NUREG/CR-7003 

PNNL-18490

Background and Derivation of 

ANS-5.4 Standard Fission Product 

Release Model 

Office of Nuclear Regulatory Research 
NUREG/CR-7003 

PNNL-18490 

Background and Derivation of 

ANS-5.4 Standard Fission Product 

Release Model 

Manuscript Completed: March 2009 

Date Published: January 2010 

Prepared by 

J.A. Turnbulla, C.E. Beyerb 

a

Consultant, United Kingdom 

b

Pacific Norhwest National Laboratory 

902 Battelle Boulevard 

Richland, WA 99352 

NRC Job Code N6326

Office of Nuclear Regulatory Research 
ii 
iii 

ABSTRACT 

This background report describes the technical basis for the newly proposed American Nuclear Society 

(ANS) 5.4 standard, Methods for Calculating the Fractional Release of Volatile Fission Products from 

Oxide Fuels. The proposed ANS 5.4 standard provides a methodology for determining the radioactive 

fission product releases from the fuel for use in assessing radiological consequences of postulated 

accidents that do not involve abrupt power transients. When coupled with isotopic yields, this method 

establishes the "gap activity," which is the inventory of volatile fission products that are released from the 

fuel rod if the cladding is breached. 

Best-estimate and conservative upper-bound 95/95 tolerance models for predicting the release of volatile 

radioactive isotopes of krypton, xenon, and iodine are described. The isotope that provides the most 

significant contribution to equivalent dose to individuals is generally I-131 for accidents that occur during 

in-reactor operation or shortly after reactor operation (e.g., the fuel-handling accident) due to its dose to 

the thyroid. The existing conservative upper-bound model for predicting the I-131 release has been 

shown to be very conservative in comparison to the available measured release data for I-131. The 2009 

model proposed herein predicts up to a factor of 2 lower release than the old ANS 5.4 release model. 
iv 
v 

FOREWORD 

The U.S. Nuclear Regulatory Commission (NRC) has worked collaboratively with the American Nuclear 

Society (ANS) Working Group dealing with Methods for Calculating the Fractional Release of Volatile 

Fission Products from Oxide Fuels, otherwise known as ANS 5.4, to develop a standard for modeling 

fission product releases from oxide fuels. In 1982, the Working Group published NUREG/CR-2507, a 

precursor to the current report with the same title. 

Over the intervening years, new data have become available from the Halden Reactor Project in Norway, 

which have shown that the assumptions used in the earlier standard may have been overly conservative. 

Collaborative efforts between the NRC and its contractor, Pacific Northwest National Laboratory, the 

nuclear industry, and the international community have lead to updated methods of determining the 

release of volatile fission products from the fuel. The technical basis for these revised methods is 

described in this report. 

The ANS-5.4 standard provides a method for determining the fractional inventory of radioactive fission 

products released to the fuel-cladding gap during normal operation. This information, coupled with 

isotopic yields, establishes the "gap activity" or the fission product inventory that may be released if the 

cladding is breached during a postulated accident. Regulatory application of these results is further 

described in Alternative Radiological Source Terms for Evaluating Design Basis Accidents at Nuclear 

Power Reactors (Regulatory Guide 1.183). 

The accident source term is intended to be representative of a major accident involving significant core 

damage and is typically postulated to occur in conjunction with a large loss-of-coolant accident (LOCA). 

Although the LOCA is typically the maximum credible accident, NRC staff experience in reviewing 

license applications has indicated the need to consider other accident sequences of lesser consequence but 

higher probability of occurrence. These design basis accidents (DBAs) were not intended to be actual 

event sequences, but rather, were intended to be surrogates that enable deterministic evaluation of the 

response of a facility’s engineered safety features. These accident analyses are intentionally conservative 

in order to compensate for known uncertainties in accident progression, fission product inventory, 

transport, and atmospheric dispersion. As the state of knowledge has evolved, improvements in the 

methods used are now reflected in updates such as that described in this report. 
vi 
vii 

CONTENTS

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

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

EXECUTIVE SUMMARY ......................................................................................................................... xi 

ACRONYMS AND ABBREVIATIONS ..................................................................................................xiii 

1.0 INTRODUCTION ......................................................................................................................... 1.1 

2.0 MATHEMATICAL FORMULATION OF RELEASE MODEL ................................................. 2.1 

3.0 FISSION PRODUCT RELEASE DATABASE ............................................................................ 3.1 

4.0 MODEL FITTING BASED ON HALDEN DATA....................................................................... 4.1 

4.1 Development of Model Coefficients from R/BKr85m Data.......................................................... 4.3 

4.2 Model Comparison to R/BKr85m Data ......................................................................................... 4.3 

4.3 Model Comparison to R/BI-131 Data ........................................................................................... 4.6 

4.4 Estimate of Model Uncertainties................................................................................................ 4.7 

4.5 Assumptions and Limitations................................................................................................... 4.10 

5.0 CONCLUSIONS............................................................................................................................ 5.1 

6.0 REFERENCES .............................................................................................................................. 6.1 
viii 
ix 

FIGURES 

Figure 1 Operating Range of Kr-85m and I-131 Release Data, R/B, from IFA-558, IFA-504, and 

IFA-633.................................................................................................................................. 3.2

Figure 2 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Burnup Between 0 and 

90 MWd/kgU for Each of Six Experimental Rods in IFA-558 and Four Experimental 

Rods in IFA-504; Assumes S/V1=120 cm-1 and S/V2=650 cm-1 ............................................. 4.4

Figure 3 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Burnup Between 0 and 

40 MWd/kgU for Six Rods in IFA-558 (Red) and Four Rods in IFA-504 (Blue); 

Assumes S/V1=120 cm-1 and S/V2=650 cm-1 .......................................................................... 4.4

Figure 4 Ratio of Calculated R/BKr85m to Measured R/BKr85m versus Burnup for Six Rods in IFA558 (Red), Four Rods in IFA-504 (Blue), and Three Rods in IFA-633 (Green); Assumes 

S/V1=120 cm-1 and S/V2=650 cm-1 .......................................................................................... 4.5

Figure 5 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Rod Power for Six Rods in 

IFA-558 (Diamond), Four Rods in IFA-504 (Square), and Three Rods IFA-633 

(Triangle); Assumes S/V1=120 cm-1 and S/V2=650 cm-1 ........................................................ 4.6

Figure 6 Predicted to Measured R/B for I-131 for IFA-558 and IFA-504; Assumes S/V1=120 cm-1

and S/V2=650 cm-1 .................................................................................................................. 4.6

Figure 7 Ratio of Calculated R/BI-131 to Measured R/BI-131 Versus Burnup Between 0 and 

56 MWd/kgU for Three Rods in IFA-558 (Red) and Four Rods in IFA-504 (Blue); 

Assumes S/V1=120 cm-1 and S/V2=650 cm-1 .......................................................................... 4.7

Figure 8 Ratio of Predicted R/BI-131 to Measured R/BI-131 Versus Rod Power for Three Rods in 

IFA-558 (Red) and Four Rods in IFA-504 (Blue); Assumes S/V1=120 cm-1 and S/V2=650 

cm-1......................................................................................................................................... 4.7

Figure 9 Predicted 95/95 (Assuming Non-Normal) R/BKr-85m Versus Measured R/BKr-85m from IFA504 and IFA-558 .................................................................................................................... 4.8

Figure 10 Predicted 95/95 (Assuming Non-Normal) R/BI-131 Versus Measured R/BI-131 from IFA504 and IFA-558 .................................................................................................................... 4.9

Figure 11 Comparison of New ANS 5.4 Model Upper Bound at 95/95 R/BI-131 Predictions to Old 

ANS 5.4 Model R/BI-131 Predictions for a BWR 10x10 Fuel Design ..................................... 4.9

TABLES 

Table 1 Half-Lives and Precursor Coefficients for Radioactive Nuclides .......................................... 2.3

Table 2 Values of S/V1 and S/V2 that Provide a Best-Estimate Fit of R/BKr85m Data Versus Burnup 

from Experimental Test Assemblies IFA-558 and IFA-504.................................................. 4.3

 
x 
xi 

EXECUTIVE SUMMARY 

This background report describes the technical basis for the newly proposed American Nuclear Society 

(ANS) 5.4 standard, Methods for Calculating the Fractional Release of Volatile Fission Products from 

Oxide Fuels. The proposed ANS 5.4 standard provides a methodology for determining the radioactive 

fission product releases for use in assessing radiological consequences of postulated accidents that do not 

involve abrupt power transients. When used with isotopic yields, this method will establish the "gap 

activity," which is the inventory of volatile fission products that are available for release from the fuel rod 

if the cladding was breached. The standard as developed applies to steady-state conditions and, therefore, 

should not be applied to accidents where abrupt temperature increases are experienced, resulting in a 

“burst release.” In addition, the standard does not consider escape-rate coefficients or other descriptions 

of the transport of fission products after release from the fuel rod void space. Finally, the standard 

assumes that no significant fuel oxidation will occur during the accident because fuel oxidation can 

significantly enhance the release. 

The current standard applies to the release of the volatile and gaseous fission products of primary 

significance, which are krypton, xenon, iodine, cesium, and tellurium. This background document 

primarily addresses the diffusion coefficients and other model coefficients for krypton, xenon, and iodine 

and the data used to determine these coefficients. The diffusion coefficients for the precursors (bromine 

and tellurium) that impact the release of krypton and iodine are discussed briefly along with the data upon 

which they are based. 

This report describes both best-estimate and conservative upper-bound 95/95 tolerance models for 

predicting the release of volatile radioactive isotopes of krypton, xenon, and iodine. The isotope that 

provides the largest contribution to equivalent dose to individuals is I-131 for accidents during in-reactor 

operation or shortly after reactor operation (e.g., the fuel-handling accident), due to its dose to the thyroid. 

The conservative upper-bound model for predicting the I-131 release has been shown to be very 

conservative in comparison to the available measured release data for I-131. The new proposed model 

predicts up to a factor of 2 lower release than the old ANS 5.4 release model. 
xii 
xiii 

ACRONYMS AND ABBREVIATIONS 

α precursor effect (unitless) 

λ decay constant 

a idealized sphere radius 

ANS American Nuclear Society 

B production rate 

Br bromine 

Bu pellet average burnup 

BWR boiling water reactor 

C nuclide concentration in fuel 

d atomic jump distance 

D diffusion coefficient 

DIDO nuclear research reactor, Harwell, Oxfordshire, U.K. 

F fractal scaling factor 

 fission rate 

I iodine 

i radial node 

j axial node 

jv cation vacancy jump rate 

k total number of radial nodes 

Kr krypton 

m total number of axial nodes

MOX mixed oxide 

MWd/kgU megawatt-days per kilogram of uranium 

NRC U.S. Nuclear Regulatory Commission 

P power 

p precursor nuclide 

PNNL Pacific Northwest National Laboratory 

r radius of sphere 

R/B release-to-birth ratio 

s seconds 

S/V surface-to-volume ratio 

t time 

T fuel temperature 

UO2 uranium dioxide 

V volume 

Vc cation vacancy concentration 

Xe xenon 

•

F
xiv 
1.1 

1.0 INTRODUCTION 

The American Nuclear Society (ANS) standard, Method for Calculating the Fractional Release of 

Volatile Fusion Products from Oxide Fuel, ANS 5.4,1

 provides a methodology for determining the 

radioactive fission product releases for use in assessing radiological consequences of postulated accidents 

that do not involve abrupt power transients. When used with isotopic yields, this method establishes the 

"gap activity," which is the inventory of volatile fission products that are released from the fuel rod if the 

cladding is breached. The standard as developed applies to steady-state conditions and, therefore, should 

not be applied to accidents where abrupt temperature increases are experienced, resulting in a “burst 

release.” The standard does not consider escape-rate coefficients or other descriptions of the transport of 

fission products after release from the fuel rod void space. The standard assumes that no significant fuel 

oxidation will be present during the accident because fuel oxidation can significantly enhance the release. 

The ANS 5.4 standard was first implemented in 1982 with Dr. Stan Turner as chairman of the Working 

Group ANS 5.4. The original methodology was based on the use of the Booth diffusion model1-4 and the 

coefficients to the model were determined from the measured release data of stable nuclides of xenon and 

krypton. The coefficients were derived using the stable nuclide release data because very little release 

data were available for the radioactive nuclides. The ANS 5.4 standard was implemented in the U.S. 

Nuclear Regulatory Commission (NRC) fuel performance code FRAPCON-2 by Pacific Northwest 

National Laboratory (PNNL).5

 The 1982 standard was not reaffirmed in 1992 because newer data were 

demonstrating that the assumptions used in the earlier standard were overly conservative; however, many 

of the original Working Group members were not available to revise the standard at this time. A new 

Working Group ANS 5.4 was formed in 2000 to revise the standard. The following documents the ANS 

5.4 standard proposed for implementation in 2009. 

The proposed 2009 standard applies to the release of the volatile and gaseous fission products of primary 

significance, which are krypton, xenon, iodine, cesium, and tellurium. This background document 

primarily addresses the diffusion coefficients and other model coefficients for krypton, xenon, and iodine 

and the data used to determine these coefficients. The diffusion coefficients for the precursors (bromine 

and tellurium) that impact the release of krypton and iodine are discussed briefly along with the data upon 

which they are based. 

The isotope that provides the largest contribution to equivalent dose to individuals is I-131 for accidents 

during in-reactor operation or shortly after reactor operation (e.g., the fuel-handling accident), due to its 

dose to the thyroid. These radioactive gaseous and volatile fission products can be divided into two 

categories: (1) short-lived radioactive nuclides (half-life less than one year) and (2) long-lived radioactive 

nuclides (half-life greater than one year). This division is significant because the most important release 

mechanism involves thermally activated migration (diffusion) processes that proceed slowly such that the 

short-lived nuclides decay appreciably before they are released from the pellet. Consequently, release 

calculations for short-lived nuclides must include their decay rate; whereas for long-lived nuclides, decay 

does not have to be considered. 

The sections below will provide the background on the development of the mathematical formulations for 

the model, the fission product release data, model fitting to the release data including the uncertainties 

estimated from the model fitting, and the assumptions and limitations of the model. 
1.2 
2.1 

2.0 MATHEMATICAL FORMULATION OF RELEASE MODEL 

The current ANS 5.4 Working Group has chosen to retain the simple phenomenological Booth diffusiontype model1-4 proposed in the 1982 standard, and has fitted the model coefficients empirically to selected 

data whose characteristics will be described later. It should be stressed that the Booth diffusion model is 

a simplification of the physical processes involved in the release of fission products but has been shown 

to provide a reasonable fit to the release of both stable and radioactive nuclides. The actual physical 

process involves gas-atom diffusion to grain boundaries where the gas precipitates out on the boundary as 

a bubble. The gas bubbles are held on the grain boundary until the boundary is sufficiently saturated that 

interlinkage of the bubbles leads to a pathway out of the fuel and release to the inner void space of the 

fuel rod. In addition, gas bubbles are also precipitated within the grains; this gas is not released until 

sufficiently high temperatures are achieved. The gas within the grain matrix and grain boundary bubbles 

can also be redissolved back into the grain matrix and subsequently re-diffused to grain matrix or grain 

boundary bubbles. The simple Booth model used for the standard accounts for bubble interlinkage and 

release using a simple empirical correlation that is a function of burnup and fuel temperature that agrees 

with fission gas release data obtained at the Halden Reactor Project. 

The “idealized” Booth model describes diffusion of fission-product atoms in a spherical grain of fuel 

material. The governing differential equation is: 

2

2

( )

r

rC

r

D B C

t

C

∂

∂ = − − ∂∂ λ

 (Eq. 1) 

where C is the nuclide concentration (atoms-cm-3) in the fuel, t is time in seconds (s), B is the production 

rate (atoms-cm-3-s-1), λ is the decay constant (s-1), r is radius of the sphere (cm), and D is the diffusion 

coefficient (cm2

-s-1). The latter term of this equation is the local mass flow of atoms at a radius r

(atoms-cm-3-s-1). Therefore, the rate of concentration change in a region of radius r is equal to the rate of 

production minus the rate of decay minus the rate of loss by mass flow out of the region. 

In the original ANS 5.4 standard, the release fraction is the ratio of the release to production rate. It is 

sometimes referred to as R/B (where B as defined above and C=0 is assumed at the sphere surface where 

r = a) is given by: 

( ) ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡ = − μ

μ

μ

1 coth 1 R / B 3

 (Eq. 2) 

where r r a

C

a

D R =

⎟

⎠

⎞ ⎜

⎝

⎛

∂

∂ = −3

 (atoms-cm-3s

-1), and 

 (unitless) 

Equation 2 is for equilibrium conditions (i.e., assumes a period of constant power operation over several 

half-lives of the nuclide for the R/B in question [generally three half-lives is sufficient]). If the 

temperature and power operation changes within less than three half-lives, this equation provides a 

conservative prediction of R/B if the maximum power and temperature is used during the time period in 

question and the power change is not large enough to elicit large burst releases. 

D

a

2 λ

μ =
2.2 

This diffusion equation assumes that a net flow of atoms occurs because of the existence of a 

concentration gradient within the sphere and that the flux of atoms is proportional to that gradient. The 

production rate B and decay constant λ in Equation 1 are known for the nuclides of interest, but the 

effective diffusion coefficients D and idealized sphere radius a in Equation 2 are unknown and must be 

determined from experimental data. 

The release fraction for the current standard uses the same equation but defines the radius of the sphere, a, 

in terms of a surface area to volume ratio, S/V, which for a sphere is a = 3/(S/V). Substituting 3/(S/V) in 

place of coefficient a in Equation 2, as proposed by Turnbull and Friskney,6

 results in the following 

relationship: 

⎥

⎦

⎤ ⎢

⎣

⎡ = − μ

μ

α

λ

1 coth 1 /

D

V R B S

 (Eq. 3) 

where S V αD

λ

μ 2

( / )

9 =

Note that α is a unitless term for precursor effects that were generally ignored in the 1982 standard with 

the exception of the nuclides Xe-133 and Xe-135. However, the current standard will include precursor 

effects for additional nuclides. This equation can be further simplified with only a small over prediction 

(by less than 5 x 10-3 relative) for release values less than 0.02 with the following relationship: 

λ

αD R / B = S /V

 (Eq. 4) 

The α term is calculated based on a derivation by Friskney and Speight7

 for precursor enhancement 

effects on diffusing species from the following relationship: 

2

2

3

1 ( / )

1 ( / )

⎥

⎦

⎤ ⎢

⎣

⎡

−

− = y x

y x

α

where 

p

Dp

y λ = and 

nuclide

Dnuclide x λ =

where Dp and λp are the diffusion coefficient and decay constant of the precursor nuclide, p, while Dnuclide

and λnuclide are the nuclide daughter product. Values of α based on the above equation are shown in 

Table 1 below. 
2.3 

Table 1 Half-Lives and Precursor Coefficients for Radioactive Nuclides

Nuclide Half-life Decay Constant, s-1 α

Xe-133 5.243 d 1.53x10-6 1.25 

Xe-135 9.10 h 2.12x10-5 1.85 

Xe-135m 15.3 min 7.55x10-4 23.5 

Xe-137 3.82 min 3.02x10-3 1.07 

Xe-138 14.1 min 8.19x10-4 1.00 

Xe-139 39.7 s 1.75x10-2 1.00 

Kr-85m 4.48 h 4.30x10-5 1.31 

Kr-87 1.27 h 1.52x10-4 1.25 

Kr-88 2.84 h 6.78x10-5 1.03 

Kr-89 3.15 min 3.35x10-3 1.21 

Kr-90 32.3 s 2.15x10-2 1.11 

I-131 8.04 d 9.98x10-7 1.0 

I-132 2.28 h 8.44x10-5 137 

I-133 20.8 h 9.26x10-6 1.21 

I-134 52.6 min 2.20x10-4 4.4 

The basic coefficients to the diffusion model were based on experiments performed during the 1970s in 

the DIDO research reactor at UKAEA Harwell, United Kingdom, published by Turnbull;6,8,9 however, 

small deviations from the original coefficients were made to provide a better fit to the fission gas release 

data obtained at the Halden Reactor Project. These small deviations are within the scatter of Turnbull’s 

DIDO release data. 

The basic assumptions for the diffusion model developed in this report are: 

1. Gas-atom diffusion from where the atoms are born in the fuel matrix is the mechanism for 

diffusion to the grain boundaries where the gas precipitates as bubbles. 

2. The gas bubbles on the grain boundaries reach a saturation point where the bubbles interlink, 

releasing the gas to the fuel rod void volume. 

3. The criterion for grain boundary interlinkage is a function of only temperature and burnup. 

4. Once the grain boundary interlinkage has occurred, the grain boundary remains linked to the rod 

internal void volume for the rest of the irradiation (i.e., no resintering of the grain boundary is 

experienced). 

5. Derivation of precursor enhancement factor α is valid if one of two conditions is met: 

a. The precursor is immobile after release. This is believed to be the case with the xenon 

precursor, iodine, which plates out on the cooler parts of the cladding or sweep gas flow lines 

until it decays to xenon, where it is then swept out to the out-of-reactor detectors. 

b. The precursor is mobile but has a half-life much less than the transit time from the fuel to the 

detector. This allows the precursor to decay to the daughter product before reaching the 

detector, which is the case for the krypton precursor, bromine. 

Further assumptions in the derivation of the coefficients to this model are: 

6. The nuclides are in radioactive equilibrium in terms of release and decay; this assumption is 

approximately correct if fuel temperatures remain constant for at least three half-lives of the 

nuclide. 
2.4 

7. The diffusion coefficients for the nuclides of interest are assumed to be the same as xenon or a 

multiple of that for xenon, i.e., D(Xe) = D(Kr) = D(I) = D(Br)/20 = D(Te)/4. The diffusion 

coefficients for iodine and noble gases are known to be similar based on the Halden, DIDO, and 

other measured release data.9,11,12 However, the diffusion coefficients for the precursors bromine 

(for krypton) and tellurium (for iodine) are of greater uncertainty. Killeen et al.13 estimated the 

bromine diffusion coefficient to be a factor of 20 higher than for the noble gases because the 

factor of 20 provided the best agreement in terms of release of the different krypton and xenon 

isotopes with similar decay constants (half-lives) for the IFA-504 release data. This factor of 20 

diffusion for bromine was also used by White and Turnbull11 to obtain good predictions of the 

IFA-558 release data. Lewis et al.14 estimated the tellurium diffusion coefficient to be a factor of 

4 greater than the noble gases based on trace irradiations15 and release from a failed fuel 

experiment in a hydrogen/steam atmosphere.16

The diffusion coefficient form was one proposed by Turnbull et al.10 as the sum of three components: 

D = D1(T) + D2(T, ) + D3( ) (Eq. 5) 

D1 is an intrinsic component applicable at high temperature and dependent only on temperature; it was 

assumed that the best values for D1 were those found by Davies and Long17 and also fit the DIDO data 

well: 

D1 = 7.6 x 10-10 exp(-7 x 104/RT), m2/s (Eq. 6) 

where T is fuel temperature in degrees K. 

The coefficient D2 was evaluated in terms of diffusion assisted by an irradiation enhanced uranium 

vacancy concentration; in this case, the diffusion coefficient depended on both temperature T and the 

fission rate : 

D2 = d2.jv. Vc, and jv, m2/s (Eq. 7) 

where d is the atomic jump distance, jv is the cation vacancy jump rate, and Vc is the cation vacancy 

concentration, which is a function of fission rate and temperature. The exact relationship for D2 was not 

provided in Reference 10 but was later provided by White and Turnbull.11 

D3 is an athermal, low-temperature diffusivity (diffusion is solely by irradiation damage) analogous to that 

derived by Matzke18 for irradiation-enhanced self-diffusion: 

D3 = 2 x 10-40 •

F , m2

/s (Eq. 8) 

where is fission rate in fissions/m3

-s. 

The pre-exponentials of the first two coefficients (D1 and D2) have since been decreased by a factor of 10 

and 1.8, respectively, (see first and second terms in Equation 9 below) to provide a better fit to the 

Turnbull et al6, 10 and the Halden Reactor Project radioactive gas release data11 as determined by 

Turnbull.8

 These data were measured by sweeping helium gas through a fuel rod that carries the 

radioactive gas within sealed flow lines to a location outside of the reactor core where it is counted with a 

detector to determine the amount of release within a given time period. These data are then converted to 

R/B. The decay that occurs between when the gas is released from the fuel to when it is counted, as well 

•

F •

F

•

F

•

F
2.5 

as detector counting efficiency, is used in determining R/B. These data are discussed further in Section 

3.0. 

The revised three-term diffusion coefficients are expressed as: 

, m2/s (Eq. 9) 

Bubble saturation and interlinkage at the grain boundaries have been modeled by several investigators 

with References 19 and 20 providing examples; however, many of these models estimate that saturation is 

dependent on external pressure on the fuel pellet. The assumption that saturation and release is dependent 

on external pressure was tested in the Halden experiment IFA-558, which demonstrated that gas pressure 

on the fuel pellet had very little or no impact on saturation and release.11 Therefore, a simple empirical 

correlation was used based on the Vitanza threshold criterion21 for release with a modification for higher 

burnup because the Vitanza threshold has been shown to underestimate the threshold for release at high 

burnup. The original Vitanza threshold fuel temperature dependence was based on fuel centerline 

temperature while that proposed in this model is based on local fuel temperature at a given radial node. 

This modification is conservative for determining release; however, it has been shown to provide a 

reasonable best estimate fit to the Halden release data of radioactive isotopes. The nodal temperature for 

the threshold, or in this case grain boundary bubble interlinkage, at low burnups is essentially that 

proposed by Vitanza as: 

273

ln(176 )

9800

+ ⋅ = BuTlink

 (Eq.10) 

if Bu ≤ 18.2 megawatt-days per kilogram of uranium (MWd/kgU), where Bu is pellet average burnup. 

For Bu > 18.2 MWd/kgU, the following relationship is used for interlinkage temperature: 

Tlink =1434 −12.85Bu + 273 (Eq. 11) 

where is in degrees K. 

The release fraction for a given nuclide for an irradiation period at constant temperature and power of 

radial node i has been modeled for a given radial node in a fuel pellet using Equation 4: 

nuclide

i nuclide

i nuclide i

D

V

S

B

R

λ

α ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ = ⎠

⎞ ⎜

⎝

⎛

,

 (Eq. 12) 

1

1

120 −

⎟ = ⎠

⎞ ⎜

⎝

⎛

cm

V

S

 if Ti ≤ Tlink 

1

2

650 −

⎟ = ⎠

⎞ ⎜

⎝

⎛

cm

V

S

 if Ti > Tlink 

Where Ti = fuel temperature for node i, in degrees K. When interlinkage occurs at a given radial nodal 

temperature (i.e., Ti > Tlink), the S/V increases from 120 cm-1 to 650 cm-1. 

Tlink

Di Ti F& Ti F& 11 25 0.5 40 7.6 10 exp( 35000/ ) 1.41 10 exp( 13800/ ) 2 10 − − −= × − + × − + ×
2.6 

Release of I-131 has been modeled differently from the shorter half-life isotopes represented by the above 

equations. Release of long-lived isotopes such as I-131 (8.04-day half-life) is based on a fractal approach 

to the effective diffusion distance, or S/V between long-lived versus short-lived isotopes, proposed by 

White.22 The fractal approach to diffusion to a given surface can be summarized by an analogy of 

measuring a coastline with rulers of different length: the longer the ruler, the shorter the coastline. The 

equivalent ruler for fission gas release is the distance that an isotope has to diffuse before decay. In this 

case, the effective surface area for short-lived species was larger (shorter diffusion distance) than that of 

long-lived species. Applying this fractal concept and equations proposed by White for diffusion leads to 

the following relationship for release of long-lived isotopes (half-lives greater than 4.48 hours) compared 

to the release of Kr-85m (4.48-hour half-life): 

Kr m

i Kr m

i

nuclide

i nuclide

D

V

S F

B

R

85

85

, −

−

⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ = ⎠

⎞ ⎜

⎝

⎛

λ

α (Eq. 13) 

Fnuclide is a fractal-scaling factor for longer-lived nuclides defined as: 

0.25

85

85 ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

=

−

−

α

λ

λ

α

nuclide Kr m

nuclide Kr m Fnuclide

(S/V)i, Di, and αnuclide are as defined above. For I-131, Equation 13 becomes: 

B m

R

B

R

131 85

2.39 ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ = × ⎠⎞ ⎜

⎝

⎛

Modeling the release in a fuel rod with k radial nodes and j axial nodes can be determined by summing 

the release for a given nuclide with decay constant, λnuclide, from each radial and axial node at constant 

temperature and burnup, which is given by the following equation: 

∑ ∑ = = ⎥

⎥

⎦

⎤

⎢

⎢

⎣

⎡

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ = ⎠⎞ ⎜

⎝

⎛ m

j

k

i

i j

node

j

ring

i j

pellet

j

ring

i j

rod

node

j

ave

pellet

j

nuclide B

R

V

V

P

P

V

V

P

P

B

R

1 1 ,

, ,

 (Eq. 14) 

where: 

P = power in kW/ft (ave=rod average, pellet=pellet [axial node] average, ring=local radial ring) 

V = volume, cm3 (rod=total rod volume, node=axial node volume, ring=radial ring volume) 

Equation 14 sums the radial and axial nodes to obtain release for a given nuclide in a fuel rod. 
3.1 

3.0 FISSION PRODUCT RELEASE DATABASE 

The radiological release database consists of R/B data from Kr-90, Xe-139, Kr-89, Xe-137, Xe-138, 

Xe-135m, Kr-87, Kr-88, Kr-85m, Xe-135, Xe-133, and I-131; half-lives are presented in Table 1. The 

experimental measurements of R/B of radioactive fission gases were obtained from three gas-flow type 

experiments (i.e., the Halden IFA-504, IFA-558, and IFA-633). The IFA-504 and IFA-558 Kr-85m data11

were used for model fitting and the limited amount of IFA-633 Kr-85m data23 and iodine data from 

IFA-504 and IFA-558 were used to verify the model. The IFA-504 experiment consisted of four rods 

irradiated to 60 to 90 gigawatt-days per kilogram of uranium (MWd/kgU) while IFA-558 consisted of six 

rods irradiated to 40 MWd/kgU. These experiments flow gas over the fuel within the Zircaloy cladding 

for each rod, thus sweeping out the radioactive gas that is then collected outside of the reactor core and 

counted by a gamma detector to determine the quantity of gas released within a specific time period. In 

order to be able to measure the R/B for modeling purposes, equilibrium must be established between the 

three rate-dependent processes of: 1) release of gas from the fuel; 2) rate of radioactive decay; and 3) gas 

production rate. For equilibrium to be established, the production rate and the fuel temperature (impacts 

diffusion rate) can not change significantly within three times the half-life of the radioactive gas release 

being measured. The model assumes that the gas species are released solely by diffusion, except for a 

small recoil component that is significant only for very short-lived species that do not impact dose 

consequences. This component will be ignored in the model presented here. 

The iodine isotopes are solid except at high temperatures and are not transported through the unheated 

flow lines of a gas flow experiment to the gamma detector; this is important in the measurement of iodine 

release. Assessment of the iodine release presents some difficulties and must be performed indirectly by 

measurement of the xenon decay products. The situation is further complicated by the fact that the decay 

products (Xe-135, Xe-135m, Xe-133, and Xe-131m) are themselves released in sufficient quantities as to 

render at-power iodine measurement difficult. This situation is circumvented by exploiting the fact that 

production and release of the isotopes effectively ceases at reactor shutdown. Any excess xenon detected 

after shutdown must have arisen from decay of iodine isotopes already released and plated out on cooler 

parts of the gas circuit. Therefore to measure iodine release, at shutdown the rods are flushed thoroughly 

to remove any xenon actually released as xenon. This is followed by a number of on-line flow 

measurements taken at intervals over the following 24 hours. In this way, the release of I-135 and I-133 

can be inferred from the Xe-135, Xe-135m, and Xe-133 activity. 

The determination of I-131 release is more complicated because 99% of its decay results in the stable 

Xe-131 isotope, while the remaining 1.086% yields xenon that has a half-life of 11.9 days and whose 

gamma energy is in close proximity to a strong gamma ray from the decay of Xe-133 (5.29-day half-life). 

The technique adopted exploits the different half-lives of the isotopes in the decay chain. If the rod is 

sealed, the concentration of Xe-131m after 12 to 14 days reaches a maximum and, when swept out to the 

gamma detector, can be distinguished from any residual amounts of Xe-133 and used to estimate the 

quantity of I-131 released immediately prior to shutdown. The requirement for a long shutdown for this 

measurement means that only a few estimates of I-131 release have been possible. In all, a total of 21 

measurements of I-131 release were made from the Halden gas flow experiments IFA-504 and IFA-558 

using this measurement method. 

The database for the gaseous and iodine species ranges from 14.4 kW/ft up to 24 MWd/kgU burnup, 

9 kW/ft up to 60 MWd/kgU, and 4 kW/ft up to 90 MWd/kgU as demonstrated in Figure 1. A linear 

interpolation between these ranges is reasonable for model application. 
3.2 

0

2

4

6

8

10

12

14

0 10 20 30 40 50 60 70 80 90

Rod Average Burnup, MWd/kgU

Rod AverageLHGR, kW/ft

IFA-558 & 504 Kr-85m IFA-633 Kr-85m I-131

Figure 1 Operating Range of Kr-85m and I-131 Release Data, R/B, from IFA-558, IFA-504, and 

IFA-633 
4.1 

4.0 MODEL FITTING BASED ON HALDEN DATA 

The radioactive isotope that delivers the largest share to equivalent dose to individuals is generally I-131 

(8.04-day half-life) for accidents during in-reactor operation or shortly after reactor operation (e.g., fuel 

handling accident) due to its dose to the thyroid and relatively long half-life. Therefore, the ANS 5.4 

Working Group concentrated on developing the most accurate estimate of the I-131 release. However, as 

noted in Section 3.0, there were only 21 release measurements of I-131. The confidence in the 

coefficients model and the model predictive uncertainties developed from this small amount of data 

would be significant. As presented in Figure 1, there were hundreds of measurements over a wide range 

of operating conditions (burnup and rod power) for the Kr-85m isotope. Because of the paucity of I-131 

data and the large amount of noble gas data, it was decided to develop the diffusion coefficients of the 

release model and S/V values both prior to and after interlinkage using the noble gas data. Because the 

diffusion coefficients for iodine and the noble gases are similar,9,11,12 the prediction of I-131 release 

should be relatively simple and can be verified by how well the model predicts the data of 21 

measurements of I-131. 

The Kr-85m release data from the Halden experiments were selected for use to derive the coefficients to 

the ANS 5.4 model due to the relatively long half-life (4.48 hours). Other, longer-lived isotopes that are 

measured by Halden in the sweep gas are Xe-133 (5.25-day half-life) and Xe-135 (9.09-hour half-life); 

however, the release data for these isotopes have a larger uncertainty than for Kr-85m measured release. 

For Xe-133, there are two reasons for the decrease in the measurement accuracy. The first is the lowenergy gamma of ~80 keV for Xe 133, while the other isotopes (including Kr-85m) have a much higher 

gamma energy with greater measurement accuracy. The detectors have been well calibrated at the higher 

energies but have not been well qualified at the lower energies near 80 keV and do not have a uniform 

response (counting efficiency) across the energy spectrum. The second reason is that, at these low 

energies, there is a problem of high background that interferes with the Xe-133 measurement. For 

Xe-135, the production BXe-135 of this isotope is not easily determined due to the fact that Xe-135 captures 

a neutron, creating stable Xe-136. The capture rate is both spectrum and flux dependent such that the 

quantity of Xe-135 can vary at different times in the reactor due to flux and spectrum changes. This 

makes the estimate of BXe-135 difficult without detailed neutronic analyses throughout the irradiation. 

The use of Kr-85m for estimating the I-131 release is similar to the approach used by Turnbull8

 in the mid 

1980s. Turnbull estimated the I-131 release from Kr-85m release using his original diffusion coefficients 

(shown in Equations 5 through 8) derived from his measurement of noble gas release data from DIDO 

due to the lack of iodine release data at this time. Turnbull further assumed that the release of I-131 was 

essentially by single-atom diffusion and hence could be calculated by simply scaling by the square root of 

the ratio of the half-lives of a chosen gaseous fission product and I-131 using Equation 12 (no fractal 

effect). Since the longest-lived gas for which reliable data were generally found was Kr-85m with a 4.48-

hour half-life from his original experiments in DIDO, this isotope was chosen for the calculation. The 

R/B for I-131 could therefore be written as: 

131

85

131 85 λ

λ m

B m

R

B

R ⎟ × ⎠

⎞ ⎜

⎝

⎛ ⎟ = ⎠

⎞ ⎜

⎝

⎛

This implies that R/B for I-131 is of the order of 6.56 times that for Kr-85m. In a later report, Turnbull24

used the 6.56 factor for comparison to the 21 measured release data of I-131 from IFA-504 and IFA-558. 

From these comparisons, he found that this methodology significantly over estimated the I-131 

measurements made in the Halden sweep gas experiments described in Section 3.0. At this time, 
4.2 

Turnbull hypothesized24 that this method contained a number of conservative assumptions that could 

explain the over prediction. His original hypothesis identified the following conservative assumptions: 

1. The scaling process neglects the fact that Kr-85m release is enhanced by rapid diffusion of its 

Br-85 precursor. This is not the case for iodine isotopes. 

2. The scaling process ignores the presence of a recoil release component. 

3. Differentiating between diffusion coefficients, release of the shorter-lived Kr-85m is best 

described using all three of the diffusion coefficient contributions, D1+ D2 + D3 in Equation 5, 

while I-131 is best described using only D1 + D2. 

Based on further calculations, Turnbull concluded24 that the first two corrections were inadequate to 

reconcile the difference in prediction versus measured I-131 release, while the third was proved incorrect 

by finite difference calculations performed by White.22 White further concluded that it was not the 

diffusion coefficient that varied with the lifetime of the isotope, but the effective surface area based on the 

assumption that the uranium dioxide (UO2) surface was actually a fractal effect. Applying the 

mathematics of fractals proposed by White leads to a constant scaling factor of 2.39 for I-131 release in 

relation to Kr-85m release: 

B m

R

B

R

131 85

2.39 ⎟

⎠

⎞ ⎜

⎝

⎛ ⎟ = × ⎠

⎞ ⎜

⎝

⎛

The fractal approach to diffusion is discussed in more detail in Section 2.0. Some members of the 

ANS 5.4 Working Group expressed doubt about the validity of the fractal phenomenon. The validity of 

the fractal phenomenon can be determined if Equation 13 for fractals can explain the relative release 

differences between long half-lived nuclides and short half-lived nuclides (e.g., a factor of 2.39 ratio 

between R/BI-131/R/BKr-85m). A disproof of a fractal effect would be if the release can be explained by a λ

0.5

(a factor of 6.59 ratio predicted for R/BI-131/R/BKr-85m) that assumes the diffusion distance for release is the 

same for both short- and long-lived nuclides. 

There are some reliable release data from short-lived nuclides, but the release data of the long-lived 

nuclides are very limited or uncertain. For example, the only nuclide release data with long enough halflives to discern whether the fractal phenomenon is valid are the R/BXe-133 and R/BI-131 data. One Working 

Group member felt that a small amount of release data from fuel irradiated at very low burnups25 did not 

show a fractal effect for measured values of R/BXe-133, but there was also considerable scatter in these data. 

One of these measured R/BXe-133 data (FIO-122) agrees with the 6.59 factor (no fractal effect), but the 

other data (FIO-124) suggest that the ratio factor between R/BI-131/R/BKr-85m is less than the 2.39 fractal 

factor. Experimental measurements of R/BXe-133 in Halden11 and by others26 have also shown very large 

uncertainty (scatter) in these data, making it difficult to discern whether the factor of 6.59 or 2.39 is valid 

for predicting the R/BI-131 release from R/BKr85m release, thus providing no conclusive evidence for either 

modeling approach. The Halden R/BI-131 data are currently the only data that exist over a wide range of 

burnups and rod powers for verification that the fractal factor of 2.39 is valid. The proposed uncertainty 

assumed for the new ANS 5.4 model is very conservative in relation to the R/BI-131 data such that it will 

bound any potential non-conservatism introduced by using the fractal mathematics, as will be 

demonstrated in the statistics of the model comparisons to the R/BI-131 data described in Section 4.4. 
4.3 

4.1 Development of Model Coefficients from R/BKr85m Data 

The coefficients in Equations 9 through 12 were derived using 174 R/BKr85m release data from six rods 

irradiated in IFA-558 and 132 R/BKr85m release data from four rods irradiated in IFA-504. Examination 

revealed that the release data from these two experimental assembly tests consisted of two separate 

populations. This is best illustrated by performing a best-estimate fit of the R/BKr85m data to determine the 

S/V1 (before interlinkage) and S/V2 (after interlinkage) values for each of these two instrumented fuel 

assemblies (IFAs) using the same three-term diffusion coefficient given above. The best-fit values of 

S/V1 and S/V2 from the IFA-504 R/BKr85m were 160 cm-1 and 800 cm-1, respectively; while the values for 

the IFA R/BKr85m were 80 cm-1 and 500 cm-1 as shown in Table 2. 

Table 2 Values of S/V1 and S/V2 that Provide a Best-Estimate Fit of R/BKr85m Data Versus Burnup 

from Experimental Test Assemblies IFA-558 and IFA-504

Experimental Test (S/V)1cm-1 (S/V)2 cm-1

IFA-558 80 500 

IFA-504 160 800 

The difference in S/V for these two data sets may be due to how the fuel was fabricated for these two 

experiments. The fuel from IFA-558 was more recently fabricated and considered to be more 

representative of today’s fuel, while the IFA-504 fuel was from an older fabrication process that usually 

resulted in a higher open porosity than current fuel fabrication processes. Generally, a higher open 

porosity results in a higher S/V and higher releases than fuel with a lower open porosity. However, there 

were no measurements of open porosity in either of these experiments; therefore, it is impossible to 

correlate the S/V to open porosity in these experiments or to definitively conclude that one is nonprototypic of all fuel currently fabricated. 

There have been other sweep gas experiments in Halden, but some are dated and less reliable than 

IFA-504 or the data are held proprietary. The Halden IFA-633 experiment collected sweep gas data from 

three UO2 and three mixed oxide (MOX) fuel rods from which there was a small amount of data (see 

Figure 1), but the currently available data only consist of six release data from the three UO2 rods. Use of 

only the IFA-558 data may not give a representative uncertainty in the release of current fuel types. 

Therefore, due to the lack of other radioactive noble or iodine release data, the IFA-504 data are included 

in the development of this model. As a result, S/V best-estimate values from these two experiments were 

averaged providing values of 120 cm-1 and 650 cm-1 for S/V1 and S/V2, respectively, that resulted in a 

predicted-to-measured value near 1.0. This is reasonable since the number of release data from each 

experiment are similar (174 versus 132). The diffusion coefficients D1, D2, and D3 are those given in 

Equation 9, grain boundary interlinkage is given in Equations 10 and 11, and the fractal effect is given in 

Equation 13. 

4.2 Model Comparison to R/BKr85m Data 

Figures 2 and 3 show the ratio of predicted-to-measured values of R/BKr85m (assuming S/V1=120 cm-1 and 

S/V2=650 cm-1 for predictions) versus burnup under equilibrium conditions with the measured values from 

sweep gas experiments in Halden for test assemblies IFA-504 and IFA-558 as provided in References 9 

and 22. A ratio greater than 1.0 indicates that the model is over predicting the data, while a value less 

than 1.0 indicates the model is under predicting the data. As expected, these figures show that the two 

experiments represent two different populations of release data and that deriving one set of S/V values 

from these two populations results in under prediction of the IFA-504 data and over prediction of the 

IFA-558 data with the under and over predictions becoming greater at burnups above 13 MWd/kgU. 
4.4 

Figure 2 presents all of the data, while Figure 3 limits the burnup level to 40 MWd/kgU to better illustrate 

the differences between the two sets of experimental data. 

0

1

2

3

4

5

6

0 10 20 30 40 50 60 70 80 90 100

Burnup (MWd/kgU)

Predicted/Measured Kr-85m

IFA-558 Rod 1

IFA-558 Rod 2

IFA-558 Rod 3

IFA-558 Rod 4

IFA-558 Rod 5

IFA-558 Rod 6

IFA-504 Rod 1

IFA-504 Rod 2

IFA-504 Rod 3

IFA-504 Rod 4

Figure 2 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Burnup Between 0 and 

90 MWd/kgU for Each of Six Experimental Rods in IFA-558 and Four Experimental Rods in 

IFA-504; Assumes S/V1=120 cm-1 and S/V2=650 cm-1

0

1

2

3

4

5

6

0 10 20 30 40

Burnup (MWd/kgU)

Predicted/Measured Kr-85m

IFA-558 Rod 1

IFA-558 Rod 2

IFA-558 Rod 3

IFA-558 Rod 4

IFA-558 Rod 5

IFA-558 Rod 6

IFA-504 Rod 1

IFA-504 Rod 2

IFA-504 Rod 3

IFA-504 Rod 4

Figure 3 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Burnup Between 0 and 

40 MWd/kgU for Six Rods in IFA-558 (Red) and Four Rods in IFA-504 (Blue); Assumes 

S/V1=120 cm-1 and S/V2=650 cm-1

As noted above, the Halden reactor has recently published measurements of R/B from three UO2 fuel rods 

(Rods 1, 3, and 5) at burnups between 35 and 40 MWd/kgU in the experimental assembly IFA-633. The 

Halden Reactor Project has indicated a plan to release additional data collected as part of the IFA-633 

experiment, but these data are currently not available. These measurements are important to verify the 

validity of the proposed best-estimate release model and to determine if a correction is needed to the 

diffusion coefficients and S/V for MOX fuel such that the standard can be modified to include MOX fuel. 

The ratio of model predicted to six measured values of R/BKr85m from the three UO2 IFA-633 rods are 

presented in Figure 4 at burnups between 35 and 40 MWd/kgU along with the IFA-504 and IFA-558 data. 
4.5 

Examination of this figure reveals that the four R/BKr85m measurements from Rods 3 and 5 are 

significantly over predicted by a factor of 5 to 7, while one of the Rod 1 predictions shows good 

agreement and the second Rod 1 prediction shows an under prediction of nearly a factor of two of the data 

(upper range of the IFA-504 ratios). These comparisons do not appear to resolve whether or not the 

IFA-504 data are representative of today’s fuel because of one data point from Rod 1 of IFA-633 that was 

under predicted with a ratio of 0.59. This under prediction is somewhat surprising considering the 

significant over prediction of the data from Rods 3 and 5 from IFA-633 and the fact that all of the UO2

fuel (Rods 1, 3, and 5) in this assembly were from the same fabrication source that is suppose to be 

representative of current UO2 fuel fabrication processes. This data comparison further demonstrates the 

need to include the IFA-504 data to provide an estimate in the uncertainty of the model for current fuel 

fabrication processes. 

0

1

2

3

4

5

6

7

8

0 10 20 30 40

Burnup (MWd/kgU)

Predicted/Measured Kr-85m

IFA-558 Rod 1

IFA-558 Rod 2

IFA-558 Rod 3

IFA-558 Rod 4

IFA-558 Rod 5

IFA-558 Rod 6

IFA-504 Rod 1

IFA-504 Rod 2

IFA-504 Rod 3

IFA-504 Rod 4

IFA-663 Rod 1

IFA-663 Rod 3

IFA-633 Rod 5

Figure 4 Ratio of Calculated R/BKr85m to Measured R/BKr85m versus Burnup for Six Rods in IFA-558 

(Red), Four Rods in IFA-504 (Blue), and Three Rods in IFA-633 (Green); Assumes 

S/V1=120 cm-1 and S/V2=650 cm-1

The R/BKr85m predicted-to-measured ratios as a function of rod power are provided in Figure 5 to examine 

whether there are any biases in the model predictions with rod power. This figure appears to show that 

the model over prediction of the IFA-558 data increases with increasing rod powers above 10 kW/ft; 

however, the IFA-504 data does not show this trend. It should be noted that on average the IFA-558 data 

are over predicted by the model; but even within the IFA-558 data, the over prediction increases with rod 

power. This over prediction would suggest that the high-temperature diffusion term, D1, should have 

smaller temperature dependence than assumed for the IFA-558 data. The R/BI-131 predictions will also be 

examined to determine if this trend exists with these data. 
4.6 

0

1

2

3

4

5

6

7

8

0 2 4 6 8 10 12 14 16

Rod Power, kW/ft

Predicted/Measured Kr85m

IFA558 IFA504 IFA633

Figure 5 Ratio of Calculated R/BKr85m to Measured R/BKr85m Versus Rod Power for Six Rods in IFA558 (Diamond), Four Rods in IFA-504 (Square), and Three Rods IFA-633 (Triangle); 

Assumes S/V1=120 cm-1 and S/V2=650 cm-1

4.3 Model Comparison to R/BI-131 Data 

The predicted-to-measured R/BI-131 is provided in Figure 6 and demonstrates that the model predictions 

are reasonably good. This suggests the data coefficients derived from R/BKr85m data apply to the release of 

I-131 and the assumptions used in the model development are valid. The ratio of predicted-to-measured 

values of R/BI-131 versus burnup (Figure 7) demonstrate that, on average, there is a small over prediction. 

The ratio of predicted-to-measured values of R/BI-131 versus rod power (see Figure 8) demonstrate that 

there is more scatter in the data at higher powers of 7 to 9 kW/ft, but there is no definitive bias with rod 

power. Overall, the model provides a reasonably accurate prediction of release for R/BI-131 considering 

uncertainties in the data and this is the form of model recommended for determining radiological release 

of the volatile nuclides. 

0.0E+00

5.0E-04

1.0E-03

1.5E-03

2.0E-03

2.5E-03

3.0E-03

0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03

Measured R/B

Predicted R/B

I-131 Predicted = Measured Linear (Predicted = Measured)

Figure 6 Predicted to Measured R/B for I-131 for IFA-558 and IFA-504; Assumes S/V1=120 cm-1 and 

S/V2=650 cm-1
4.7 

0.00

0.50

1.00

1.50

2.00

2.50

0 10 20 30 40 50 60

Burnup, MWd/kgU

Predicted/Measured I-131

558-R1

558-R3

558-R6

504-R1

504-R2

504-R3

504-R4

Figure 7 Ratio of Calculated R/BI-131 to Measured R/BI-131 Versus Burnup Between 0 and 56 MWd/kgU 

for Three Rods in IFA-558 (Red) and Four Rods in IFA-504 (Blue); Assumes S/V1=120 cm-1

and S/V2=650 cm-1

0

0.5

1

1.5

2

2.5

0 1 2 3 4 5 6 7 8 9 10

Rod Power, kW/ft

I-131 Pred/Meas

IFA558

IF504

Figure 8 Ratio of Predicted R/BI-131 to Measured R/BI-131 Versus Rod Power for Three Rods in IFA-558 

(Red) and Four Rods in IFA-504 (Blue); Assumes S/V1=120 cm-1 and S/V2=650 cm-1

4.4 Estimate of Model Uncertainties 

The uncertainty in model predictions will be assessed in terms of the predictions of the Kr-85m and I-131 

data separately because there is a significant difference in uncertainty in the model prediction of these two 

data sets. 

4.4.1 Estimate of Model Uncertainties from Predictions of R/BKr-85m Data 

The R/BKr85m release values (see Figure 9) vary by over two orders of magnitude; therefore, in order to 

normalize these large differences, the statistical analysis was performed on the Ln P/M. The IFA-504 and 

IFA-558 ratio of predicted to measured represent two separate distributions (particularly at burnups 

greater than 10 MWd/kgU), both of which are nearly normal as illustrated in Figures 3 and 4; therefore, 

this combined data set represents a bi-normal distribution. Assuming a normal distribution for the 
4.8 

combined data set is a non-conservative assumption, but assuming they are a non-normal data set is a 

conservative assumption. Therefore, a non-normal distribution was chosen to determine the upper 95/95 

bounding model uncertainty for predicting the R/BKr85m. A mean and a standard deviation for a nonnormal distribution do not have any statistical meaning such that the multiplier, K95/95, on a prediction is 

based on an nth largest negative value of under prediction from the database where the nth value is 

determined from the number of data used to establish model coefficients. Utilizing the non-normal 

distribution at a 95/95 tolerance level (bounding with 95% probability at a 95% confidence level) for 

300 data points (given in Table 2 of Regulatory Guide 1.12627), the ninth largest negative value of 

Ln P/M (under prediction) is -1.616, which represents an under prediction of 5.03 from the measured 

value. In order to bound future predictions at a 95/95 tolerance level, the best-estimate model prediction 

is multiplied by 5.03, which is rounded to 5 considering the data and conservatisms in this estimate. 

Figure 9 provides the 95/95 tolerance upper-bound predictions compared to the R/BKr85m data. 

1.0E-04

1.0E-03

1.0E-02

1.0E-05 1.0E-04 1.0E-03 1.0E-02

Measured R/B Kr-85m

Predicted R/B Kr-85m

558r1

558r2

558r3

558r4

558r5

558r6

504r1

504r2

504r3

504r4

Pred=Meas

Linear

(Pred=Me

as)

Figure 9 Predicted 95/95 (Assuming Non-Normal) R/BKr-85m Versus Measured R/BKr-85m from IFA-504 

and IFA-558 

4.4.2 Estimate of Model Uncertainties from Predictions of R/BI-131 Data 

A similar statistical analysis was performed for the model predictions of the R/BI-131 data with the 

exception that a normal distribution was assumed based on examination of Figures 6 and 7. The mean of 

the Ln P/M is 0.2263 (over prediction) with a standard deviation of 0.4381. There were 17 R/BI-131 data 

with three degrees of freedom; therefore, the K95/95 tolerance factor becomes exp(-0.2263+2.5888*0.4381) 

= 2.48. This value is a factor of 2 lower than the K95/95 tolerance factor, 5, derived from the R/BKr85m data. 

It is recommended that the factor of 5 from the R/BKr85m data comparisons also be used for predictions of 

all radioactive isotopes, including I-131 predictions that will address the concerns about the validity of the 

fractal factor used to perform the best-estimate predictions of the R/BI-131 data. Using a K95/95 tolerance

factor of 5 for predicting the R/BI-131 data demonstrates a very conservative over prediction of these data 

(see Figure 10). 
4.9 

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

0.0E+00 5.0E-04 1.0E-03 1.5E-03 2.0E-03 2.5E-03 3.0E-03

R/B I-131 Measured

Predicted R/B I-131 95/95 

R/B I-131 Predicted=Measured

Figure 10 Predicted 95/95 (Assuming Non-Normal) R/BI-131 Versus Measured R/BI-131 from IFA-504 

and IFA-558 

Upper-bound 95/95 tolerance predictions (using a factor of 5) of R/BI-131 of the new proposed ANS 5.4 

model have been performed with the FRAPCON-3.328 fuel rod performance code used to provide fuel 

temperature predictions for a generic boiling water reactor (BWR) 10x10 fuel design; the results are 

provided in Figure 11. The power history used assumed a rod average power of 31.5 kW/m up to a 

burnup of 22 MWd/kgU, then decreased linearly to 23.5 kW/m at 62 MWd/kgU (rod average). Also 

included in Figure 11 is a calculation using the same code and BWR 10x10 input, but using the old 

ANS 5.4 model for calculating the R/BI-131. This illustrates how the new proposed ANS 5.4 model 

provides a factor of 2 less peak release for iodine isotopes than the old model for fuel rod average burnups 

greater than 30 MWd/kgU. 

0.E+00

1.E-02

2.E-02

3.E-02

4.E-02

5.E-02

6.E-02

7.E-02

8.E-02

9.E-02

0 10 20 30 40 50 60 70

Burnup, MWd/kgU

Predicted R/B 1-131

Old ANS 5.4 New ANS 5.4 95/95

Figure 11 Comparison of New ANS 5.4 Model Upper Bound at 95/95 R/BI-131 Predictions to Old 

ANS 5.4 Model R/BI-131 Predictions for a BWR 10x10 Fuel Design 
4.10 

4.5 Assumptions and Limitations 

The assumptions used in model development are: 

1. Gas-atom diffusion from where the atoms are born in the fuel matrix is the mechanism for 

diffusion to the grain boundaries where the gas precipitates as bubbles. 

2. The gas bubbles on the grain boundaries reach a saturation point where the bubbles interlink, 

releasing the gas to the fuel rod void volume. 

3. The criterion for grain boundary interlinkage is a function of only temperature and burnup. 

4. Once the grain boundary interlinkage has occurred, the grain boundary remains linked to the rod 

internal void volume for the rest of the irradiation (i.e., no resintering of the grain boundary is 

experienced). 

5. The nuclides are in radioactive equilibrium in terms of release and decay, which is approximately 

correct if fuel temperatures remain constant for at least three half-lives of the nuclide. 

6. Precursor effects can be accounted for by a multiplier, α, on the diffusion coefficient, per 

Friskney and Speight.8

 The diffusion coefficients for the bromine and tellurium precursors are 

assumed to be a factor of 4 and 20 greater, respectively, than the noble gases and iodines. 

The limitations of the developed model are the following: 

• The model does not account for burst releases due to large sudden temperature (power) increases 

greater than 300°K. 

• The model does not account for transport of fission products after release from the fuel rod due to 

a cladding defect. 

• The model does not apply to release of stable nuclides or nuclides with half-lives greater than one 

year. Other models are available to determine release of stable nuclides. 

• Application of the model to predict release with temperature changes on the order of less than 

three half-lives for an isotope can be performed in a conservative manner by assuming the 

maximum temperature during the time period has been constant for the three half-lives of the 

isotope. 

• The model does not apply to release from failed fuel where fuel oxidation is possible. Fuel 

oxidation can enhance the radiological release. 

• The model does not apply to commercial fuel operation with rod-average burnups greater than 

70 MWd/kgU. Data used for model development extend to 90 MWd/kgU but are at relatively 

low linear heat generation rates between 70 to 90 MWd/kgU. 

• The model is based on fuel with densities between 95% to 98% of theoretical density, grain sizes 

between 6 to 15 μm (mean linear intercept), and open porosities between 0.1% to 3.0 % 

theoretical density. Therefore, the model should only be applied to fuel within these ranges. 

• The model is based on release from UO2 fuel only; therefore, it currently does not apply to 

(U,Pu)O2 fuel or fuel types other than UO2. The ANS 5.4 Working Group and the NRC are in 

discussions with the Halden Reactor Project to release those data applicable to (U,Pu)O2 fuel to 

the NRC (a member of the project). Once these data are received, an assessment can be 

performed to determine whether the current model can be applied to predicting gap release 

fractions for (U,Pu)O2 fuel. 
5.1 

5.0 CONCLUSIONS 

A newly proposed ANS 5.4 release model has been developed for determining the radioactive fission 

product releases for use in assessing radiological consequences of postulated accidents that do not involve 

abrupt power transients. This proposed ANS 5.4 model has been reviewed by the ANS 5.4 Working 

Group, and submitted for approval as the new ANS 5.4 standard. When used with isotopic yields, this 

proposed model will predict the "gap activity," which is the inventory of volatile fission products that are 

released from the fuel rod if the cladding is breached. The standard model as developed applies to steadystate conditions and, therefore, should not be applied to accidents where abrupt temperature increases are 

experienced, resulting in a “burst release." The standard does not consider escape-rate coefficients or 

other descriptions of the transport of fission products after release from the fuel rod void space. The 

standard assumes that no significant fuel oxidation will be present during the accident because fuel 

oxidation can significantly enhance the release. 

This report describes both best-estimate and conservative upper-bound 95/95 tolerance models for 

predicting the release of volatile radioactive isotopes of krypton, xenon, and iodine. The conservative 

upper-bound model for predicting the I-131 release is very conservative in comparison to the available 

measured release data for I-131. The new proposed model predicts up to a factor of 2 lower release than 

the old ANS 5.4 release model. 
5.2 
6.1 

6.0 REFERENCES 

1. American Nuclear Society, Method for Calculating the Fractional Release of Volatile Fission 

Products from Oxide Fuel, ANSI/ANS 5.4 -1982 Also defined in S.E. Turner et al., “Background 

and Derivation of ANS-5.4 Standard Fission Product Release Model,” U.S. Nuclear Regulatory 

Commission Report, NUREG/CR-2507, 1982. 

2. A.H. Booth, “A Method for Calculating Fission Gas Diffusion from UO2 Fuel and its Application to 

the X-2-f Loop Test,” Atomic Energy of Canada Report, CRDC-721, 1957. 

3. A.H. Booth, “A Suggested Method for Calculating the Diffusion of Radioactive Rare Gas Fission 

Products from UO2 Fuel Elements and a Discussion of Proposed In-Reactor Experiments that May Be 

Used to Test its Validity,” DCI-27 AECL-700, Atomic Energy of Canada Limited, 1957. 

4. A.H. Booth and G.T. Rymer, “Determination of the Diffusion Constant of Fission Xenon in UO2

Crystals and Sintered Compacts,” Atomic Energy of Canada Report, CRDC-720, 1958. 

5. W.N. Rausch and F.E. Panisko, “ANS54: A Computer Subroutine for Predicting Fission Gas 

Release,” U.S. Nuclear Regulatory Commission Report, NUREG/CR-1213, 1979. 

6. J.A. Turnbull and C.A. Friskney, “The Relation Between Microstructure and the Release of Unstable 

Fission Products During High-Temperature Irradiation of Uranium Dioxide,” Journal of Nuclear 

Materials, vol. 71, issue 2, January 1978. 

7. C.A. Friskney and M.V. Speight, “A Calculation on the In-Pile Diffusional Release of Fission 

Products Forming a General Decay Chain,” Journal of Nuclear Materials, vol. 62, October 1976. 

8. J.A. Turnbull, “A Model for Calculating the Gap Inventory of 131I in Intact Fuel Rods,” Paper 56, 

BNES Conference on Nuclear Fuel Performance, London 1985. 

9. J.A. Turnbull, R.J. White, and C. Wise, “The Diffusion Coefficient for Fission Gas Atoms in 

Uranium Dioxide,” IAEA Conference, Preston, Lancs, UK, IAEA-TC-659/3.5, 1988. 

10. J.A. Turnbull et al., “The Diffusion Coefficients of Gaseous and Volatile Species During the 

Irradiation of Uranium Dioxide,” Journal of Nuclear Materials, vol. 107, issues 2-3, June 1982. 

11. R.J. White and J.A. Turnbull, “The Measurement of Fission Product Release Using the Gas Flow 

Rigs: A Review of Experiments, Methodology and Results from 1980-1997,” OECD Halden Project 

Report No. HWR-553, February 1998. 

12. B.J. Lewis, C.E.L. Hunt, and F.C. Iglesias, “Source Term of Iodine and Noble Gas Fission Products 

in the Fuel-to-Sheath Gap of Intact Operating Nuclear Fuel Elements,” Journal of Nuclear Materials,

vol. 172, pp. 197-205, 1990. 

13. J. Killeen, E. Skattum, and A. Haaland, “Review of Thermal Behaviour and Fission Product Release 

From the Gas Flow Rig IFA-504,” OECD Halden Reactor Project Report, HWR-187, April 1987. 

14. B.J. Lewis, B. Andre, G. Ducros, and D. Maro, “A Model for Nonvolatile Fission Product Release 

During Reactor Accident Conditions,” Nuclear Technology, vol. 116, pp. 34-54, October 1996. 

15. S.G. Prussin, D.R. Olander, W.K. Lau, and L. Hansson, “Release of Fission Products (Xe, I, Te, Cs, 

Mo and Tc) From Polycrstalline UO2,” Journal of Nuclear Materials, vol. 154, pp. 25-37, 1988. 

16. J.P. Leveque et al., “The HEVA Experimental Program,” Nuclear Technology, vol. 108, p. 33, 1994. 

17. D. Davies and G. Long, AERE Report No. 4347, 1963. 
6.2 

18. H.J. Matzke, “Gas Release Mechanisms in UO2—A Critical Review,” Proc. Int. Summer School on 

the Physics of Ionized Gases, Hercegnovi, Yugoslavia, 1970. Also Irradiation Effects, vol. 53, 

pp. 219-242, 1980. 

19. M.O. Tucker and J.A. Turnbull, International Conference on Physical Metallurgy of Reactor Fuel 

Elements, Berkeley Nuclear Laboratories, Gloucestershire, UK, September 2-7, 1973. 

20. D.M. Dowling, R.J. White, and M.O. Tucker, “The Effect of Irradiation-Induced Re-Solution on 

Fission Gas Release,” Journal of Nuclear Materials, vol. 110, issue 1, August 1983. 

21. C. Vitanza , E. Kolstad, and V. Graziani, “Fission Gas Release from UO2 Pellet Fuel at High 

Burnup,” ANS Topical Meeting on LWR Fuel Performance. Portland, Oregon, May 1979. 

22. R.J. White, “The Fractal Nature of the Surface of Uranium Dioxide: A Resolution of the ShortLived/Stable Gas Release Dichotomy,” OECD Halden Reactor Report No. HWR-550, February 1998. 

Also published in Journal of Nuclear Materials, vol. 295, issues 2 and 3, pp. 133-148, June 2001. 

23. E. Rø and G.D. Rossiter, “The SBR MOX and UO2 Comparison Test in Gas Flow Rig IFA-633: An 

Update of Results,” HWR-823, Enlarged Halden Programme Group Meeting, Lillehammer, Norway, 

October 2005. 

24. J.A. Turnbull, “The Treatment of Radioactive Fission Product Release Measurements and Provision 

of Data for Development and Validation of the ANS Model,” OECD Halden Reactor Project Report 

No. HWR-667, February 2001. 

25. T.J. Hastings et al. “Tests to Determine the Release of Short-Lived Fission Products from UO2 Fuel 

Operating at Linear Powers of 45 and 60 kW/m: Methods and Results,” AECL-7920, Atomic Energy 

of Canada Limited, Chalk River Laboratories, Chalk River, Ontario, Canada, September 1985. 

26. M. Charles, P. Chenebault, and P. Melin, “Mechanisms of Fission Gas Release from Different Types 

of Fuel Rods During Normal Operation: Results and Analysis of “CONTACT” Experiments,” Light 

Water Reactor Fuel Performance Proceedings, Orlando, Florida, April 21 -24, 1985, 

DOE/NE/34130-1, vol. 2, pp. 4-53. 

27. U.S. Nuclear Regulatory Commission, Regulatory Guide 1.126, An Acceptable Model and Related 

Statistical Methods for the Analysis of Fuel Densification, March 1977. 

28. Lanning, D.D., C.E. Beyer, and K.J. Geelhood. 2005, FRAPCON-3 Updates, including Mixed Oxide 

Properties, NUREG/CR-6534 (PNNL-11513) Vol. 4, U.S. Nuclear Regulatory Commission, 

Washington D.C. 
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Background and Derivation of ANS-5.4 Standard Fission Product Release Model

JANUARY 2010

NRC Job Code N6326

J.A. Turnbull and C.E. Beyer Technical

Pacific Northwest National Laboratory

902 Battelle Blvd. P.O. Box 999

Richland, WA 99352

Division of Systems Analysis

Office of Nuclear Regulatory Research

U.S. Nuclear Regulatory Commission

Washington DC 20555-0001

This background report describes the technical basis for the newly proposed American Nuclear Society (ANS) 5.4 standard,

Methods for Calculating the Fractional Release of Volatile Fission Products from Oxide Fuels. The proposed ANS 5.4 standard

provides a methodology for determining the radioactive fission product releases from the fuel for use in assessing radiological

consequences of postulated accidents that do not involve abrupt power transients. When coupled with isotopic yields, this

method establishes the "gap activity," which is the inventory of volatile fission products that are released from the fuel rod if the

cladding is breached.

Best-estimate and conservative upper-bound 95/95 tolerance models for predicting the release of volatile radioactive isotopes of

krypton, xenon, and iodine are described. The isotope that provides the most significant contribution to equivalent dose to

individuals is generally I-131 for accidents that occur during in-reactor operation or shortly after reactor operation (e.g., the

fuel-handling accident) due to its dose to the thyroid. The existing conservative upper-bound model for predicting the I-131

release has been shown to be very conservative in comparison to the available measured release data for I-131. The proposed

2009 model predicts up to a factor of 2 lower release than the old ANS 5.4 release model.

Fission products

Radionuclide and fission gas release

Nuclear fuel performance code