sediments could still 

require intervention.

• After the passage of the pulse of released activity, aqueous river concentrations increase 

with downstream distance from the release point for the remainder of the one-year 

simulation period. This is because the desorption rate from the bed sediments is sufficiently 

low that equilibrium between activity sorbed to the bed sediments and activity in the 

overlying water column is never attained during the simulation. This disequilibrium drives 

the continuous desorption of radionuclides from bed sediments along the entire downstream 

length of the river, resulting in a progressive accumulation of desorbed radionuclides as 

water travels downstream. This effect will depend on the magnitude of the source term, Kd

values, and desorption rates. 

6.3 Site-Specific Applications

Sensitivity analyses for modeling parameters in this scoping study can be used to inform followon modeling of more realistic sites and conditions. The relatively high radionuclide 

concentrations in the lake result largely from limited mixing that prevents most of the large 

volume from being accessed for dilution at early time. While common scenarios not addressed 

in this scoping study can accelerate dilution, the insight from the sensitivity analysis was that an 

intermediate increase in the turbulent mixing coefficient can result in similar, but earlier, peak 

concentrations and longer persistence of elevated concentrations. Generic distribution 

coefficients (i.e., Kds) would not be expected to reproduce site-specific radionuclide 

sorption/desorption behavior, which is generally a function of the solid concentrations, solids 

geometry, bed configuration and conditions, mineralogical and organic matter character of the 

solids, and the geochemical conditions controlling the radionuclide speciation. The insight from 

the sensitivity analysis (Section 5.1.3.3.) was that changing the bed thickness can directly affect 

post-pulse water column concentrations (i.e., long-term desorption phase) even though there is 

no significant reduction of water column concentrations during the passage of the release pulse 

(i.e., short-term sorption phase).

This was an exploratory study that relied on previous studies for many parameters. While 

reasonable values were chosen, they are necessarily not specific to any site. The selection of a 

site and use of site- (and time-) specific values for parameters (e.g., river discharge rates, 

dispersion, transit times, and Kd values) will undoubtedly alter results in important ways. 

Characteristics of other rivers (e.g., more tributaries, more meanders, and more flow dynamics) 

and the use of river water may be different, altering the relative importance of certain features. 

For example, irrigation with river water is of particular interest to dose calculations for western 

sites, whereas its use may be quite limited in many eastern rivers. 
6-5

Possible site-specific extensions to the scoping analyses that were performed could include the 

following: 

• lake processes: wind-driven flow, thermal stratification, and radionuclide-sediment 

interactions;

• unsteady flow: flood and drought conditions, and event-based flow regimes (e.g., storms);

• sediment transport: multiple bed layers, multiple sediment sizes, erosion, and bedload 

transport; and

• radionuclide-sediment interactions: sorption to sediments moving very slowly as bedload in 

an alluvial river, nonuniform sediment distributions, desorption kinetics and hysteresis of 

adsorbed radionuclides (e.g., recalcitrant fractions), and multicomponent sorption controls 

(e.g., competitive sorption).

The scoping analyses also provide a framework for simpler modeling approaches that may be 

appropriate for site-specific analysis or emergency planning including the following:

• one dimensional river simulations where transverse and vertical mixing are sufficiently 

efficient;

• reduced inventory size: 131I, 134Cs, and 137Cs for short-term analyses; 134Cs and 137Cs for 

long-term analyses; and 

• scaling of the current results to calculate concentrations for larger/smaller releases and 

shorter/longer durations.

7-1

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APPENDIX A

–

MODELING QUALITY ASSURANCE

A-1

APPENDIX A

MODELING QUALITY ASSURANCE

A.1 Lake Transport Modeling

A check of the Transient Energy Transport HYdrodynamics Simulator (TETHYS) code was 

made by comparing simulated concentrations to an analytic solution in a simple approximation 

of the lake setting. The lake was approximated as a semi-infinite rectangular domain of constant 

width and depth. The outline of this approximation is overlayed as a black rectangle on the lake 

setting (Figure A-1). A schematic of the simplified domain is shown in Figure A-2 and the 

nomenclature is defined in Table A-1. The lake has a nominal discharge of 100 cfs through an 

approximantely constant width section of the lake. The depth profile at the central transect is 

shown in Figure A-1b, from which an average depth of 7.8 m was calculated. A constant tracer 

mass flux was released over a 10-day period from the shoreline of the three-dimensional (3D) 

large lake model shown in Figure A-1a. Probes are located at radii of 0.5 mi and 1.0 mi to 

moniter the progression of the contaminant from the source location (Figure A-2). Other 

dimensions and parameters are shown in Table A-1.

a b

Figure A-1. Domain of Simplified Two-Dimensional Model in the Context of the Large 

Lake Model and Depth Profile at x = 0 
Appendix A

A-2

Figure A-2. Schematic and Notation of Two-Dimensional Approximation of Large Lake 

Model

Table A-1. Parameters of Simplified Analytical Model

Parameter Nomenclature Value Unit

Lake discharge VV̇ 100 cfs

Mean flow velocity U 3.5 × 10-4 m/s

Lake width w 1,000 m

Lake depth d 7.8 m

Probe radius #1 R1 805 m

Probe radius #2 R2 1,609 m

Diffusivity constant D 0.04 m2/s

Tracer discharge rate mṁ 1 g/s

Tracer discharge duration tr 10 days

Decay constant k 0 1/s

Probe 1 Coordinates (Source) P1 [0, 0, 0] m

Probe 2 Coordinates P2 [-805, 0, 0] m

Probe 3 Coordinates P3 [805, 0, 0] m

Probe 4 Coordinates P4 [1,609, 0, 0] m

Probe 5 Coordinates P5 [1,261, -1,000, 0] m

Probe 6 Coordinates P6 [-1,261, -1,000, 0] m

Probe 7 Coordinates P7 [-1,609, 0, 0] m

The unbounded 3D analytical solution was derived from the integral formation of a timedependent source term presented by Shi (2004):

CC(xx, yy, zz,tt) = γγ � 1

(tt − ττ)3/2 exp �− αα

(tt − ττ) − ββ(tt − ττ)�

tt

0

dττ
A-3

where

γγ = mṁ

8(ππππ)3/2 exp �

xxxx

2 �

αα = xx2 + yy2 + zz2

4

ββ =

2

4 + kk

and CC is concentration, xx, yy, and zz are spatial coordinates, and tt is time. During continuous 

injection from t = 0 to t = tr:

CC0(xx, yy, zz,tt) = γγ√ππ

2√αα �exp�2�αα �erfc ��αα

tt

+ �ββ � + exp�−2�αα �erfc ��αα

tt − �ββ ��

The solution following the release period (t > tr) is:

CC0(xx, yy, zz,tt) = γγ√ππ

2√αα �exp�2�αα � �erf�� αα

(tt − ttrr) + �ββ(tt − ttrr)� − erf ��αα

tt

+ �ββ ��

+ exp�−2�αα � �erf�� αα

(tt − ttrr) − �ββ(tt − ttrr)� − erf ��αα

tt − �ββ ���

For the bounded case of the semi-infinite lake, the solution is reflected about the lake banks in 

the y-direction and the surface and lake-bed in the z-directions, such that the above equations 

become:

αα = xx2 + �yy + 2nnyyww�

2

+ (zz + 2nnzzdd)2

4

CC(xx, yy, zz,tt) = � � 4CC0

∞

nnyy=−∞

∞

nnzz=−∞

For the geometry defined in Table A-1, this converges to a stable result when −2 ≤ nnyy ≤ 2 and 

−25 ≤ nnzz ≤ 25. 

TETHYS was configured to simulate the domain of the analytic solution using the same 

parameters (Table A-1). Simulation results were sampled at the locations shown in Figure A-2

and the analytic solution was computed for the same locations. Simulation results were very 

close to the analytic solution (Figure A-3). 
Appendix A

A-4

Figure A-3. Comparison of TETHYS Simulation Results with Analytic Solution

A.2 River Transport Modeling

In order to check the reasonability of the Modular Aquatic Simulation System in 2 Dimensions 

(MASS2) numerical solutions for the small and large river contaminant transport solutions, 

simple analytical solutions were computed based on an adaptation of the solution provided in 

van Genuchten et al. (2013). The van Genuchten analytic solution is based on the following 

assumptions:

• the longitudinal (x-direction) turbulent mixing is much less significant than the longitudinal 

advective transport;

• the transverse (y-direction) turbulent mixing coefficient has a constant value of εy;

• the contaminant is conservative;

• the contaminant flux is a constant and steady F;

• the point release of contamination occurs at x=0, y=y0; and

• the river discharge is steady and has uniform flow depth H and water speed u, and width, B.

For the case where the shoreline boundaries are sufficiently distant from the release point, a 

simple unbounded solution can be used to compute the contaminant concentration CU(x,y) for 

positions laterally across the river and longitudinally downstream from the source, x.

CCUU(xx, yy) = FF exp �

−uu (yy − yy0)2

4xxεεyy

� [2 HH �ππ εεyyxx]

−1

Superpositioning of reflected solutions for CU accounts for the presence of the shoreline 

boundaries. This is necessary to obtain bounded solutions for the contaminant activities, 

CB(x,y). These solutions ensure that lateral diffusion does not occur laterally beyond the near 

and far shores. The number of reflected terms, n, is based on what is considered necessary to 
A-5

develop a satisfactory solution respecting the solid boundaries of the shorelines. The literature 

suggests that n should be greater than four. All solutions presented here are based on n equal 

to 10. The modified solution accounting for boundary reflection is based on the summation of a 

series of unbounded solutions that are laterally offset from the position of the contaminant 

release. This is given by van Genuchten et al. (2013) below:

CCBB (xx, yy) = CCUU(xx, yy) + �CCUU�xx, kkkk − yy0 + (−1)kkyy� + CCUU(xx, −kkkk + yy0 − (−1)kkyy)

nn

kk=1

For this project, first-order decay needed to be included. This process was added to the 

unbounded contaminant equation based on first-order decay with a decay rate, r, where the

downstream position x is a precise predictor of the elapsed time-of-travel of a parcel of 

contaminant released at x=0:

CCUU(xx, yy) = FF exp �

−uu (yy − yy0)2

4xxεεyy

� [2 HH �ππ εεyyxx]

−1 exp(−rr

xx

uu

)

The analytical solution is based on a steady release. This differs from the 10-day release 

scenario that was evaluated using MASS2. While this prevents the analytical solution from 

capturing the initial rise and final decline of the contamination levels, it does allow for 

comparison to the peak concentrations that could be expected. It is also expected that the 

contaminant will attain a peak level of contaminant concentration and sustain that level for a 

duration lasting about as long as the release duration (i.e., 10 days).

A Matlab program was used to compute solutions to the above equation for domains 

approximating those simulated by MASS2 in the large and small discharge river cases. 

Dimensions of the two domains are listed in Table A-2. The actual flow depth and width varied 

widely in both river settings. Those listed in Table A-2 are estimates. Again, the domain 

assumed by the analytic solution is a rough approximation of the actual river setting. The 

source term and radionuclide-specific parameters used in the analytical transport solution are 

summarized in Table A-3.

Table A-2. Small and Large River Scenario Flow and Mixing Parameters Used in the 

Analytical Transport Solution

River Case

Width B Depth H Discharge Velocity u

Transverse turbulent 

mixing coefficient εy

m m m3/s,(cfs) (m/s) m2/s

Small 150 4.0 141.58 (5,000) 0.236 0.19

Large 550 7.0 2,831.68 (100,000) 0.736 0.19
Appendix A

A-6

Table A-3. Small and Large River Scenario Aqueous Radionuclide Inventory, Flux and 

Decay Characteristics and Parameters Used in the Analytical Transport 

Solution.

Case Radionuclide

Decay 

coefficient, 

r(a)

Water 

Volume 

Released

Release 

Duration Release Rate, F

Fully Mixed 

Activity, Small 

River

Fully 

Mixed 

Activity, 

Large 

River

1/days m3 days Bq/s Bq/m3 Bq/m3

1 144Ce 0 1,000 10 868,056 6131 307

2 134Cs 0 1,000 10 13,020,833,333 91,965,267 4,598,263

3 137Cs 0 1,000 10 8,391,203,704 59,266,505 2,963,325

4 3H 0 1,000 10 49,189,815 347,424 17,371

5 131I 0.09495 1,000 10 12,731,481,481 NA NA

6 106Ru 0 1,000 10 2,314,815 16,349 817

7 125Sb 0 1,000 10 3,472,222 24,524 1,226

8 90Sr 0 1,000 10 240,162,037 1,696,248 84,812

(a) Decay rates are internally converted from d-1 to s-1 in the analytical solution calculation.

Comparisons of simulated small river peak activity values with those from the analytic solution 

are shown in Figure A-4 through Figure A-11. MASS2 compare closely for the longer lived 

radionuclides. Complete lateral mixing is achieved within the upper 10 mi of the 50 river mi

considered; that is, the near and far bank concentrations are nearly equal to each other and the 

simply calculated fully mixed activity levels expected for each long-lived radionuclide treated as 

conservative. For the decaying radionuclide (131I, Figure A-8), the complete lateral mixing 

occurs for both numerical and analytic models as it does for the long-lived radionuclides. 

However, the numerical model shows a trend of less decay than the analytical and what would 

be indicated by a simple calculation of fully mixed but decayed activity as estimated from the 

time-of-travel to each downstream location.

Comparisons of simulated large river peak activity values with those from the analytic solution 

are shown in Figure A-12 through Figure A-19. When compared with the small river, the large 

river is wider and has a higher velocity. Complete transverse mixing is not achieved within the 

50 river mi considered; that is, the near and far bank concentration are unequal to each other 

but approach the simply calculated, fully mixed activity levels expected for each isotope. Within 

the upper 10 mi, the numerical model shows slightly less lateral mixing than the analytic model. 

However, both models show increased and very comparable levels of lateral mixing at distances 

of 20 mi and greater. 

The quality of the comparison is good for the large and small rivers for all radionuclides treated 

as conservative; all solutions seem to be converging to the expected fully mixed activity levels. 

This also holds true for the large river 131I case, where the swift currents reduced travel times 

and therefore diminishes the impact of 131I decay. In the small river 131I case, where travel time 

is longer, there is a larger level difference between the analytical solutions and the MASS2 

solution. All MASS2 and analytical solution comparisons show agreement that is better (and 

most often much better) than order of magnitude. There is no indication that the MASS2 model 

is producing results that are inconsistent with expectations for conservative transport cases.
A-7

Figure A-4. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 144Ce Activity at Near and Far Banks. 

Figure A-5. MASS2 And Analytical Solution Longitudinal Small River Solutions for 

Estimated 134Cs Activity at Near and Far Banks.
Appendix A

A-8

Figure A-6. MASS2 And Analytical Solution Longitudinal Small River Solutions for 

Estimated 137Cs Activity at Near and Far Banks.

Figure A-7. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 3

H Activity at Near and Far Banks.
A-9

Figure A-8. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 131I Activity at Near and Far Banks.

Figure A-9. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 106Ru Activity at Near and Far Banks.
Appendix A

A-10

Figure A-10. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 125Sb Activity at Near and Far Banks.

Figure A-11. MASS2 and Analytical Solution Longitudinal Small River Solutions for 

Estimated 90Sr Activity at Near and Far Banks.
A-11

Figure A-12. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 144Ce Activity at Near and Far Banks.

Figure A-13. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 134Cs Activity at Near and Far Banks.
Appendix A

A-12

Figure A-14. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 137Cs Activity at Near and Far Banks.

Figure A-15. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 3

H Activity at Near and Far Banks.
A-13

Figure A-16. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 131I Activity at Near and Far Banks.

Figure A-17. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 106Ru Activity at Near and Far Banks.
Appendix A

A-14

Figure A-18. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 125Sb Activity at Near and Far Banks.

Figure A-19. MASS2 and Analytical Solution Longitudinal Large River Solutions for 

Estimated 90Sr Activity at Near and Far Banks.

A.3 Source Term Details

A.3.1 Reactor Fuel Content for PWR and BWR of Various Burnups

This appendix lists core-average radionuclide inventories calculated by ORIGEN-ARP as a 

function of peak rod burnup for 60 radionuclides developed by Ramsdell et al. (2001). 

Table A-4 contains the inventories for PWR fuel, and Table A-5 contains the inventories for 

BWR fuel.
A-15

Table A-4. PWR Core-Averaged Inventory of Radionuclides as a Function of Burnup (Bq/MTU) (from N

Nuclide

Peak Rod Burnup. GWd/MTU

22 24 25 42 43 46 48 50 60 62 6

H-3 1.16E+13 1.27E+13 1.32E+13 2.16E+13 2.21E+13 2.35E+13 2.45E+13 2.54E+13 3.00E+13 3.09E+13 3.22

Co-58 3.55E+14 3.59E+14 3.61E+14 3.92E+14 3.92E+14 3.96E+14 4.00E+14 4.03E+14 4.14E+14 4.18E+14 4.18

Co-60 1.80E+14 1.95E+14 2.02E+14 3.26E+14 3.33E+14 3.54E+14 3.68E+14 3.81E+14 4.51E+14 4.66E+14 4.85

Kr-85m 8.33E+15 8.18E+15 8.07E+15 6.92E+15 6.88E+15 6.70E+15 6.51E+15 6.40E+15 5.85E+15 5.74E+15 5.55

Kr-85 2.62E+14 2.81E+14 2.90E+14 4.29E+14 4.37E+14 4.55E+14 4.70E+14 4.81E+14 5.33E+14 5.44E+14 5.59

Kr-87 1.68E+16 1.65E+16 1.63E+16 1.39E+16 1.38E+16 1.34E+16 1.31E+16 1.28E+16 1.17E+16 1.14E+16 1.10

Kr-88 2.36E+16 2.31E+16 2.28E+16 1.93E+16 1.91E+16 1.85E+16 1.80E+16 1.76E+16 1.60E+16 1.56E+16 1.51

Rb-86 2.66E+13 2.94E+13 3.08E+13 5.74E+13 5.92E+13 6.44E+13 6.77E+13 7.14E+13 8.92E+13 9.25E+13 9.81

Sr-89 3.30E+16 3.23E+16 3.20E+16 2.68E+16 2.66E+16 2.57E+16 2.51E+16 2.45E+16 2.19E+16 2.14E+16 2.07

Sr-90 2.27E+15 2.44E+15 2.53E+15 3.81E+15 3.89E+15 4.07E+15 4.18E+15 4.33E+15 4.85E+15 4.96E+15 5.11

Sr-91 4.03E+16 3.96E+16 3.92E+16 3.37E+16 3.36E+16 3.26E+16 3.18E+16 3.13E+16 2.86E+16 2.80E+16 2.72

Sr-92 4.18E+16 4.11E+16 4.07E+16 3.59E+16 3.58E+16 3.49E+16 3.42E+16 3.37E+16 3.14E+16 3.08E+16 3.01

Y-90 2.37E+15 2.55E+15 2.64E+15 3.99E+15 4.06E+15 4.25E+15 4.40E+15 4.51E+15 5.11E+15 5.22E+15 5.37

Y-91 4.18E+16 4.07E+16 4.03E+16 3.49E+16 3.46E+16 3.36E+16 3.29E+16 3.23E+16 2.95E+16 2.89E+16 2.81

Y-92 3.28E+12 3.35E+12 3.37E+12 3.96E+12 4.03E+12 4.14E+12 4.18E+12 4.26E+12 4.59E+12 4.63E+12 4.74

Y-93 3.12E+16 3.08E+16 3.05E+16 2.76E+16 2.75E+16 2.69E+16 2.65E+16 2.62E+16 2.48E+16 2.44E+16 2.40

Zr-95 5.24E+16 5.21E+16 5.17E+16 4.85E+16 4.86E+16 4.78E+16 4.75E+16 4.71E+16 4.54E+16 4.50E+16 4.43

Zr-97 4.86E+16 4.83E+16 4.83E+16 4.67E+16 4.71E+16 4.68E+16 4.65E+16 4.65E+16 4.59E+16 4.56E+16 4.52

Nb-95 5.28E+16 5.24E+16 5.21E+16 4.89E+16 4.86E+16 4.83E+16 4.79E+16 4.72E+16 4.55E+16 4.55E+16 4.48

Mo-99 5.29E+16 5.29E+16 5.25E+16 5.18E+16 5.22E+16 5.22E+16 5.18E+16 5.18E+16 5.14E+16 5.14E+16 5.14

Tc-99m 4.66E+16 4.66E+16 4.66E+16 4.63E+16 4.63E+16 4.63E+16 4.59E+16 4.59E+16 4.59E+16 4.59E+16 4.55

Ru-103 3.81E+16 3.89E+16 3.92E+16 4.37E+16 4.40E+16 4.48E+16 4.51E+16 4.59E+16 4.81E+16 4.85E+16 4.88

Ru-105 2.25E+16 2.33E+16 2.37E+16 2.96E+16 3.01E+16 3.12E+16 3.17E+16 3.24E+16 3.55E+16 3.59E+16 3.68

Ru-106 9.36E+15 1.02E+16 1.07E+16 1.75E+16 1.78E+16 1.89E+16 1.96E+16 2.04E+16 2.37E+16 2.44E+16 2.53

Rh-105 2.14E+16 2.23E+16 2.26E+16 2.80E+16 2.85E+16 2.94E+16 2.99E+16 3.06E+16 3.32E+16 3.36E+16 3.43

Sb-125 2.05E+13 2.21E+13 2.28E+13 3.50E+13 3.57E+13 3.77E+13 3.89E+13 4.03E+13 4.63E+13 4.77E+13 4.96

Sb-127 1.98E+15 2.03E+15 2.05E+15 2.36E+15 2.38E+15 2.43E+15 2.45E+15 2.49E+15 2.64E+15 2.66E+15 2.70

Te-127m 3.21E+14 3.32E+14 3.36E+14 3.96E+14 4.00E+14 4.11E+14 4.14E+14 4.22E+14 4.48E+14 4.55E+14 4.63

Te-127 1.95E+15 2.00E+15 2.02E+15 2.33E+15 2.36E+15 2.41E+15 2.43E+15 2.47E+15 2.62E+15 2.64E+15 2.68

Te-129m 1.57E+15 1.59E+15 1.59E+15 1.70E+15 1.71E+15 1.73E+15 1.74E+15 1.75E+15 1.79E+15 1.80E+15 1.81

Te-129 7.81E+15 7.92E+15 7.92E+15 8.40E+15 8.44E+15 8.51E+15 8.55E+15 8.58E+15 8.84E+15 8.84E+15 8.88

Te-131n1 4.85E+15 4.92E+15 4.96E+15 5.40E+15 5.48E+15 5.55E+15 5.55E+15 5.62E+15 5.85E+15 5.85E+15 5.88

Te-132 3.96E+16 3.96E+16 3.96E+16 3.96E+16 4.00E+16 4.00E+16 3.96E+16 4.00E+16 4.00E+16 3.96E+16 3.96

I-131 2.73E+16 2.73E+16 2.74E+16 2.77E+16 2.78E+16 2.78E+16 2.78E+16 2.79E+16 2.79E+16 2.80E+16 2.80

I-132 4.00E+16 4.03E+16 4.03E+16 4.03E+16 4.07E+16 4.07E+16 4.03E+16 4.07E+16 4.07E+16 4.07E+16 4.07

I-133 5.81E+16 5.81E+16 5.81E+16 5.70E+16 5.74E+16 5.70E+16 5.70E+16 5.70E+16 5.66E+16 5.62E+16 5.62

I-134 6.55E+16 6.51E+16 6.51E+16 6.33E+16 6.33E+16 6.33E+16 6.25E+16 6.25E+16 6.18E+16 6.14E+16 6.14

I-135 5.51E+16 5.51E+16 5.48E+16 5.44E+16 5.48E+16 5.44E+16 5.44E+16 5.44E+16 5.40E+16 5.40E+16 5.40
A-16

Table A-4. (contd)

Nuclide

Peak Rod Burnup. GWd/MTU

22 24 25 42 43 46 48 50 60 62 6

Xe-133 5.81E+16 5.81E+16 5.81E+16 5.74E+16 5.74E+16 5.74E+16 5.70E+16 5.70E+16 5.66E+16 5.66E+16 5.62

Xe-135 2.39E+16 2.38E+16 2.36E+16 2.06E+16 2.05E+16 2.01E+16 1.97E+16 1.95E+16 1.77E+16 1.74E+16 1.71

Cs-134 2.13E+15 2.49E+15 2.68E+15 6.40E+15 6.66E+15 7.40E+15 7.96E+15 8.47E+15 1.11E+16 1.17E+16 1.25

Cs-136 9.88E+14 1.08E+15 1.13E+15 2.02E+15 2.08E+15 2.25E+15 2.36E+15 2.48E+15 3.11E+15 3.23E+15 3.43

Cs-137 2.68E+15 2.92E+15 3.04E+15 5.00E+15 5.11E+15 5.44E+15 5.70E+15 5.92E+15 6.99E+15 7.22E+15 7.55

Ba-139 5.25E+16 5.25E+16 5.22E+16 5.03E+16 5.03E+16 5.03E+16 4.96E+16 4.96E+16 4.88E+16 4.85E+16 4.85

Ba-140 5.25E+16 5.22E+16 5.22E+16 5.07E+16 5.07E+16 5.03E+16 5.00E+16 5.00E+16 4.92E+16 4.88E+16 4.85

La-140 5.33E+16 5.33E+16 5.29E+16 5.22E+16 5.25E+16 5.22E+16 5.18E+16 5.18E+16 5.18E+16 5.14E+16 5.14

La-141 4.81E+16 4.81E+16 4.77E+16 4.59E+16 4.63E+16 4.59E+16 4.55E+16 4.51E+16 4.44E+16 4.40E+16 4.40

La-142 4.74E+16 4.74E+16 4.70E+16 4.48E+16 4.51E+16 4.48E+16 4.40E+16 4.40E+16 4.33E+16 4.29E+16 4.26

Ce-141 4.85E+16 4.85E+16 4.81E+16 4.66E+16 4.66E+16 4.63E+16 4.59E+16 4.59E+16 4.48E+16 4.48E+16 4.44

Ce-143 4.63E+16 4.59E+16 4.59E+16 4.29E+16 4.29E+16 4.26E+16 4.22E+16 4.18E+16 4.07E+16 4.03E+16 4.00

Ce-144 3.74E+16 3.81E+16 3.85E+16 4.00E+16 3.96E+16 3.96E+16 3.92E+16 3.92E+16 3.81E+16 3.77E+16 3.74

Pr-143 4.55E+16 4.51E+16 4.51E+16 4.22E+16 4.22E+16 4.14E+16 4.14E+16 4.11E+16 3.96E+16 3.96E+16 3.92

Nd-147 1.91E+16 1.91E+16 1.91E+16 1.87E+16 1.88E+16 1.87E+16 1.86E+16 1.86E+16 1.85E+16 1.84E+16 1.84

Np-239 4.48E+17 4.55E+17 4.59E+17 5.37E+17 5.44E+17 5.59E+17 5.62E+17 5.74E+17 6.18E+17 6.25E+17 6.40

Pu-238 2.82E+13 3.52E+13 3.89E+13 1.42E+14 1.50E+14 1.76E+14 1.95E+14 2.14E+14 3.17E+14 3.39E+14 3.70

Pu-239 1.17E+13 1.21E+13 1.23E+13 1.41E+13 1.41E+13 1.42E+13 1.42E+13 1.42E+13 1.41E+13 1.41E+13 1.40

Pu-240 9.10E+12 1.00E+13 1.05E+13 1.91E+13 1.95E+13 2.06E+13 2.13E+13 2.20E+13 2.55E+13 2.60E+13 2.66

Pu-241 2.80E+15 3.22E+15 3.42E+15 5.66E+15 5.81E+15 6.18E+15 6.44E+15 6.66E+15 7.18E+15 7.29E+15 7.47

Am-241 2.31E+12 2.87E+12 3.16E+12 8.29E+12 8.55E+12 9.29E+12 9.73E+12 1.02E+13 1.16E+13 1.18E+13 1.20

Am-242 7.77E+14 9.81E+14 1.08E+15 3.20E+15 3.34E+15 3.74E+15 3.96E+15 4.22E+15 5.25E+15 5.40E+15 5.66

Cm-242 3.05E+14 4.07E+14 4.63E+14 1.93E+15 2.03E+15 2.32E+15 2.52E+15 2.72E+15 3.66E+15 3.81E+15 4.03

Cm-244 4.11E+12 6.40E+12 7.84E+12 9.99E+13 1.11E+14 1.51E+14 1.83E+14 2.19E+14 4.66E+14 5.33E+14 6.44
A-17

Table A-5. BWR Core-Averaged Inventory of Radionuclides as a Function of Burnup (Bq/MTU) (from N

Nuclide

Peak Rod Burnup, GWd/MTU

22 24 25 42 43 46 48 50 60 62 

H-3 1.15E+13 1.24E+13 1.30E+13 2.10E+13 2.14E+13 2.28E+13 2.36E+13 2.45E+13 2.88E+13 2.96E+13 3.08E

Co-58 3.13E+14 3.11E+14 3.12E+14 3.40E+14 3.42E+14 3.39E+14 3.41E+14 3.44E+14 3.59E+14 3.61E+14 3.65E

Co-60 1.65E+14 1.78E+14 1.85E+14 2.92E+14 2.98E+14 3.16E+14 3.28E+14 3.40E+14 4.00E+14 4.11E+14 4.29E

Kr-85m 6.51E+15 6.51E+15 6.44E+15 5.48E+15 5.44E+15 5.33E+15 5.22E+15 5.11E+15 4.63E+15 4.10E+15 4.40E

Kr-85 2.57E+14 2.75E+14 2.85E+14 4.14E+14 4.22E+14 4.40E+14 4.51E+14 4.63E+14 5.11E+14 5.18E+14 5.29E

Kr-87 1.32E+16 1.32E+16 1.30E+16 1.10E+16 1.09E+16 1.07E+16 1.04E+16 1.02E+16 9.18E+15 8.95E+15 8.70E

Kr-88 1.85E+16 1.84E+16 1.82E+16 1.52E+16 1.51E+16 1.48E+16 1.44E+16 1.41E+16 1.26E+16 1.22E+16 1.19E

Rb-86 2.33E+13 2.51E+13 2.63E+13 4.96E+13 5.14E+13 5.40E+13 5.74E+13 6.03E+13 7.73E+13 8.07E+13 8.58E

Sr-89 2.58E+16 2.54E+16 2.52E+16 2.11E+16 2.08E+16 2.02E+16 1.98E+16 1.94E+16 1.72E+16 1.68E+16 1.62E

Sr-90 2.25E+15 2.42E+15 2.50E+15 3.77E+15 3.85E+15 4.03E+15 4.14E+15 4.26E+15 4.77E+15 4.88E+15 5.00E

Sr-91 3.17E+16 3.17E+16 3.13E+16 2.66E+16 2.65E+16 2.60E+16 2.55E+16 2.48E+16 2.26E+16 2.21E+16 2.15E

Sr-92 3.29E+16 3.28E+16 3.25E+16 2.83E+16 2.82E+16 2.78E+16 2.73E+16 2.67E+16 2.47E+16 2.42E+16 2.37E

Y-90 2.34E+15 2.50E+15 2.60E+15 3.90E+15 3.98E+15 4.16E+15 4.31E+15 4.42E+15 4.98E+15 5.09E+15 5.24E

Y-91 3.25E+16 3.21E+16 3.19E+16 2.73E+16 2.71E+16 2.64E+16 2.59E+16 2.55E+16 2.31E+16 2.26E+16 2.20E

Y-92 3.31E+16 3.31E+16 3.28E+16 2.85E+16 2.84E+16 2.79E+16 2.75E+16 2.69E+16 2.49E+16 2.44E+16 2.39E

Y-93 2.45E+16 2.45E+16 2.43E+16 2.17E+16 2.16E+16 2.14E+16 2.11E+16 2.07E+16 1.95E+16 1.92E+16 1.89E

Zr-95 4.12E+16 4.08E+16 4.08E+16 3.80E+16 3.80E+16 3.75E+16 3.73E+16 3.70E+16 3.56E+16 3.53E+16 3.49E

Zr-97 3.83E+16 3.84E+16 3.83E+16 3.71E+16 3.71E+16 3.71E+16 3.69E+16 3.66E+16 3.62E+16 3.60E+16 3.59E

Nb-95 4.16E+16 4.12E+16 4.08E+16 3.84E+16 3.80E+16 3.77E+16 3.75E+16 3.72E+16 3.58E+16 3.55E+16 3.51E

Mo-99 4.14E+16 4.18E+16 4.18E+16 4.11E+16 4.11E+16 4.11E+16 4.11E+16 4.07E+16 4.07E+16 4.03E+16 4.03E

Tc-99m 3.67E+16 3.70E+16 3.69E+16 3.63E+16 3.64E+16 3.66E+16 3.64E+16 3.62E+16 3.61E+16 3.60E+10 3.60E

Ru-103 3.02E+16 3.05E+16 3.07E+16 3.43E+16 3.46E+16 3.51E+16 3.56E+16 3.59E+16 3.77E+16 3.81E+16 3.85E

Ru-105 1.77E+16 1.82E+16 1.84E+16 2.32E+16 2.35E+16 2.44E+16 2.48E+16 2.52E+16 2.78E+16 2.82E+16 2.90E

Ru-106 8.36E+15 9.03E+15 9.36E+15 1.45E+16 1.48E+16 1.57E+16 1.62E+16 1.68E+16 1.94E+16 1.99E+16 2.06E

Rh-105 1.71E+16 1.75E+16 1.77E+16 2.22E+16 2.25E+16 2.33E+16 2.36E+16 2.40E+16 2.63E+16 2.66E+16 2.73E

Sb-125 1.78E+14 1.92E+14 1.99E+14 3.05E+14 3.10E+14 3.26E+14 3.37E+14 3.47E+14 3.95E+14 4.04E+14 4.16E

Sb-127 1.55E+15 1.58E+15 1.59E+15 1.84E+15 1.86E+15 1.90E+15 1.93E+15 1.94E+15 2.07E+15 2.08E+15 2.12E

Te-127m 2.57E+14 2.64E+14 2.68E+14 3.13E+14 3.15E+14 3.23E+14 3.28E+14 3.32E+14 3.53E+14 3.57E+14 3.63E
A-18

Table A-5. (contd)

Nuclide

Peak Rod Burnup, GWd/MTU

22 24 25 42 43 46 48 50 60 62 65 

Te-127 1.53E+15 1.56E+15 1.58E+15 1.82E+15 1.84E+15 1.89E+15 1.91E+15 1.93E+15 2.05E+15 2.07E+15 2.11E

Te-129m 1.24E+15 1.24E+15 1.25E+15 1.34E+15 1.34E+15 1.35E+15 1.36E+15 1.37E+15 1.41E+15 1.41E+15 1.42E

Te-129 6.14E+15 6.22E+15 6.25E+15 6.59E+15 6.62E+15 6.70E+15 6.73E+15 6.73E+15 6.92E+15 6.92E+15 6.99E

Te-131mn 3.81E+15 3.85E+15 3.89E+15 4.26E+15 4.26E+15 4.37E+15 4.37E+15 4.40E+15 4.55E+15 4.59E+15 4.63E

Te-132 3.11E+16 3.13E+16 3.13E+16 3.12E+16 3.13E+16 3.14E+16 3.14E+16 3.12E+16 3.13E+16 3.12E+16 3.13E

I-131 2.15E+16 2.14E+16 2.15E+16 2.18E+16 2.18E+16 2.18E+16 2.18E+16 2.18E+16 2.19E+16 2.19E+16 2.19E

I-132 3.15E+16 3.17E+16 3.17E+16 3.17E+16 3.19E+16 3.20E+16 3.20E+16 3.18E+16 3.20E+16 3.19E+16 3.19E

I-133 4.59E+16 4.59E+16 4.59E+16 4.48E+16 4.51E+16 4.51E+16 4.51E+16 4.48E+16 4.44E+16 4.40E+16 4.40E

I-134 5.14E+16 5.14E+16 5.14E+16 4.96E+16 5.00E+16 5.00E+16 4.96E+16 4.92E+16 4.85E+16 4.81E+16 4.81E

I-135 4.33E+16 4.37E+16 4.33E+16 4.29E+16 4.29E+18 4.29E+16 4.29E+16 4.26E+16 4.26E+16 4.22E+16 4.26E

Xe-133 4.59E+16 4.40E+16 4.44E+16 4.51E+16 4.51E+16 4.33E+16 4.37E+16 4.48E+16 4.37E+16 4.44E+16 4.44E

Xc-135 2.21E+16 2.12E+16 2.11E+16 1.87E+16 1.86E+16 1.78E+16 1.74E+16 1.71E+16 1.58E+16 1.55E+16 1.52E

Cs-134 2.13E+15 2.44E+15 2.60E+15 5.99E+15 6.22E+15 6.88E+15 7.29E+15 7.77E+15 1.01E+16 1.07E+16 1.14E

Cs-136 9.58E+14 1.03E+15 1.07E+15 1.92E+15 1.98E+15 2.10E+15 2.22E+15 2.33E+15 2.95E+15 3.06E+15 3.26E

Cs-137 2.67E+15 2.90E+15 3.02E+15 4.96E+15 5.07E+15 5.40E+15 5.59E+15 5.81E+15 6.88E+15 7.07E+15 7.40E

Ba-139 4.14E+16 4.14E+16 4.14E+16 3.96E+16 3.96E+16 3.96E+16 3.96E+16 3.92E+16 3.85E+16 3.81E+16 3.81E

Ba-140 4.11E+16 4.14E+16 4.14E+16 3.96E+16 3.96E+16 3.96E+16 3.96E+16 3.92E+16 3.85E+16 3.85E+16 3.81E

La-140 4.18E+16 4.40E+16 4.29E+16 4.11E+16 4.11E+16 4.33E+16 4.22E+16 4.07E+16 4.11E+16 4.03E+16 4.07E

La-141 3.77E+16 3.81E+16 3.77E+16 3.62E+16 3.62E+16 3.62E+16 3.60E+16 3.56E+16 3.50E+16 3.47E+16 3.46E

La-142 3.74E+16 3.74E+16 3.74E+16 3.54E+16 3.53E+16 3.53E+16 3.51E+16 3.47E+16 3.39E+16 3.36E+16 3.34E

Ce-141 3.81E+16 3.81E+16 3.81E+16 3.65E+16 3.65E+16 3.63E+16 3.62E+16 3.60E+16 3.52E+16 3.50E+16 3.49E

Ce-143 3.64E+16 3.65E+16 3.63E+16 3.39E+16 3.39E+16 3.37E+16 3.34E+16 3.30E+16 3.20E+16 3.16E+16 3.14E

Ce-144 3.14E+16 3.18E+16 3.19E+16 3.16E+16 3.15E+16 3.12E+16 3.10E+16 3.08E+16 2.97E+16 2.95E+16 2.91E

Pr-143 3.58E+16 3.53E+16 3.52E+16 3.33E+16 3.31E+16 3.26E+16 3.24E+16 3.24E+16 3.11E+16 3.11E+16 3.07E

Nd-147 1.51E+16 1.51E+16 1.51E+16 1.47E+16 1.48E+16 1.48E+16 1.47E+16 1.47E+16 1.46E+16 1.45E+16 1.45E

Np-239 3.49E+17 3.50E+17 3.53E+17 4.14E+17 4.18E+17 4.22E+17 4.33E+17 4.40E+17 4.81E+17 4.88E+17 5.00E

Pu-238 3.10E+13 3.85E+13 4.26E+13 1.51E+14 1.59E+14 1.86E+14 2.05E+14 2.25E+14 3.31E+14 3.53E+14 3.85E

Pu-239 1.15E+13 1.19E+13 1.21E+13 1.34E+13 1.34E+13 1.34E+13 1.34E+13 1.34E+13 1.31E+13 1.31E+13 1.30E

Pu-240 9.18E+12 1.04E+13 1.10E+13 1.97E+13 2.01E+13 2.14E+13 2.23E+13 2.32E+13 2.65E+13 2.69E+13 2.76E
A-19

Table A-5. (contd)

Pu-241 2.81E+15 3.04E+15 3.16E+15 5.44E+15 5.59E+15 5.85E+15 5.92E+15 6.03E+15 6.70E+15 6.81E+15 6.96E

Am-241 2.94E+12 3.66E+12 4.03E+12 9.62E+12 9.95E+12 1.09E+13 1.14E+13 1.19E+13 1.33E+13 1.34E+13 1.36E

Am-242 8.07E+14 9.88E+14 1.09E+15 3.06E+15 3.20E+15 3.56E+15 3.81E+15 4.03E+15 5.03E+15 5.18E+15 5.40E

Cm-242 3.63E+14 4.77E+14 5.40E+14 1.97E+15 2.06E+15 2.36E+15 2.56E+15 2.76E+15 3.65E+15 3.81E+15 4.00E

Cm-244 4.88E+12 7.55E+12 9.25E+12 1.09E+14 1.21E+14 1.62E+14 1.94E+14 2.30E+14 4.85E+14 5.51E+14 6.62E

APPENDIX B

–

DETAILED FLOW AND TRANSPORT MODELING RESULTS

B-1

APPENDIX B

DETAILED FLOW AND TRANSPORT MODELING RESULTS

B.1 Lake Transport Results

B.1.1 Lake Short-Term Simulations

 

Figure B-1. Simulated lake aqueous-only 144Ce activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

 

Figure B-2. Simulated lake aqueous-only 134Cs activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 
B-2

 

Figure B-3. Simulated lake aqueous-only 137Cs activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

Figure B-4. Simulated lake aqueous-only 3H activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

3 

Figure B-5. Simulated lake aqueous-only 131I activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 
B-3

 

Figure B-6. Simulated lake aqueous-only 106Ru activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

 

Figure B-7. Simulated lake aqueous-only 125Sb activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

 

Figure B-8. Simulated lake aqueous-only 90Sr activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 
B-4

B.1.2 One Year 

 

Figure B-9. Simulated lake aqueous-only 134Cs activity over a full year at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-10. Simulated lake aqueous-only 137Cs activity over a full year at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-5

 

Figure B-11. Simulated lake aqueous-only 131I activity over a full year at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-12. Simulated lake aqueous-only 90Sr activity over a full year at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-6

B.1.3 Sensitivity

B.1.3.1 Increased Mixing Coefficient

 

Figure B-13. Comparision of lake aqueous-only 137Cs activity concentrations from the 

one-year and increased mixing coefficient simulations at locations along 

the same (left) and opposite (right) shore as the release

B.2 Small River

B.2.1 Aqueous Only

 

Figure B-14. Simulated small river aqueous-only 144Ce activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-7

 

Figure B-15. Simulated small river aqueous-only 134Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-16. Simulated small river aqueous-only 137Cs activity over time at several

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-17. Simulated small river aqueous-only 3H activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-8

 

Figure B-18. Simulated small river aqueous-only 131I activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-19. Simulated small river aqueous-only 106Ru activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-20. Simulated small river aqueous-only 125Sb activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-9

 

Figure B-21. Simulated small river aqueous-only 90Sr activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-10

B.2.2 Small River with Sediment

Figure B-22. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

144Ce activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-11

Figure B-23. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

134Cs activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-12

 

Figure B-24. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

137Cs activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-13

Figure B-25. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 131I 

activity over time at several locations along the same shore as the release 

(left) and the opposite shore (right). 
B-14

Figure B-26. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

106Ru activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-15

Figure B-27. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

125Sb activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-16

Figure B-28. Simulated small river aqueous (top), sorbed (middle), and total (bottom) 

90Sr activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-17

 

Figure B-29. Simulated small river bed-sorbed 144Ce activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-30. Simulated small river bed-sorbed 134Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-31. Simulated small river bed-sorbed 137Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-18

 

Figure B-32. Simulated small river bed-sorbed 131I activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

 

Figure B-33. Simulated small river bed-sorbed 106Ru activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-34. Simulated small river bed-sorbed 125Sb activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-19

 

Figure B-35. Simulated small river bed-sorbed 90Sr activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 
B-20

B.2.3 One Year

Figure B-36. Small river total suspended (top), particulate (middle), and total (bottom) 

134Cs activity over time at several locations on the same (left) and opposite 

(right) shore of the release location.
B-21

Figure B-37. Small river total suspended (top), particulate (middle), and total (bottom) 

137Cs activity over time at several locations on the same (left) and opposite 

(right) shore of the release location.
B-22

Figure B-38. Small river total suspended (top), particulate (middle), and total (bottom) 

131I activity over time at several locations on the same (left) and opposite 

(right) of the release location.
B-23

Figure B-39. Small river total suspended (top), particulate (middle), and total (bottom) 

90Sr activity over time at several locations on the same (left) and opposite 

(right) of the release location.
B-24

 

Figure B-40. Small river bed-sorbed 134Cs activity over time at several locations on the 

same (left) and opposite (right) shore of the release location.

 

Figure B-41. Small river bed-sorbed 137Cs activity over time at several locations on the 

same (left) and opposite (right) shore of the release location.

 

Figure B-42. Small river bed-sorbed 131I activity over time at several locations on the 

same (left) and opposite (right) of the release location.
B-25

 

Figure B-43. Small river bed-sorbed 90Sr activity over time at several locations on the 

same (left) and opposite (right) of the release location.

B.3 Large River 

B.3.1 Large River Aqueous Only (Short-term)

Figure B-44. Simulated large river aqueous-only 144Ce activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-26

 

Figure B-45. Simulated large river aqueous-only 134Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-46. Simulated large river aqueous-only 137Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-47. Simulated large river aqueous-only 3

H activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-27

 

Figure B-48. Simulated large river aqueous-only 131I activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-49. Simulated large river aqueous-only 106Ru activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

Figure B-50. Simulated large river aqueous-only 125Sb activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-28

 

Figure B-51. Simulated large river aqueous-only 90Sr activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-29

B.3.2 Large River with Sediment (Short-term)

Figure B-52. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 

144Ce activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-30

Figure B-53. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 

134Cs activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-31

Figure B-54. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 

137Cs activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-32

Figure B-55. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 131I 

activity over time at several locations along the same shore as the release 

(left) and the opposite shore (right). 
B-33

Figure B-56. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 

106Ru activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-34

Figure B-57. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 

125Sb activity over time at several locations along the same shore as the 

release (left) and the opposite shore (right). 
B-35

Figure B-58. Simulated large river aqueous (top), sorbed (middle), and total (bottom) 90Sr 

activity over time at several locations along the same shore as the release 

(left) and the opposite shore (right). 
B-36

 

Figure B-59. Simulated large river bed-sorbed 144Ce activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-60. Simulated large river bed-sorbed 134Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

Figure B-61. Simulated large river bed-sorbed 137Cs activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-37

Figure B-62. Simulated large river bed-sorbed 131I activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 

Figure B-63. Simulated large river bed-sorbed 106Ru activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 

 

Figure B-64. Simulated large river bed-sorbed 125Sb activity over time at several 

locations along the same shore as the release (left) and the opposite shore 

(right). 
B-38

 

Figure B-65. Simulated large river bed-sorbed 90Sr activity over time at several locations 

along the same shore as the release (left) and the opposite shore (right). 
B-39

B.3.3 One-year Extended Domain

Figure B-66. Simulated extended large river aqueous (top), sorbed (middle), and total 

(bottom) 134Cs activity over a full year at several locations along the same 

shore as the release (left) and the opposite shore (right). 
B-40

Figure B-67. Simulated extended large river aqueous (top), sorbed (middle), and total 

(bottom) 137Cs activity over a full year at several locations along the same 

shore as the release (left) and the opposite shore (right). 
B-41

 

Figure B-68. Simulated extended large river aqueous (top), sorbed (middle), and total 

(bottom) 131I activity over a full year at several locations along the same 

shore as the release (left) and the opposite shore (right). 
B-42

Figure B-69. Simulated extended large river aqueous (top), sorbed (middle), and total 

(bottom) 90Sr activity over a full year at several locations along the same 

shore as the release (left) and the opposite shore (right). 
B-43

 

Figure B-70. Simulated extended large river bed-sorbed 134Cs activity over a full year at 

several locations along the same shore as the release (left) and the 

opposite shore (right). 

Figure B-71. Simulated extended large river bed-sorbed 137Cs activity over a full year at 

several locations along the same shore as the release (left) and the 

opposite shore (right). 

Figure B-72. Simulated extended large river bed-sorbed 131I activity over a full year at 

several locations along the same shore as the release (left) and the 

opposite shore (right). 
B-44

 

Figure B-73. Simulated extended large river bed-sorbed 90Sr activity over a full year at 

several locations along the same shore as the release (left) and the 

opposite shore (right). 

B.3.3.1 Unimpounded

 

Figure B-74. Simulated unimpounded large river aqueous (top left), sorbed (top right), 

and total (bottom) 134Cs activity over a full year at several locations. 
B-45

Figure B-75. Simulated unimpounded large river bed-sorbed 134Cs activity over a full 

year at several locations. 

 

Figure B-76. Simulated unimpounded large river aqueous (top left), sorbed (top right), 

and total (bottom) 137Cs activity over a full year at several locations. 
B-46

Figure B-77. Simulated unimpounded large river bed-sorbed 137Cs activity over a full 

year at several locations. 

 

Figure B-78. Simulated unimpounded large river aqueous (top left), sorbed (top right), 

and total (bottom) 131I activity over a full year at several locations. 
B-47

Figure B-79. Simulated unimpounded large river bed-sorbed 131I activity over a full year 

at several locations. 

 

Figure B-80. Simulated unimpounded large river aqueous (top left), sorbed (top right), 

and total (bottom) 90Sr activity over a full year at several locations along the 

same shore as the release (left) and the opposite shore (right). 
B-48

Figure B-81. Simulated unimpounded large river bed-sorbed 90Sr activity over a full year 

at several locations. 

B.3.3.2 Impounded

 

Figure B-82. Simulated impounded large river aqueous (top left), sorbed (top right), and 

total (bottom) 134Cs activity over a full year at several locations along the 

same shore as the release (left) and the opposite shore (right). 
B-49

Figure B-83. Simulated impounded large river bed-sorbed 134Cs activity over a full year 

at several locations. 

 

Figure B-84. Simulated impounded large river aqueous (top left), sorbed (top right), and 

total (bottom) 137Cs activity over a full year at several locations. 
B-50

Figure B-85. Simulated impounded large river bed-sorbed 137Cs activity over a full year 

at several locations. 

 

Figure B-86. Simulated impounded large river aqueous (top left), sorbed (top right), and 

total (bottom) 131I activity over a full year at several locations. 
B-51

Figure B-87. Simulated impounded large river bed-sorbed 131I activity over a full year at 

several locations. 

 

Figure B-88. Simulated impounded large river aqueous (top left), sorbed (top right), and 

total (bottom) 90Sr activity over a full year at several locations. 
B-52

Figure B-89. Simulated impounded large river bed-sorbed 90Sr activity over a full year at 

several locations. 

B.3.4 Sensitivity Tests

B.3.4.1 Decreased Radionuclide Release

 

Figure B-90. Comparison of decreased release and original simulated large river 137Cs

activity concentrations at 10 (left) and 50 (right) miles from the release. 
B-53

Figure B-91. Simulated decreased release large river aqueous (top), sorbed (middle), 

and total (bottom) 137Cs activity over a full year at several locations along 

the same shore as the release (left) and the opposite shore (right). 
B-54

 

Figure B-92. Simulated decreased release large river bed-sorbed 137Cs activity over a full 

year at several locations along the same shore as the release (left) and the 

opposite shore (right). 

 

Figure B-93. Comparison of decreased release and original simulated 131I activity 

concentrations at 10 (left) and 50 (right) miles from the release. 
B-55

Figure B-94. Simulated decreased release large river aqueous (top), sorbed (middle), 

and total (bottom) 131I activity over a full year at several locations along the 

same shore as the release (left) and the opposite shore (right). 
B-56

 

Figure B-95. Simulated decreased release large river bed-sorbed 131I activity over a full 

year at several locations along the same shore as the release (left) and the 

opposite shore (right). 

B.3.4.2 Increased Bed Depth

Figure B-96. Comparison of increased bed and original simulated 137Cs activity 

concentrations at 10 (left) and 50 (right) miles from the release

Figure B-97. Comparison of increased bed and original simulated 137Cs activity 

concentrations in the bed at 10 (left) and 50 (right) miles from the release.
B-57

Figure B-98. Simulated increased bed depth large river aqueous (top), sorbed (middle), 

and total (bottom) 137Cs activity over a full year at several locations along 

the same shore as the release (left) and the opposite shore (right). 
B-58

Figure B-99. Simulated increased bed depth large river bed-sorbed 137Cs activity over a 

full year at several locations along the same shore as the release (left) and 

the opposite shore (right). 

Figure B-100. Comparison of increased bed and original simulated 131I activity 

concentrations at 10 (left) and 50 (right) miles from the release
B-59

Figure B-101. Simulated increased bed depth large river aqueous (top), sorbed (middle), 

and total (bottom) 131I activity over a full year at several locations along the 

same shore as the release (left) and the opposite shore (right). 
B-60

 

Figure B-102. Simulated increased bed depth large river bed-sorbed 131I activity over a full 

year at several locations along the same shore as the release (left) and the 

opposite shore (right). 

B.3.4.3 Increased Sediment Load

Figure B-103. Comparison of water column activity concentration from the original oneyear large river and increased sediment load simulation. Sorbed phase 

(top) and total (bottom) 137Cs activity concentrations at 10 and 50 (left) 

and 80 and 103 (right) below the release location are shown.
B-61

Figure B-104. Comparison of bed activity from the original one-year large river and 

increased sediment load simulation at 10 and 50 (left) and 80 and 103 

(right) below the release location are shown.
B-62

Figure B-105. Simulated increased sediment load large river aqueous (top), sorbed 

(middle), and total (bottom) 137Cs activity over a full year at several 

locations along the same shore as the release (left) and the opposite 

shore (right). 
B-63

 

Figure B-106. Simulated increased sediment load large river bed-sorbed 137Cs activity 

over a full year at several locations along the same shore as the release 

(left) and the opposite shore (right).





NUREG/CR-7231 Modeling of Radionuclide Transport in Freshwater Systems Associated 

with Nuclear Power Plants