SANDIA REPORT

SAND 2013-9684

Unlimited Release

Printed November 2013

A Methodology to Quantify the Release 

of Spent Nuclear Fuel from Dry Casks 

during Security-Related Scenarios 

S.G. Durbin and R.E. Luna

Prepared by

Sandia National Laboratories

Albuquerque, New Mexico 87185 and Livermore, California 94550

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ii

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iii

SAND2013-9684

Unlimited Release

Printed November 2013

A Methodology to Quantify the Release 

of Spent Nuclear Fuel from Dry Casks 

during Security-Related Scenarios

S.G. Durbin and R.E. Luna

Advanced Nuclear Fuel Cycle Technologies

Sandia National Laboratories

P.O. Box 5800

Albuquerque, New Mexico 87185-MS0537

Abstract

Assessing the risk to the public and the environment from a release of radioactive material 

produced by accidental or purposeful forces/environments is an important aspect of the 

regulatory process in many facets of the nuclear industry. In particular, the transport and 

storage of radioactive materials is of particular concern to the public, especially with regard to 

potential sabotage acts that might be undertaken by terror groups to cause injuries, panic, 

and/or economic consequences to a nation. For many such postulated attacks, no breach in 

the robust cask or storage module containment is expected to occur. However, there exists 

evidence that some hypothetical attack modes can penetrate and cause a release of radioactive 

material. This report is intended as an unclassified overview of the methodology for release 

estimation as well as a guide to useful resource data from unclassified sources and relevant 

analysis methods for the estimation process.
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v

TABLE OF CONTENTS

ABBREVIATIONS/DEFINITIONS.....................................................................................VII

1 INTRODUCTION............................................................................................................. 1

1.1 Background........................................................................................................................ 1

1.2 Objective ............................................................................................................................ 1

2 DETERMATION OF RELEASE FRACTION ............................................................. 3

2.1 Previous Source Term Models......................................................................................... 3

2.2 Current Source Term Model ........................................................................................... 4

2.2.1 Damage Mass (mDam)........................................................................................... 6

2.2.2 Sandia Release Fraction (RFSNL) ......................................................................... 7

2.2.3 Spent Fuel Ratio (SFR) ........................................................................................ 7

2.2.4 Enrichment Factor (EF)........................................................................................ 8

2.2.5 Release Fraction from HED (RFHED) .................................................................. 8

2.2.6 Deposition Fraction in the Cask (fDep, Cask).......................................................... 9

2.2.7 Deposition Fraction while Escaping (fDep, Esc) ..................................................... 9

2.2.8 Aerosol Size Distributions.................................................................................. 10

2.3 Model Comparisons with GRS Results......................................................................... 10

3 SUMMARY ..................................................................................................................... 12

4 REFERENCES................................................................................................................ 15

APPENDIX A EXAMPLE CALCULATION ..................................................................... 17
vi

FIGURES

Figure 2.1 Schematic showing hypothetical fuel damage in PWR 17×17 fuel assembly. .... 7

Figure 2.2 Mass of aerosols with AED < 10 μm normalized by affected mass as a function 

of energy density. ................................................................................................. 9

Figure 2.3 Aerodynamic particle size distributions from spent fuel acted on by a high 

energy device...................................................................................................... 10

TABLES

Table 2.1 Comparison of the GRS test results to the current model predictions. .............. 11

Table 3.1 Summary of model parameters........................................................................... 13
vii

ABBREVIATIONS/DEFINITIONS

AED Aerodynamic equivalent diameter

BCL

BWR

CRUD

DOE

EF

GRS

GSD

GWd/MTHM

HED

INEL

IRSN

MMD

Battelle Columbus Laboratories

Boiling water reactor

Chalk River unidentified deposit

Department of Energy

Enrichment factor

Gesellschaft für Anlagen- und Reaktorsicherheit (Translation: Society 

for Plant and Reactor Safety)

Geometric standard deviation

Gigawatt-days per metric ton of heavy metal

High energy device

Idaho National Engineering Laboratory

Institut de Radioprotection et de Sûreté Nucléaire (Translation: 

Radioprotection and Nuclear Safety Institute)

Mass median diameter

PWR Pressurized water reactor

SFR

SNF

Spent fuel ratio

Spent nuclear fuel

SNL Sandia National Laboratories
viii

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1

1 INTRODUCTION 

1.1 Background

Assessing the risk to the public and the environment from a release of radioactive material 

produced by accidental or purposeful forces/environments is an important aspect of the 

regulatory process in many facets of the nuclear industry. In particular, the transport and storage 

of radioactive materials is of particular concern to the public, especially with regard to potential 

sabotage acts that might be undertaken by terror groups to cause injuries, panic, and/or economic 

consequences to a nation. For many such postulated attacks, no breach in the robust cask or 

storage module containment is expected to occur. However, there exists evidence that some 

hypothetical attack modes can penetrate and cause a release of radioactive material.

1.2 Objective

While a detailed analysis of a security scenario that causes release is classified, the evaluation 

process may be described in a generic manner that identifies the principal mathematics and 

assumptions behind the determination of a release fraction. That framework together with a 

compendium of experimental data, analyses, and analytical tools provide a useful understanding 

of potential consequences of many scenarios of concern. This report is intended as an overview 

of the methodology for release estimation as well as a guide to useful resource data from 

unclassified sources and relevant analysis methods for the estimation process.
2

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3

2 DETERMATION OF RELEASE FRACTION

This chapter presents the general methodology and terminology associated with the 

determination of release fractions from radiological casks subjected to malevolent events. 

Previous models proposed by the Department of Energy (DOE) and the Institut de 

Radioprotection et de Sûreté Nucléaire (IRSN) (Translation: Radioprotection and Nuclear Safety 

Institute) are presented along with the current model being used to determine source terms for 

security-related scenarios.

2.1 Previous Source Term Models

The DOE, in its Handbook of Airborne Release Fractions/Rates and Respirable Fractions for 

Nonreactor Nuclear Facilities, provides a general formulation for estimation of the source term 

for released airborne materials as shown below.

Source Term = MAR DR ARF RF LPF 

where

MAR = Material-at-Risk (Curies or grams)

DR = Damage Ratio

ARF = Airborne Release Fraction 

RF = Respirable Fraction of the ARF, and

LPF = Leakpath Factor

⋅ ⋅ ⋅⋅

The first four terms define the amount of respirable material created within the container where 

the material was located. Among these,

• DR relates to the damaged volume created by an attack as compared to the total volume 

of material at risk.

• ARF relates to how the energy imparted by the attack mode is converted to particles 

small enough to be airborne within the containment volume and, therefore, available for 

release should there be an escape path to the environment.

• RF is a measure of what fraction of ARF is in a size range that would make it respirable 

and thus contribute to long term radiological impacts if there is a release to the 

environment.

• LPF is intended to capture the effect of voiding a fraction of the container volume 

carrying particles to the environment, deposition within the container, and deposition that 

occurs along the path to release to the environment. The last two of which are particle 

size dependent.

Most of the content of the “Handbook” is devoted to providing values for ARF and RF for 

materials and configurations relevant to DOE’s production facilities. This handbook can be an 

important source of data for the calculations of interest here.
4

In a recent report by Loiseau, et al. from the IRSN, the same basic formulation is adopted, except 

for the LPF factor.

Source Term = MAR FDAM FSUS FRES FEXP FRED 

where

MAR = Material At Risk

FDAM = Damaged Fraction

FSUS = Fraction of material in suspension or in aerosol form

FRES = Respirable Fraction of FSUS

⋅ ⋅⋅⋅⋅

Their formulation replaces the LPF in the formulation of the “Handbook” with the last two 

factors in the multiplicative chain.

• FEXP = The fraction of the source that is expelled from the containment volume as a 

result of pressurization effects

• FRED = Reduction Factor that includes deposition processes and chemical reactions 

within the containment volume and deposition along the exit path way.

The two formulations differ only in the fact that the Loiseau formulation gives more specificity 

in the LPF than in the DOE handbook. This formulation also acknowledges the contribution of a 

pressurized gas within the container as a vehicle to force aerosols to the external environment.

By inspection it is clear that the “source term” is measured in units such as Curies or grams of a 

specific material or mixture. But frequently, the source term is non-dimensionalized using 

MAR, which might be the entire content of the volume or a discrete definable sub-part of the 

total content. A relevant example is a spent fuel cask or storage module in which the MAR 

might be the Cs-137 content of all the contained assemblies. The source term would then be 

expressed in Cs-137 curies. In that case the non-dimensional source term in the sense usually 

used would be ST = DR ARF RF LPF ⋅ ⋅⋅ , where these factors are all related to Cs-137 release.

This type of formulation has the advantage of allowing application to various initial loadings of 

the material of interest as long as the physical and chemical properties of the materials of 

concern are similar.

2.2 Current Source Term Model

The current source term model is described next. This model builds on the concepts of the DOE 

and IRSN models, but also incorporates a limited set of data from full-scale testing (Sandoval 

1983 and Lange 1994). The representation of the model presented in this report has been 

simplified in order to demonstrate the logic underlying its derivation. Concepts such as gap fines 

in the outer rim of spent fuel and spallation of Chalk River Unidentified Deposits (CRUD) are 

ignored. However, the doses derived from the source terms defined by this model are unlikely to 

be significantly different from the full model as these enhanced treatments do not affect the 

release fractions of the transuranic radioisotopes, which dominate the dose. The transuranic 

species are treated the same in both models. Also, the reader is cautioned when analyzing casks 
5

containing boiling water reactor (BWR) fuel assemblies. All of the available large scale test data 

this is incorporated into this model was collected using pressurized water reactor (PWR) fuel 

assemblies. Previous treatments of BWR casks have considered the PWR equivalent cask when 

using this model.

Like the DOE model, the source term (ST) is proportional to the amount of material that is 

damaged during the causal event (mDam). This term is expressed in the DOE and IRSN models 

as the product of MAR DR ⋅ and MAR FDAM ⋅ , respectively. However, this mass is defined as 

only the mass of affected fuel in the first cell for spent fuel applications. This limitation of the 

damaged mass is due to observations from full-scale testing conducted by Gesellschaft für 

Anlagen- und Reaktorsicherheit (GRS) (Translation: Society for Plant and Reactor Safety) 

(Lange, 1994). The amount of this material that is aerosolized in the respirable range is defined 

by two separate source terms, STPrompt and STDelayed. The respirable range is defined as particles 

smaller than 10 μm aerodynamic equivalent diameter (AED).

The prompt source term (STPrompt) defines the amount of respirable particles ejected immediately 

from the cask as a result of the action of the high energy device (HED). This quantity is 

determined by multiplying the damaged mass by the release fraction determined from the fullscale transportation cask test performed by Sandoval at Sandia National Laboratories (RFSNL) 

(Sandoval, 1983) and by the spent fuel ratio (SFR). The spent fuel ratio is defined as the amount 

of respirable aerosol generated by an assault on spent fuel divided the amount of respirable 

aerosol created by the exact same action on a surrogate material. Luna gives these values as 

RFSNL = 7.6E-4 and SFR = 3 (Luna, 1999). Finally, the enrichment factor (EF) describes the 

enhanced release of volatile radioisotopes as a result of the HED interaction. Luna’s 

interpretation of the SFR data from Battelle Columbus Laboratories (BCL) (Schmidt, 1982) and 

Idaho National Engineering Laboratory (INEL) (Alvarez, 1982) gives EF = 5 (Luna, 1999). 

Discussions about these and other parameters in the model are presented in more detail in the 

following sections.

The delayed source term (STDelayed) gives the amount of respirable particles that are transported 

by the gas inside the cask and the fuel itself. This term assumes the aerosol is well mixed with 

the internal gas. The release fraction (RFHED) used to define this source term comes from 

examination of the work of Jardine, Molecke, and Alvarez in which they measured the amount of 

respirable aerosol that is generated when fracturing various brittle materials as a function of 

impact energy. Two deposition factors are applied to further modify this quantity. The first, 

Dep, Cask f = 0.7 , describes the amount of aerosols that deposit within the cask. The second 

fraction, Dep, Esc f = 0.4, gives the amount of aerosols that deposit in the leak path during 

blowdown of the cask (Sprung, 2000). Finally, the last term in the equation defines the fraction 

of the respirable aerosol that will be swept from the cask by the internal gas. Note that this 

quantity approaches a value of 1 as the total volume of gas in the cask at STP becomes 

significantly larger than the cask free volume. To be clear, the cask free volume is defined as the 

volume of the empty cask interior minus the volume occupied by the fuel assemblies and support 

structures.
6

( ) ( )

( ) ( ) ( ) ( ) ( )

Prompt Dam Dam SNL

Free

Delayed Dam Dam HED SNL Dep, Cask Dep, Esc

Free Cask Rods

ST = m or A RF SFR EF , Note: Mass or activity are acceptable to define the source term

V ST = m or A SFR EF RF - RF 1 - f 1 - f 1 - 

V +V +V

⋅ ⋅⋅

 ⋅⋅⋅ ⋅ ⋅ ⋅

Tot Prompt Delayed

Dam

Dam

ST = ST + ST

where

m = mass of damaged fuel in first cell that is aerosolized in the respirable range

A = activity of damaged fuel in first cell that is aerosolized in the respir

    

Spent Fuel 

Surrogate 

Tot

able range

RF

SFR = spent fuel ratio = , Aerosols AED < 10 μm RF

EF = enrichment, or enhancement, factor for volatile radioisotopes (e.g. Cs-137)

ST = total amount of respirable aer

Prompt

Delayed

SNL

osols released from the container

ST = respirable fraction of aerosols that are promptly released

ST = respirable fraction of aerosols that swept out of the container by gas blowdown

RF =

HED

Dep, Cask

Dep

 respirable fraction of aerosols measured in the SNL full-scale test

RF = respirable fraction of aerosols generated by the HED

f = fraction of respirable aerosol deposited within the cask

f

( )

, Esc

Free

He He Free

= fraction of respirable aerosol deposited while escaping

V = cask free volume Physical free volume of gas defined within the cask

V = "excess" volume of helium backfill gas at STP V = V ⋅ o i

i o

o o

i

i

Rods

T P - 1

T P

STP = standard temperature and pressure, T and P

T = initial cask gas temperature

P = initial cask gas pressure

V = volume of plenum and decay product gase

            ⋅    

       

s from damaged fuel pins at STP

2.2.1 Damage Mass (mDam)

The action of an HED penetrating into radioactive material causes some characteristic volume of 

damage. This volume then translates to a mass of damaged material. For the example of spent 

nuclear fuel, the simplest way to calculate the damaged mass from the volume of damage is to 

assume the fuel exists in a homogenous state. Essentially, the mass or Curie content of the entire 

assembly for any particular radionuclide is assumed to exist in equal measure throughout the 

volume of the assembly where fuel exists, i.e., the assembly footprint times the length of fuel. 

Figure 2.1 shows the application of this concept to a typical 17×17 PWR fuel assembly. Note 

that the fuel pins are shown discreetly in the figure, but are assumed to be spread homogenously 

throughout the volume of the fuel assembly in the expression for mDam. In the example given in 

the figure inset, the mass of uranium from a typical, fresh fuel assembly is determined for a hole 

with a diameter of 3 cm and a depth of 4 cm. This principal can also be used for damage 

volumes other than cylinders as well as for determining Curies of release rather than mass.
7

Figure 2.1 Schematic showing hypothetical fuel damage in PWR 17×17 fuel assembly.

2.2.2 Sandia Release Fraction (RFSNL)

A test series was conducted in the early 1980’s comprised of three tests, two quarter-scale and 

one full-scale (Sandoval, 1983). The full-scale test involved an obsolete, single assembly spent 

fuel cask that was attacked using a relatively large HED. This HED device fully penetrated one 

wall and the assembly but did not fully penetrate the second wall. The cask was loaded with a 

single, unpressurized 15×15 PWR fuel assembly using surrogate DUO2 pellets in Zircaloy 

cladding. The cask was placed inside a tank that was sealed after the HED detonation to 

facilitate collection of aerosols produced by the attack. The amount of respirable aerosol 

collected amounted to 3 grams, which was about 7.6E-4 of the mass of DUO2 within the hole in 

the spent fuel assembly produced by the action of the HED. 

The quarter-scale test mimicked the dimensions of the full scale test with one exception: the fuel 

assembly was composed of 25 fuel rods that were shorter versions of those used for the full scale 

test. Attempts were made to scale the HED, but the resulting damage to the scaled cask and 

assembly was slightly greater than in the full scale test in that both walls of the cask were 

penetrated. The amount of respirable material released to the containment tank was 

approximately six times that for the full scale test relative to the mass of DUO2 within the hole 

produced by the HED. This has been taken to mean that a through hole minimizes the amount of 

material trapped within the cask when the fast moving gas and particle cloud flows right through 

the cask.

2.2.3 Spent Fuel Ratio (SFR)

Spent fuel is highly fractured and is affected by neutron bombardment as well as growth and 

decay of fission products over time. Although spent fuel is mostly UO2, the DUO2 aerosol data 

from SNL, INEL, and BCL experiments must be scaled in order to scale to the results expected 

from spent fuel. Note that the DUO2 surrogate material in these tests was constructed of 

A A

Section A-A

17×17 PWR

Fuel Damage

21 cm

21 cm

( ) ( )

( )

( )

Dam 2 Fuel

2

Dam

Damage volume Inventory = Inventory mass or activity

Outer dimension Fuel Length

e.g., Assume a penetration creates a hole 3 cm in diameter with a depth of 4 cm

0.25 π 0.03 m 0.04 m

m = 

0.21 m

⋅ ⋅

⋅⋅ ⋅

2 460 kg U = 8.0E-2 kg U

3.7 m ⋅ ⋅
8

unbroken pellets, further necessitating the use of a correcting factor. A factor referred to as the 

Spent Fuel Ratio (SFR) was developed in order to link results for spent fuel and DUO2

surrogates. Values for SFR that were considered by Sandoval for use in his source term report 

(Sandoval, 1982) ranged from about 0.4 to 6.

Using data from INEL (Alvarez, 1982), BCL (Schmidt, 1982), and Kraftwerk Union (Ruhmann, 

1985) estimates of SFR were developed (Luna, 1999 and Luna, 2004). These reviews of 

previously available data suggest that the value SFR is approximately 3 but had a possible range 

of 1 to 12. Luna postulates that a SFR smaller than unity is implausible given the highly 

fractured condition of spent fuel compared to the relatively solid DUO2 surrogate pellets.

2.2.4 Enrichment Factor (EF)

Certain radioactive fission products, primarily Cs-134 and Cs-137, may volatilize at 

temperatures readily achieved by interaction with a HED. The use of an enrichment factor 

attempts to account for this phenomenon. Enrichment factors are reported in both the SFR 

reports by BCL (Schmidt, 1982) and INEL (Alvarez, 1982). These factors appear to be size 

dependent and range from EF ≈ 1 to 11 for particles AED > 4 μm and < 0.5 μm, respectively. 

An intermediate value of EF = 5 was adopted for the Yucca Mountain evaluation and is accepted 

for this report as well (Luna, 1999).

2.2.5 Release Fraction from HED (RFHED)

The amount and size distribution of the particles produced by impacts delivered to brittle 

materials have been the subject of several experimental programs related to nuclear fuel and 

nuclear waste disposal forms. A primary study was performed at Argonne National Laboratory 

(Jardine, 1982). For these experiments, a single cylindrical sample was placed between two 

hardened steel plates inside a sealed sampling chamber. Each specimen received a dynamic 

impact by dropping a mass from a predetermined height. The resulting particulate was diameterclassified to produce a size distribution expressed in log-normal terms with a mass median 

diameter (MMD) and a geometric standard deviation (GSD). Over a wide variety of brittle 

materials (glasses, ceramics, rock, cements) with a factor of 2 to 3 in material density, the 

fraction of the total pellet mass in particles smaller than 10 μm AED was directly related to the 

energy density (J/cc).

Another study of particular interest is the work conducted at Sandia National Laboratories to reexamine the spent fuel ratio (Molecke, 2006). Although no tests were conducted using actual 

spent fuel, a large number of tests were performed using surrogates, CeO2 and DUO2, to 

measure the mass fraction of respirable particles produced from interaction with HED’s. These 

results represent the largest database most relevant to the energy densities of interest. Finally, a 

small number of results are available from the original SFR determination efforts (Alvarez, 

1982).

All these data are plotted in Figure 2.2. A power-law fit was applied to the data (black line). A 

large amount of scatter is evident about the curve fit. An upper and lower confidence interval 

were defined by adding and subtracting, respectively, two times the standard error of the line to 

the curve fit constant. The hashed red portion in the upper right of the plot shows the region of 

interest for HED assault scenarios. Previous analysis of this data by Luna indicated that 5% of 

the affected, or damaged, mass would be in the respirable range. As shown on this plot, this 
9

estimate is still valid, but any value of about 0.7 to 13% is also possible. Given that no observed 

respirable percentage in this dataset exceeded 5%, the estimate of 5% is maintained for the 

remainder of this report.

Figure 2.2 Mass of aerosols with AED < 10 μm normalized by affected mass as a function of energy 

density.

2.2.6 Deposition Fraction in the Cask (fDep, Cask)

In order to complete the model empirically, an estimate of the amount of respirable aerosol 

deposited in the cask was needed. Because this is an empirical model the fraction deposited was 

varied between 0 and 1 to determine the deposition fraction that optimized the prediction of the 

GRS full-scale, SNL full-scale, and SNL quarter-scale results.

For a 5% respirable generation (RFHED) from the initial energy deposition, the cask deposition 

fraction needed to be approximately 0.7, i.e., about 30% of the respirable aerosol originally 

created was available for release through the entrance hole in the cask. With greater or smaller 

respirable aerosol creation, the deposition fraction would have to be correspondingly larger or 

smaller in order to best match the five experiments that served as the database for determining 

fDep, Cask.

2.2.7 Deposition Fraction while Escaping (fDep, Esc)

The fraction of respirable aerosols that deposit while escaping from the cask is based on 

estimates from Figure 7.11 in NUREG/CR-6672 (Sprung, 2000). This estimation is based on the 

amount of time the aerosols for various radioactive species are resident in the cask. This 

residence time is in turn proportional to the size of the leak path. The deposition fraction 

asymptotically approaches constant values for large breaches in the cask. The value chosen for 
10

the current model treatment is equivalent to the average deposition fraction for all species with 

the exception of noble gases, or fDep, Esc = 0.4. The deposition fraction for the different species 

varies between 0.35 to 0.5.

2.2.8 Aerosol Size Distributions

When inputting the source terms into dose consequence/dispersion models, some codes allow the 

user to define aerosol sizes. Figure 2.3 shows the cumulative mass fraction as a function of AED 

for the BCL spent fuel data (Schmidt, 1982) and an aerosol distribution described by a MMD =

1.5 μm and GSD = 2.5. This choice of size parameters represents the highest possible 

percentage of the smallest aerosols based on the data and is therefore a slightly conservative 

choice for aerosol transport. An aerosol with MMD = 1.5 μm and GSD = 2.5 is recommended 

for dispersion modeling of the respirable source terms provided by this model.

Figure 2.3 Aerodynamic particle size distributions from spent fuel acted on by a high energy device.

Data reproduced from Schmidt (1982) Figure 5-4.

2.3 Model Comparisons with GRS Results

The results obtained in the GRS test series (Lange, 1994) are compared to the current model 

predictions for these test conditions are shown in Table 2.1. The model predicts the measured 

respirable aerosol to within an error of 36%. The model also tends to overestimate the source 

term. The fact that the model reasonably predicts the GRS results is no guarantee that it is a 

reliable model for general use. However, incorporation of the Sandoval data and a reasonable 

phenomenological model provides a somewhat stronger level of confidence in its use.
11

Table 2.1 Comparison of the GRS test results to the current model predictions.

Test Identifier Test (g) Model (g) Error (%)

GRS 1 1.05 1.02 2.9

GRS 2 0.962 1.31 -36

GRS 3 0.375 0.422 -13
12

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13

3 SUMMARY

The heuristic model developed to determine the source term from penetrations to dry casks 

resulting in damage to the spent fuel has been documented in this report. This model captures 

the current, best understanding of the complex physics involved with high energy devices (HED) 

acting on spent nuclear fuel. The model also makes use of the limited database available from 

large-scale testing conducted with DUO2 surrogates. Some simplifications are invoked for 

presentation purposes in this report but are not expected to significantly impact the dose 

calculated from the model given here and the full model.

Table 3.1 summarizes the model parameters. A range of possible values is also defined for each 

parameter where available from the original source materials. As evident in the table, many of 

these variables have ranges of an order of magnitude or greater. However, the best estimate 

values shown in the table have been shown capable of reproducing the releases from the GRS 

full-scale tests within 36%.

Table 3.1 Summary of model parameters.

Parameter Best Estimate Possible Range Source

RFSNL 7.6E-4 Undefined Sandoval 1983, Luna 1999

RFHED 0.05 0.007 – 0.13 Alvarez 1982, Jardine 1982, Molecke 2006

SFR 3 0.4 – 12 Alvarez 1982, Schmidt 1982, Sandoval 1983, 

Ruhmann, 1985, Luna 1999, Luna 2004

EF 5 1 – 11 Alvarez 1982, Schmidt 1982

fDep, Cask 0.7 Undefined Sandoval 1982, Lange 1994

fDep, Esc 0.4 0.35 – 0.5 Sanders 2000
14

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15

4 REFERENCES

(Alvarez, 1982) Alvarez, J. L., et al, “Waste Forms Project: Correlation Testing”, Idaho National 

Engineering Laboratory Report EGG-PR-5590, September 1982.

(DOE, 1994), “DOE Handbook: Airborne Release Fractions/Rates and Respirable Fractions for

Nonreactor Nuclear Facilities”, US Department of Energy, DOE-HDBK-3010-94, December 

1994.

(Jardine, 1982) Jardine, L. J.,et al, “Final Report of Experimental Laboratory Scale Brittle 

Fracture Studies of Glasses and Ceramics”, Argonne national Laboratory Report ANL-82-39, 

October 1982.

(Loiseau, 2009), “Assessing consequences of nuclear material; transport sabotage per use of 

armor piercing weapon”, Loiseau, O., Autrusson, B., and Funk, P., Packaging, Transport, 

Storage and Security of Radioactive Material, V20/3, pp 93-97, 2009.

(Lange, 1994) Lange, F., G. Pretzsch, J. Döhler, E. Hörmann, H. Busch, W. Koch, 

“Experimental Determination for UO2 Release from a Spent Fuel Transport Cask after Shaped 

Charge Attack,” Proc. INMM 35th Meeting, Naples, Florida, July 17-20, 1994.

(Luna, 1999) Luna, R.E., K. S. Neuhauser, M. G. Vigil, “Projected Source Terms for Potential 

Sabotage Events Related to Spent Fuel Shipments”, Sandia National Laboratories Report 

SAND99-0963, June 1999.

(Luna, 2004) Luna, R. E., and H. R. Yoshimura, “Aerosol Generation From Spent Fuel in High 

Energy Impact Environments: Searching for Better Definition of the Elusive SFR”, Proceedings 

of Waste Management 2004, Tucson, AZ, February 29 to March 4, 2004.

(Molecke, 2006) Molecke, M. A., et al, “Spent Fuel Sabotage Aerosol Test Program:FY 2005-06 

Testing and Aerosol Data Summary”, Sandia National Laboratories Report SAND2006-5674, 

October 2006.

(NRC, 2013) “Spent Fuel Transportation Risk Assessment”, US NRC Report NUREG-2125, 

December 2013 (expected).

(Ruhmann, 1985) Ruhmann, H., et al, “Research Programme into the Behaviour of Burnt-up 

Fuel Assemblies under strong Mechanical Impacts”, Kraftwerk Union Aktiengesellschaft Report 

R917/85/002 (BMFT KWA 5215/7), March 1985.

(Sandoval, 1983) Sandoval, R. P., et al, “An Assessment of the Safety of Spent Fuel 

Transportation in Urban Environs”, Sandia National Laboratories, Report SAND82-2365, June 

1983.

(Schmidt, 1982) Schmidt, E.W., et al, “Final Report on Shipping Cask Sabotage Source Term 

Investigation,” BMI-2095, NUREG/CR-2472, Battelle Columbus Laboratory, Columbus, OH. 

Oct. 1982.
16

(Sprung, 2000) Sprung, J. L., et al, “Re-examination of Spent Fuel Shipment Risk Estimates”, 

Sandia National Laboratories Report SAND2000-0234 (NUREG/CR-6672), March 2000.
17

APPENDIX A EXAMPLE CALCULATION

Problem Statement: A cask with 24 PWR assemblies that have an effective burnup of

45GWd/MTHM and are 10 years from offload is attacked resulting in a penetration with a 

diameter of 3 cm and a depth of 4 cm. Determine the source terms for Am-241 and Cs-137.

Given: The cask is filled with helium at Pi = 5.1 bar (5 atm) and Ti = 600 K. The free volume 

within the cask is 6 m3. Each fuel rod contains 7.5E-4 m3 of gas at STP. Assume the gas in the 

cask at the end of the depressurization is at STP, Po = 1.0 bar (1 atm) and To = 298.15 K.

The rod-to-rod pitch is approximately 1.26 cm.

The inventory of a single PWR fuel assembly 10 years from offload with a final burnup of 45 

GWd/MTHM is given in Table A.1.

Table A.1 Inventory of the most important radioisotopes for dose consequences in a single PWR fuel 

assembly at 10 years from offload and a burnup of 45 GWd/MTHM.

Americium-241:

( )

( )

( ) ( ) ( ) ( ) ( )

2

Dam Dam

2

Fuel Fuel

Prompt Dam

SNL

Fuel Fuel

A V 0.25 π 0.03 m 0.04 m

 = = = 7.2E-6, where A is activity in Curies

A V 24 0.21 m 3.7 m

ST A = RF SFR EF = 7.2E-6 7.6E-4 3 1 = 1.6E-8, where EF = 1

A A

Continued on next 

⋅⋅ ⋅

⋅ ⋅

⋅ ⋅ ⋅ ⋅ ⋅⋅

page

Radionuclide

PWR 

Inventory (Ci)

AM-241 1130

CE-144 75

CM-244 2653

CO-60 2326

CS-134 4353

CS-137 51140

EU-154 3209

KR-85 2938

PU-238 2625

PU-239 128

PU-240 128

PU-241 51220

RU-106 315

SR-90 35170

Y-90 35180
18

( ) ( ) ( ) ( ) Delayed Dam Free

HED SNL Dep, Cask Dep, Esc

Fuel Fuel Free He Rods

o i 3

He Free

i o

ST A V = SFR EF RF - RF 1 - f 1 - f 1 - 

A A V +V +V

T P 298 K 5.07 bar V = V - 1 = 6 m 1

T P 600 K 1.01 bar

  ⋅⋅⋅ ⋅ ⋅ ⋅   

         ⋅⋅ ⋅ ⋅ −                  

( ) ( )

( ) ( )

( ) ( )

3

Dam 3 3

Rods 2 2 Single Rod

3

Free

33 3

Free He Rods

Delayed

Fuel

 = 9 m

Diameter Depth 0.03 m 0.04 m

V = V = 7.5E-4 m = 5.7E-3 m

pitch 0.0126 m

V 6 m 1 - = 1 = 0.6

V +V +V 6 m 9 m + 5.7E-3 m

ST

 = 7.2E-6 3

A

 

   

⋅ ⋅ ⋅ ⋅

        −

    +

⋅ ( ) ( ) ( ) ( ) [ ]

( ) ( )

( ) ( )

Tot Prompt Delayed

Fuel Fuel

Prompt Delayed

Tot Fuel

Fuel

1 0.05 7.6E-4 1 0.7 1 0.4 0.6 = 1.1E-7

ST ST + ST

= = 1.6E-8 + 2.7E-7 = 1.3E-7

A A

ST + ST 1130 Ci ST = A = 1.3E-7 24 Assemblies = 3.5E-3 Ci

A Assembly

⋅ ⋅ − ⋅− ⋅− ⋅

  ⋅⋅⋅   

Cesium-137:

( )

( ) ( ) ( ) ( ) ( )

( ) ( )

Dam

Fuel

Prompt Dam

SNL

Fuel Fuel

Delayed Dam

HED SNL Dep, C

Fuel Fuel

A = 7.2E-6, see Americium-241 calculation for details

A

ST A = RF SFR EF = 7.2E-6 7.6E-4 3 5 = 8.2E-8, where EF = 5

A A

ST A = SFR EF RF - RF 1 - f

A A

⋅ ⋅ ⋅ ⋅ ⋅⋅

⋅⋅⋅ ⋅( ) ( )

( )

( )

Free

ask Dep, Esc

Free He Rods

3

He

3

Rods

Free

Free He Rods

V 1 - f 1 - 

V +V +V

V = 9 m see Americium-241 calculation for details

V = 5.7E-3 m see Americium-241 calculation for details

V 1 - = 0.6 see

V +V +V

  ⋅ ⋅   

 

    ( )

( ) ( ) ( ) ( ) ( ) ( ) [ ] Delayed

Fuel

 Americium-241 calculation for details

ST

 = 7.2E-6 3 5 0.05 7.6E-4 1 0.7 1 0.4 0.6 = 5.7E-7

A

Continued on next page

⋅ ⋅ ⋅ − ⋅− ⋅− ⋅
19

( ) ( )

( ) ( )

Tot Prompt Delayed

Fuel Fuel

Prompt Delayed

Tot Fuel

Fuel

ST ST + ST

= = 8.2E-8 + 5.7E-7 = 6.6E-7

A A

ST + ST 51140 Ci ST = A = 6.6E-7 24 Assemblies = 0.81 Ci

A Assembly

  ⋅ ⋅⋅   

Observations: For casks pressurized beyond Pi > 2 bar, the delayed release dominates the total 

source term. Also, the gas released from the rods is negligible compared to the helium from the 

cask for internal cask pressures greater than Pi > 2 bar.

The enrichment factor of EF = 5 is primarily for isotopes of cesium but may also be applied to 

ruthenium-106. An enrichment factor of EF = 1 is appropriate for all other species in Table A.1.

If the contribution to the dose from krypton-85 is required, the analyst should use the ratio of the 

gas volume from damaged rods to the volume of gas from a single rod scaled to the entire 

inventory of Kr-85 as shown below. Here, the volume of gas from damaged rods is more 

proportional to the mid-plane area of the damage volume normalized by the square of the pitch.

( )

( )

( )

Dam Fuel

KR85 2

Rods

KR85 2

Diameter Depth A ST = 

pitch N

0.03 m 0.04 m 2938 Ci ST = = 84 Ci, for the previous example problem

0.0126 m 264

⋅ ⋅

⋅  

⋅   

Enhanced spallation and release of cobalt-60 contained in the CRUD is ignored in this modeling 

treatment but does not significantly affect the final dose.
20

DISTRIBUTION

Sandia Internal:

6223 MS0747 Samuel Durbin (3)

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9532 MS0899 Technical Library (electronic copy)