RAPPORTIRSN
INSTITUT
DE RADIOPROTECTION
ET DE SÛRETÉ NUCLÉMREFaire avancer la sûreté nucléaire

SUMMARY REPORT ON THE FRENCH
BURNUP CREDIT WORKING GROUPKNOWLEDGE REGARDING PWR UOXFUEL[Tapez ici le titre du rapport]
French Burnup Credit WG
Rapport n°PSN-EXP/SNC/2017-177

A
A R E VAoza

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Titre
Sous-titre
Title
SUMMARY REPORT ON THE FRENCH BURNUP CREDIT WORKING GROUP KNOWLEDGE REGARDING PWRUOX FUEL
Sub title
Auteur/author(s)French Burnup Credit WG

Type dedocument :Document
type :

Date de diffusion :Distribution date :Référence(s) :PSN-EXP/SNC/2017-177

E-mail de l'auteur :@irsn.fr

Elément DPPA
Mots-clés (Max. 5) :Key-words (Max. 5):burnup credit, burnup, profile, fission products, actinides, irradiation,
validation, correction factor

ABSTRACTThe "Burnup Credit" Working Group was established in 1997 to examine the various parameters, such as
the irradiation conditions, the burnup profile and the nuclides (actinides and fission products), to betaken into consideration in the criticality studies that take credit from burnup.
This report offers an overview of the work that has been completed or agreed under this framework. It
presents the group findings on the following topics:-

the axial distribution of nuclides or the axial burnup profile;-methods for validating the actual burnup and its axial distribution;-

the calculation of nuclide concentrations after irradiation;-

the calculation methods that will be used to determine the effective multiplication factor forsystems containing used fuel assemblies.
This document gathers together the work carried out by the French Burnup Credit Working Group; it is
not a guide validating a particular method for taking burnup credit into account. All of the findingspresented here may serve as a basis in industry for defining a method to take account of burnup credit
in criticality studies; any industrial body effectively adopting such a method will also be responsible fordefining it, based on its knowledge of the used fuel assemblies and the configuration to be addressed.
This document forms a collection of the work completed by the Working Group up to 1 January 2007
but does not necessarily reflect ongoing work in the various institutes.

IRSEI

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regarding PWR UOX fuel

HISTORIQUE DES MODIFICATIONS/CHANGE HISTORY

Indicederévision

Date

AuteurAuthorRevisionA

I RS

French.9sidelec&' Credit WG

BurnupPages ouparagraphes
modifiés

Nature des modifications

Pages orparagraphschonged/Nature of the changes_

Initial document

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CONTENTS
1
2

INTRODUCTION ............................................................................... 7
CONSERVATIVE BURNUP PROFILES ...................................................... 10
2.1
2.1.1
2.1.2
2.1.3
2.2
2.3
2.3.1
2.3.2
2.4

3

CHOICE OF THE BURNUP PROFILE FOR THE STUDIES................................................. 11
Generic studies (approaches based on feedback) .................................................... 11
Specific profiles ............................................................................................ 17
Discretization of the selected profile .................................................................. 18
RADIAL BURNUP GRADIENT ............................................................................... 19
VALIDATION METHODS FOR THE BURNUP PROFILE SELECTED FOR THE STUDIES ................ 20
Measurement uncertainties .............................................................................. 21
Measured values to be used .............................................................................. 23
CONCLUSION ON THE POTENTIALLY USABLE PROFILES AND VALIDATION METHODS ............ 25

NUCLIDE CONCENTRATIONS IN THE USED FUEL ASSEMBLIES....................... 26
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
3.3

4

IRRADIATION HISTORY ..................................................................................... 28
Associated physical phenomena ......................................................................... 28
Working group conclusions on the irradiation conditions ........................................... 33
CONCENTRATIONS OBTAINED FROM THE DEPLETION CODES ....................................... 39
Depletion calculation codes .............................................................................. 39
French calculation codes ................................................................................. 40
CONSERVATIVE CONCENTRATIONS ...................................................................... 41

METHOD FOR CALCULATING THE EFFECTIVE MULTIPLICATION FACTOR ........ 43
4.1
CALCULATION SEQUENCE ................................................................................. 43
4.2
VALIDATION OF THE CROSS SECTION LIBRARIES AND CRITICALITY CALCULATIONS ............. 44
4.3
CALCULATION CONVERGENCE AND LOOSE NEUTRON COUPLINGS FOR CODES USING A MONTECARLO METHOD .......................................................................................................... 46
4.4
CONCLUSIONS ON THE CALCULATION METHODS ...................................................... 47

5
6
7

CONCLUSIONS ............................................................................... 50
REFERENCES................................................................................. 53
APPENDICES ................................................................................. 57

IRSW

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelThis report results from the work conducted by the members of the French Burnup Credit
Working Group between 1997 and 2007. The English translation was checked by the members
between 2015 and 2016.
The Working Group would like to take this opportunity to mention Mister Didier Biron, whoworked hard to increase knowledge on burnup credit in France. The Working Group wishes to
pay tribute to him through this report.

IRSW

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1 INTRODUCTION
In the early 1980s, a method was developed to take account of the burnup 1 to enable
criticality studies to consider the decrease in reactivity, due to the burnup of uranium oxidebased fuels irradiated in light water reactors; this method was initially implemented todemonstrate the safety of the dissolution of highly enriched (4.4 wt%) used fuels at COGEMA
UP2-400 plant at La Hague, and was subsequently extended to assembly transportation and to
the design of the UP3 and UP2-800 plants.
This method, which was accepted by the French Safety Authority, takes into account thedisappearance of uranium 235 and 238, and the appearance of the following actinides:
uranium 236 and plutonium 238, 239, 240, 241 and 242. The burnup used in the studies must
be lower than or equal to the mean burnup measured operationally over the 50 least
irradiated centimeters of the assembly.
Given the increase in the initial enrichment of PWR Uranium Oxide (UOX)-based fuels,
coupled with the considerable interim storage needs for used fuel assemblies, it was deemednecessary to define a method to take account of the burnup that would be less penalizing
than that used previously; this would be approached by considering hypotheses closer to thephysics of the phenomena (burnup profile modelling, consideration of fission products, etc.),
but with conservatism to guarantee the conservative nature of the results.
In order to examine the various parameters of such a method, a Burnup Credit Working Groupwas established in 1997, bringing together EDF, FRAMATOME, CEA, COGEMA, SGN,
TRANSNUCLEAIRE and IPSN. The findings presented in this report derive from the discussions
and studies conducted by this group, along with the international publications produced inthis field.
The aim of this document is to present all of the aspects to be addressed as part of this new
approach, together with the resulting studies; it also provides an overview of the work
already completed and the tasks underway.
The consideration of BurnUp Credit (BUC) is based on the modelling of the different physicalphenomena associated with irradiation. These physical phenomena depend on the appearance
and disappearance of nuclides, during the irradiation of the assemblies in the reactor whensubjected to a variable neutron flux, and during cooling after fuel irradiation. Consequently,
a BUC approach is structured around the following points:

1

The burnup corresponds to the energy produced by a fuel per mass unit. This value is typically given in MWd/MTHM
or GWd/MTHM (where MTHM denotes metric tons of initial heavy metal).

IRSW

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuel- the calculation of the concentrations of the different selected nuclides right at the end of
irradiation or after a given cooling time;- the axial and radial distribution of these nuclide concentrations, or the axial and radial
burnup "profile";- the guaranteed irradiation level of the assemblies and the axial burnup distribution;- finally, the calculation of the effective multiplication factor for a given burnup profile andthe associated nuclide concentrations.
Each of the above steps must be addressed in a way that guarantees conservatism when
taking burnup credit into account, and will be covered by a dedicated chapter:- Chapter 2 discusses the different axial burnup profiles that might be used in the studies;for a given mean burnup, it examines the impact of the axial burnup distribution along theassembly and describes the validation methods studied by the Working Group,
demonstrating that the profile chosen for the criticality studies is penalizing compared tothe actual axial burnup profile;- Chapter 3 is devoted to the analysis of parameters for assessing the nuclide concentrationsin the used fuel for a given burnup and cooling time; the conservatism of theconcentrations obtained is associated with the irradiation and cooling histories selected forthe calculations, as well as the results from the validation of the depletion codes used;- Chapter 4 focuses on the sequencing of the criticality calculations taking burnup credit
into account; in particular, it describes how a given discretized burnup profile can be usedto:

introduce the nuclide concentrations for the various selected nuclides, for eachestablished burnup zone (taking into account the calculation methods used todetermine their concentrations);

calculate the effective multiplication factor; in this context, different calculation
configurations were studied, including the configuration for an isolated assembly(this configuration can be used to assess the intrinsic effect of taking burnup credit
into account for an assembly), interim storage configurations in normal andaccident conditions (in pools at La Hague), and transport configurations;

IRSW

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regarding PWR UOX fuelChapter 4 then presents the work carried out on the validation of cross-section libraries
and criticality calculation codes for the consideration of burnup credit. The loose
coupling and source convergence issues for the Monte Carlo calculations are also
discussed in this chapter;-

finally, the conclusion reviews all of the results obtained, the studies currently inprogress and future actions to be considered.

This document gathers together the work carried out by the French Burnup Credit
Working Group up to 1 January 2007; it is not a guide validating a particular method fortaking burnup credit into account.
The findings presented here may serve as a basis in industry for defining a method to takeaccount of burnup credit in criticality studies; any industrial body defining such a method
must take full responsibility for its development, giving consideration to the configuration
to be addressed, the analyzed scenarios and its knowledge of the used fuel assemblies.

IRSW

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regarding PWR UOX fuel2 CONSERVATIVE BURNUP PROFILES
The studies conducted in the framework of the OECD, described in reference documents 1, 2,
3, 4, 5 and 6, revealed that the hypothesis of considering a uniform burnup across the entire
assembly, and equal to the mean burnup, is not conservative when the average burnup
exceeds 30 GWd/MTHM.
Indeed, for some configurations, typically with high irradiation rates, the ends of theassembly become considerably under-irradiated and govern the system overall reactivity
level.
The work carried out by the Burnup Credit Working Group on determining an axial burnup
profile was structured around two lines of research:-

the first involved initially determining axial burnup profile families, based on either
measurements taken in the reactor or burnup profile calculations with three-dimensional
codes, and then defining penalizing profiles for each defined profile family; this work,
based on calculated profiles, is described in reference document 15;-

the aim of the second was to classify the actual axial burnup profiles measured in the La
Hague plant into different families.

From these studies, along with the discussions held by the Burnup Credit Working Group, it
was found that:-the systematic use of a penalizing (perturbed) profile could lead to excessive
conservatism (for example, the perturbed profile studied in reference document 14 leads
to a conservatism of up to 11,000 pcm in k) and the conservative nature of the selected
profile is, in any case, difficult to establish for all types of core management. However,validated approaches based on core calculations, using measurements taken in thereactor (not yet explored by the Working Group), could provide a possible alternative andbe the subject of work presented in a later version of this report;-

the presentation of 3,000 17x17 PWR profiles measured at La Hague showed that there
was little difference between the normalized profiles of the used fuel assemblies arriving
at La Hague for any given burnup range (see report in reference 10).

Based on an experimental approach, one possible method, presented at the Burnup Credit
Working Group meeting on 12 March 2001 (see reference 7), would involve considering anaxial burnup profile similar to the standard one, and making measurements to check thatthe measured burnup at each point is actually higher than the burnup used in the studies.

IRSW

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regarding PWR UOX fuelAs soon as the axial burnup profile is validated by a measurement, any profile can beselected for the criticality studies. However, if the chosen profile is required to cover the
majority of the assemblies, it will need to be defined based on the profiles observed todate.
It will then be possible to justify the criticality safety of the storage or transportation ofparticularly perturbed profiles, which are not covered by a "standard" profile, by conducting a
specific study:-

either by defining a very penalizing profile;-or by reducing the burnup used in the study.

Finally, in some cases (such as the used fuel pits at La Hague), where the operator needs toguarantee only a minimal burnup (less than one irradiation cycle), it would be useful todefine a method that accounts for the burnup without the needs for a systematic
measurement of either the profile or the mean burnup.
The following points are presented in turn in the remainder of this chapter:-

possible approaches to the creation of an axial profile and the discretization selected forit;-studies relating to a possible horizontal burnup gradient;-

the validation methods explored.

2.1 CHOICE OF THE BURNUP PROFILE FOR THE STUDIES
Two profile types are presented below. These relate to:-the "standard" profiles, which are likely to be encountered for the majority of used fuelassemblies;-

the specific profiles, which are likely to be seen in very exceptional circumstances or to
be used in a penalizing way.

2.1.1 GENERIC STUDIES (APPROACHES BASED ON FEEDBACK)The members of the Working Group considered it useful to define a profile for each studied
burnup range, based on the series of profiles observed at La Hague, which could then be usedsystematically for criticality studies implementing used fuel assemblies.

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regarding PWR UOX fuelThe observations made at La Hague showed that the normalized burnup profiles2 were similar
withinthefollowing

threeburnupranges:[10 GWd/MTHM; 20 GWd/MTHM],[20 GWd/MTHM; 30 GWd/MTHM] and over 30 GWd/MTHM, with a flattening of the profile inthe mid-section and a rise in the slope at the ends, when the burnup increases (seereferences 9 and 10).
Given these observations, it appears that a standard burnup profile can be defined for eachburnup range, which covers most of the cases met and that its conservativeness can bedemonstrated (for example, by making measurements to check that the actual burnup profileis always within the range of curves currently observed).
Several approaches may be considered, the principles of which are detailed in Appendix 8.
An approach suggested by IRSN (see reference 8) and illustrated in Figure 1 below, involves
defining a conservative profile. A burnup profile may be deemed conservative if, on any partof the used fuel assembly, the burnup is lower than that of the actual profile. It should be
noted that such a profile is not a normalized one (the mean is less than 1), which ispenalizing.
BU(Z)/BU

Upper profile
Lower profile

Measurement uncertainty
Discretization

zie.
Figure 1: Principle for determining an overall profile from 137Cs profile measurements
for 1300 MWe PWR assemblies
Another approach was also examined by EDF (refer to Appendix 8 and reference document 9)
to suggest a "Best Estimate" profile that would be representative of the majority ofassemblies, based on the profiles observed at La Hague. This profile is not intended to be

2

The normalized profile is defined as follows: ( P(z) BF(z) BF(z) dz / H).

H

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regarding PWR UOX fuelconservative but could be used at a later stage as part of a specific BUC approach. Details of
this point will be provided in the next revision of this document.
COGEMA gave the Working Group a database containing the measurements (taken in the T1
burnup pit at the plant at La Hague) for the axial burnup profile of 644 used fuel assemblies
in EDF 1300 MWe reactors, grouped into two series, named R103 and R202, and reprocessedat La Hague. COGEMA provided the gross count rates for 134Cs and 137Cs at centimetre intervals
along two opposite sides (named route 1 and route 2 throughout the remainder of thisdocument) of each of the assemblies and, deduced from these measurements, the mean
burnup for each assembly and each side.
The majority of the assemblies reveals an initial 235U enrichment of 3.10 wt%. The otherassemblies, with an initial 235U enrichment of 1.50 wt%, 1.80 wt%, 2.40 wt% and 2.95 wt%, arethose from the first cores. These are associated with a fuel management with a balanceenrichment of 3.10 wt%.
Over 94% of the assemblies had an average burnup of between 30 and 40 GWd/MTHM. The
other assemblies had an average burnup of between 10 and 30 GWd/MTHM.
Table 1 below shows the distribution of the assemblies according to their mean burnup, foreach of the two series and each of the two routes.
Table 1: Population of assemblies based on their burnups for the series
and routes studied

Number of assemblies
Series R103

Series R103

Series R202

Series R202

Route 1

Route 2

Route 1

Route 2

BU < 25 GWd/MTHM

10

14

13

13

25 < BU < 30 GWd/MTHM

6

3

7

34

30 < BU < 40 GWd/MTHM

290

289

318

291

BU > 40 GWd/MTHM

0

0

0

0

Total assemblies

306

306

338

338

From the data provided by EDF/DPI/DPN/UNIPE, it can be seen that 33% of the measured
assemblies were irradiated in the final cycle under control rods (R or G) and that 10% were
irradiated under control rods for over two thirds of the time spent in the reactor. The

IRSW

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regarding PWR UOX fueldatabase therefore contains a large number of assemblies placed under control rods during
the irradiation process.
The representativeness of this database (assemblies with an initial 235U enrichment equal to
3.1 wt% and a burnup of between 30 and 40 GWd/MTHM) remains to be confirmed for otherburnups and enrichments, by providing axial burnup curve measurements for additional
assemblies.
In order to compare the axial burnup curves, the initial data were formatted in advance. At
each axial point (at centimetre intervals) of the active height of the assembly, the local countrate was divided by the total count rate and then multiplied by the height of the assembly toobtain a curve "centered" around the mean value 1. For each route, after removing theinconsistent points (negative or close to 0), and for each point, the measured local burnup
was divided by the mean burnup value of the route studied, and by the number ofmeasurement points.
The analysis of the formatted data finally revealed:

a slight drop for the assembly profiles with a low burnup (less than 20 GWd/MTHM). It
was also noted that the burnup values at the ends of the assemblies were lower for
lightly irradiated assemblies than for moderately or highly irradiated assemblies. The
figure below illustrates this phenomenon. The axial point is measured from the bottom of
the assembly;consistent burnup measurements between routes 1 and 2 (profile and burnup): therelative mean difference between the burnups for routes 1 and 2 did not exceed 4% for
the selected fuel elements (the burnup uncertainty measurement had been calculated at5%). This phenomenon implies an equivalent burnup on both sides of the assemblies;

consistency between the assemblies burnup profiles, ranging between 30 and
40 GWd/MTHM. This observation enables us to conclude that the position of an assembly
during irradiation, whether it is under a control rod or not, has no specific impact on its
burnup profile when the assembly comes to the end of its life.

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regarding PWR UOX fuel1, 4Normalized burnup

1, 2

0, 8

0, 6

0,4

— FXOONX (BU-11.6 GVVd/NiT1-1M)0, 2— FX01CD (BU-40.0 GVVd/NiT1-1M)

CD

0 C, C'D

LO

0,

CNI

L.C,
CNI .1 .1 .1 .1

C7
7

CNI

C'D
C'D

CD 0, 0C'D CD CD Cr,

Axial point (cm)Figure 2: Normalized axial burnup profiles for two assemblies from the COGEMA database:
FX00NX (BU=11.6 GWd/MTHM) and FX01CD (40.0 GWd/MTHM)
Based on this feedback, EDF suggested establishing an axial burnup profile representative of
the assemblies contained in the COGEMA database with initial 235U enrichment equal to
3.1 wt% and with a mean burnup of between 30 and 40 GWd/MTHM. To do this, at each axial
point (totalling 427 for a 1300 MWe PWR assembly) an arithmetic mean is calculated based on
all of the normalized profiles, corresponding to assemblies with an initial 235U enrichment
equal to 3.1 wt% and a mean burnup of between 30 and 40 GWd/MTHM. The mean profile
obtained for each assembly is then normalized again. This profile may be considered as beinga mean model of the profiles supplied by COGEMA.
To illustrate the low variability of the studied profiles, Figure 4 shows the normalized mean
curves together with the maximum and minimum overall curves obtained for the set ofassemblies with a mean burnup of between 30 and 40 GWd/MTHM. The differences between
the overall curves and the mean curve are quantified in Appendix 8.
Table 2 and Figure 3 below show the mean profile obtained, discretized according to
12 zones.

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regarding PWR UOX fuelTable 2: Description of the mean profile discretized according to 12 zones
Zone

Length (cm)Beginning of zone

End of zone

Normalized BU

1

6

0

6

0.457

2

2

6

8

0.543

3

3

8

11

0.653

4

5

11

16

0.747

5

20

16

36

0.919

6

17

36

53

0.977

7

293.8

53

346.8

1.0618

8

35

346.8

381.8

1.014

9

17

381.8

398.8

0.935

10

20

398.8

418.8

0.736

11

5

418.8

423.8

0.545

12

3

423.8

426.8

0.476

1.2 -

T

7

7

Q. G •

r.0"0 0,6
.11
N
(6

E
o
0,4

—.—Norma I ized mean axial curve—À—Mea n curve d iscrelized accord i ng ha 12 zones
0.2

LIO

LIO
CID GO 0 C,

LIO

LIO
LIO LO CO G/ 0 I-

I-

LIO
LIO

CO
I+
LIO
CY
GO
CNI CO CO CO CO CO CO CO CO CO

CNI

Axial point (cm)Figure 3: Normalized mean axial curves representative of an assembly with initialenrichment equal to 3.1 wt% and a burnup of between 30 and 40 GWd/MTHM from the
COGEMA database, together with the mean curve discretized according to 12 zones

I RS

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regarding PWR UOX fuel17/1141,4Normalized burnup

10,8—à—Minimum overall curve
0,4—.—Normalized mean axial curve—à—Maximum overall curve
o
0

50

100

150

200

250

300

350

400

450

Axial point (cm)Figure 4: Normalized mean axial curves, and minimum and maximum overall curves, obtained
from the assemblies with initial enrichment equal to 3.1 wt% and a burnup of between 30 and
40 GWd/MTHM from the COGEMA database
In conclusion, the statistical analysis of the burnup profiles supplied by COGEMA does notreveal any particular axial deformation attributable to operation with partially inserted rods.
The mean profile obtained is representative of the curves likely to be observed in French PWR
operating modes used currently, or envisaged in the near future, including for the EPR. This
representativeness will be extended to other axial burnup curve measurements for fuelassemblies. If there is no significant change in the operating mode for these reactors, andsince the profile obtained is not found to be highly variable, there does not appear to be any
reason why this profile should not be used in the criticality safety studies that take burnup
credit into account. However, the studies that use this profile will need to incorporate
margins to ensure the overall conservatism of the approach.
2.1.2 SPECIFIC PROFILES

A specific method needs to be defined for the assemblies whose burnup profiles are notincluded within the range of curves observed at La Hague.
One of the options for taking "specific" cases into account would be to calculate a "penalizing"profile.
As an example, the calculations performed at EDF and presented in the report inreference 15, made it possible to create a particularly penalizing burnup profile (profile"no. 8"); using this highly perturbed profile can lead to a significant increase in reactivity

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regarding PWR UOX fuelwhich, according to the study conducted by IRSN in reference 17 may reach 11,000 pcm(in k) for an assembly initially enriched at 4.5 wt% and irradiated at 44 GWd/MTHM.
In any event, the penalizing nature of the profile obtained using these specific methods must
undergo validation. This point is addressed in chapter 2.3.
2.1.3 DISCRETIZATION OF THE SELECTED PROFILE

During the meeting of the Working Group on 12 March 2001, a conservative and penalizing
profile discretization method was discussed. The smaller the number of zones leads to a more
penalizing profile (meaning a higher keff). This methodology consists of taking the burnup in aparticular fuel zone to be equal to the minimum burnup of the profile assumed for that zone.
Such a breakdown therefore resulted in the creation of a profile that was not normalized.
This hypothesis is shown in the figure below.
In this respect, the use of this undeniably conservative hypothesis does not lead to any
notable overestimation of reactivity.

Selected profile
BurnupZ axisFigure 5: Discretization of the selected profile in 10 axial zones
Studies were also conducted to determine the appropriate number of axial zones (which
would not be too penalizing in terms of the value of the effective multiplication factor andwhich would not require an excessive number of measurements).
Twelve zones appeared to be a reasonable option (the increase in the number of zones from11 to 17 would lead to a gain of around 500 pcm); this choice is the result of an industrial
decision, and means that if the calculation time is increased (due to an increase in thenumber of zones) then the value of the effective multiplication factor decreases. Several

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regarding PWR UOX fueltypes of axial breakdown were studied in the above-mentioned document, together with the
breakdown corresponding to a constant burnup difference for each axial zone.
It should be noted that choosing a sensible number of zones can depend on the type of profile
used.

2.2 RADIAL BURNUP GRADIENT
An assembly burnup has a more or less pronounced horizontal gradient, depending mainly on
its position during the last cycle (at the periphery of the core, for example).
With regard to the spatial distribution of the nuclides in the used fuel assembly, studies haverevealed, notably in the DOE document (reference 16), that differences can exist between
the burnups on two opposite sides of a used fuel assembly; the calculated values in the
aforementioned document are, as a maximum, approximately:-

25% for burnups corresponding to 1 irradiation cycle;-

15% for burnups corresponding to 2 irradiation cycles;-

15% for burnups corresponding to 3 irradiation cycles.

Burnup measurements taken at COGEMA at La Hague for three orders of reprocessing(863 assemblies), on two sides of the fuel, revealed a maximum difference3 of 22% between
the two sides for a 1300 MWe PWR assembly with a burnup of around 34 GWd/MTHM (seeminutes of meeting in reference 10).
The study conducted at IRSN and cited in reference 11 show that this radial burnup gradient
represents an increase in reactivity of around 600 pcm for two assemblies placed side by side(with the most reactive surfaces against one another), with initial enrichment equal to
4.0 wt% and irradiated up to 33 GWd/MTHM. For interim storage configurations andtransportation in a borated basket, this effect does not exceed 500 pcm.
However, in the case of four assemblies isolated in water, the use of a horizontal burnup
gradient of 22%, modelled by two zones, leads to an increase in reactivity of around 650 pcm
for one irradiation cycle and around 1,600 pcm for three cycles.
One should therefore remain cautious of the risk of a horizontal burnup gradient appearing.
Indeed, such a burnup gradient may have a significant effect on the keff value of the studied
3

Difference derived directly from the measured values without taking uncertainties into account.

IRSW

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regarding PWR UOX fuelconfiguration, particularly when the assemblies are neutronically coupled (in the absence ofborated baskets, for example).
Three approaches may be considered to address this phenomenon:-

the first relates to the possible ways of measuring this horizontal burnup gradient;-

the second involves the possibility of systematically lowering the assemblies burnup to
take this phenomenon into account in a very conservative way; in this case, the effect interms of reactivity of using an actual gradient may be analyzed in order to quantify theconservatism associated with reducing the burnup;-

a final option would be to model the assemblies burnup gradient by considering, forexample, the least irradiated surfaces against one another for the criticality calculations.

2.3 VALIDATION METHODS FOR THE BURNUP PROFILE SELECTED FOR THE STUDIESThe decision to take account of a burnup profile appears to be justified, subject to thevalidation of the actual burnup for the used fuel assemblies that will be stored ortransported. The Working Group therefore deemed it necessary to study the available
validation methods.
Initially, only the existing assembly burnup measurement methods were studied, together
with their limitations. Other validation methods are currently being examined by particularmembers of the Working Group (EDF and AREVA-NP).
Burnup measurement methods are used to determine an assembly means burnup as well as
the burnup profile. The approaches are as follows:-

to determine an assembly mean burnup, a measurement of the used fuel assembly
neutron emission, a gamma spectrometry measurement or a total gamma measurement istaken;-

to measure the burnup profile, a gamma spectrometry measurement is taken.

The burnup measurement is based on the relationship between the emission (neutron or
gamma) of certain nuclides and the burnup. It relies on an iterative process using themeasured neutron (or gamma) radiation values of certain nuclides and the predicted(tabulated) values of these neutron (or gamma) emissions, based on the burnup, using adepletion code in conjunction with the measurement procedure.

IRSW

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regarding PWR UOX fuelThe neutron measurement is used to determine neutron emission, basically due to theelements 242Cm and 244Cm, which is, as an initial approximation, proportional to the fourth
power of the burnup. As the neutron beam is not collimated, this method can be used todetermine an assembly mean burnup.
Gamma spectrometry is used to determine the relationship between the gamma emission of
the elements 134Cs and 137Cs, which is directly proportional to the burnup. These are local
measurements, which can also be used to determine the burnup profile, either by making
repeated measurements of the 134Cs/137Cs ratio in several different places, or by making
successive measurements of the axial profile of 137Cs.
In the remainder of this chapter, by taking an approach based on the burnup profiles
feedback, we suggest first studying the measurement uncertainties and then defining themeasurement points that would need to be established based on the discretized profile usedin the criticality safety study (derived from the approach presented in the previous chapter).
2.3.1 MEASUREMENT UNCERTAINTIESGiven the nature of the process used to determine the burnup, there are two sources of
uncertainty associated with the measurements involved:-

uncertainties relating to measurement precision (in turn linked to the measurement
method and the precision of the device used);-

uncertainties relating to the depletion calculation codes used to associate the burnup
with the measured concentrations (or concentration ratio).

With regard to this last point, the uncertainties are linked to the modelling hypotheses usedin the calculation codes (modelled relationship chains, resolution of equations, etc.), thesource data (efficiency, cross-sections, etc.), and any influence that the irradiation
conditions might have on the concentrations of the measured nuclides.
Moreover, with regard to an assembly mean burnup, it should be noted that the reactor
operator provides a mean value, which could be used to reduce the measurement
uncertainties.
In this context, it appears that the uncertainties associated with burnup measurement need
to be analyzed. Details of this analysis are provided in Appendix 14.

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regarding PWR UOX fuelAbsolute gamma spectrometry measurement of 137Cs
This type of measurement benefits from the fact that 137Cs is radioactive for a very longtime and that this nuclide is, therefore, barely affected if a cooling time error isintroduced into the calculations. Furthermore, the fission yield from uranium is identicalto that from plutonium. The mass balance of 137Cs is thus proportional to the burnup andis independent of the assembly irradiation conditions.
The measurement uncertainty depends on the quality of the calibration, the measuringconditions and the processing speed. It ranges from 15% to 25% and mainly results fromthe uncertainty of the relative position of the detector in relation to the assembly. Thismethod has not been officially adopted at La Hague.



Gamma spectrometry measurement of the 134Cs/137Cs ratio
This has been the official method used for over 15 years to measure the assemblies inFrance and in other countries. It was first implemented in 1980 for CNA fuel, which had a
cladding made of stainless steel.
The benefit of this method (as compared to absolute 137Cs measurement) is that it allows
a self-calibration of the apparatus, and it is much less sensitive to the measurement
conditions. However, the production of 134Cs is highly dependent on the irradiation
history.
This method can be used to validate the burnup with an accuracy of approximately 15%.

Gamma spectrometry measurement of 60Co, 144Pr or 154Eu
The measurement of 60Co can provide feedback on the assemblies thermal output. Thismeasurement is also used to position the assembly grids and the fissile column.
The 144Pr/137Cs ratio can be used to estimate the cooling time for a used fuel assembly.
The gamma spectrometry measurement of the 154Eu/137Cs ratio can also help determine
the burnup, although with a higher level of uncertainty than with the 134Cs/137Cs method(due to uncertainties on the europium parent nuclides cross-sections).

Passive neutron measurement
A gamma spectrometry measurement (for 134Cs and 137Cs) has negligible sensitivity fromthe fourth row of rods.
Passive neutron measurement compensates for this shortcoming. It is very easy to
perform but requires a validated depletion calculation code to determine the in-line
production of curium (or prior calculations for each assembly).
This method yields low uncertainty values (of around 10%) for standard burnups for
assemblies undergoing reprocessing ( 3 cycles).

IRSW

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regarding PWR UOX fuel2.3.2 MEASURED VALUES TO BE USEDIf we take a profile with N axial zones, we then need to check N+1 burnup values toguarantee that, at any point, the actual burnup is greater than the burnup considered in the
study.
Selected profile
Burnup

•

1■
Ik•
•

It

f
•

•
•

•

•

•

•

•

•

.

•

,
•
•
•

•

•
•
•

•
•
•
y
•
•
•
•

•

Z axisFigure 6: Burnup values that need to be guaranteed by the measurement
Checking the correspondence between the measured burnup and that selected for the study,
at each and every point, is only a valid method if the measuring system gives the exact valueof the burnup.
The experimental determination of the burnup, involving experimental measurement methods
and providing calculation results, is complex and leads to uncertainties.
Therefore, if the operator needs to process assemblies with a mean actual burnup equal to
BUactual, then the criticality studies will be performed with a burnup BUstudy equal, at most, to
BUactual x (1 - i), where i is a coefficient linked to the uncertainty of the measurement (itshould be stated whether this uncertainty corresponds to 1, 2 or 3 ); the actual mean burnupof the assembly will be greater than the mean burnup in the study, taking into account theuncertainties associated with the measurement and the method used to discretize the axial
profile. This point is shown in the figure below.

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regarding PWR UOX fuelActuel burnup

Burnup à

Untertainty linke-dto
m easu rem ent m ethods

Minimum burnup
to be m e.mure d
■
;Le.

J

Profile used in thestudyrf

Z axisFigure 7: Incorporation of measurement uncertainties
Finally, it was noted that if the burnup used in a study is much lower than the assemblies
actual burnup, then the number of measuring points can be reduced. This is illustrated in the
figure below.

BurnupActuel burnup

Measure-d points

Burnupto bemeasuredPrpfile ud intheeudy

Zaiz

Figure 8: Case in which the burnup needed to justify a configuration is much lower than theactual burnup - 4 measuring points needed

I RS

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regarding PWR UOX fuel25/1142.4 CONCLUSION ON THE POTENTIALLY USABLE PROFILES AND VALIDATIONMETHODS
The Working Group is currently conducting studies to determine a burnup profile, basedon the range of used fuel profiles measured at La Hague, that could be used genericallywith the vast majority of the used fuel assemblies. This profile will be provided for aburnup range and must undergo validation (by measurement, for example).
For assemblies with a burnup profile that is likely to be very specific (assemblies subject
to refined profiles), or when no systematic measurement is adopted, a specific process
can be defined. This process must guarantee the conservatism of the approach (byconsidering sufficiently low burnup values, for example).
Whenever a "standard" burnup profile is used in a study, several types of model may beconsidered. For example, penalizing discretization involves taking the burnup in aparticular zone to be equal to the minimum burnup in that zone. Each industrial body candetermine the optimal number of zones (in terms of the increase in reactivity or
calculation time) to select for the studies.
It also seems necessary to ensure that the mean burnup value and the axial burnup
profile are reliably determined. To date, the only method explored by the Working Groupto guarantee the axial burnup distribution involves measurement. If the correspondence
between the profile used in the studies and the actual burnup profile is checked by ameasurement, this must guarantee in particular that, at any point, the actual burnup is
greater than the burnup used in the study. In certain cases, where the operator does notwish to take any measurements, the use of a penalizing profile may be considered.
However, the conservatism of the choice of profile must be provided by other profile
validation methods.

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regarding PWR UOX fuel3 NUCLIDE CONCENTRATIONS IN THE USED FUEL ASSEMBLIES
Burnup credit is the negative reactivity caused by the burnup of the fuel when it is irradiatedin the reactor core. This increase in negative reactivity corresponds to the appearance anddisappearance of different nuclides during the irradiation process. It therefore appears
necessary to consider all of the fissile elements produced during irradiation (those playing anappreciable role in the chain reactions) and desirable to take account of the largest numberof absorbent nuclides produced during irradiation (actinides and fission products) whose
presence in the fuel is certain (without considering volatile nuclides or those with too shortdecay time compared to the cooling times proposed for the study).
The actinides and fission products selected for the OECD benchmarks are as follows:-

Actinides: Uranium 234, 235, 236 and 238, Plutonium 238, 239, 240, 241 and 242,
Americium 241 and 243, and Neptunium 237;-

Fission products: Samarium 149 and 152, Rhodium 103, Neodymium 143, Cesium 133 andGadolinium 155, in addition to 101Ru, 95Mo, 99Tc, 147Sm, 150Sm, 151Sm, 145Nd, 109Ag and 153Eu;
these 15 fission products are responsible for approximately 80% of the negative reactivity
caused by all of the fission products (according to reference document 12).

The first six fission products listed above (149Sm, 152Sm, 103Rh, 143Nd, 133Cs and 155Gd) are alone
responsible for 50% of the negative reactivity introduced by all of the fission products. The
choice of these six fission products was justified for the first time at the ICNC at Oxford in1991 (see publication reference 13). This choice was based on the following criteria:-

minimising the number of fission products (FPs) and, therefore, the associated problems,
while maintaining a large proportion of the FPs total absorption;-

disregarding the gaseous and volatile bodies;-retaining the stable bodies, or those with a daughter product that has greater absorption
than the parent;-

minimising the non-solubility and precipitation problems in the acid phase, more
specifically for dissolution.

The choice of the 15 fission products was based on the same types of criteria as those listed
above.
The following table presents an estimate of the negative reactivity provided by each nuclide
for a PWR UO2 fuel, with initial 235U enrichment equal to 3.3 wt%, subjected to irradiation up
to 40 GWd/MTHM followed by five years of cooling.

IRSW

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regarding PWR UOX fuelTable 3: Negative reactivity in pcm (105.k/k) of burnup credit nuclides(initial enrichment = 3.3 wt%, burnup = 40 GWd/MTHM, cooling time = 5 years)

Actinides

Negative reactivity
Fission products
(pcm)

234

Negative reactivity
(pcm)

143

900

235

145

Nd

410

236

147

Sm

230

149

1030

150

270

151

500

152

Sm

490

241

95

Mo

290

242

Pu

710

103

Rh

1360

237

Np

620

155

Gd

1500

241

Am

1290

153

Eu

390

243

280

109

Ag

250

99

Tc

440

U

120

U
U

910

238

U

238

Pu

Sm

310

239

Pu

240

Pu

Sm
Sm

8370

Pu

Am

Nd

101

Ru

133

Cs

220
750

However, it should be pointed out that the use of these fission products and actinides in thecriticality calculations means that it is necessary to be able to accurately estimate theirabundance after irradiation and to validate the cross-sections of these nuclides in
configurations close to the actual ones. This constraint may lead the criticality expert to
exclude some of the nuclides listed above. Thus, given the lack of critical experiments withfission products, the Americans currently limit themselves to actinides when taking burnup
credit into consideration.
As soon as the choice of nuclides is finalized, it must be ensured that the depletioncalculations, which provide the composition of a used fuel, produce conservative results interms of used fuel composition. This conservatism depends on two factors:-

the accurate description of the irradiation conditions of each modelled assembly or thedefinition of a "penalizing" irradiation history for all of the assemblies. It seems obviousthat accurately describing the irradiation and cooling conditions is not compatible with
conducting generic studies for a given type of assembly; the Working Group has,
therefore, been interested in studying irradiation and cooling conditions;

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regarding PWR UOX fuelthe validation of the chosen depletion codes in the selected field of use (possible use ofcorrection factors to ensure the conservatism of the calculated used fuel composition).

The following paragraphs are devoted to describing the selected approach for each of the twopoints above.

3.1 IRRADIATION HISTORY
For a given burnup, the irradiation conditions may have a significant effect on theconcentration of the selected nuclides. Indeed, according to the reports produced by the
Burnup Credit Working Group in references 14 and 15, together with the DOE report inreference 16, it appears that the fuel reactivity increases when the irradiation conditions
lead to:-a neutron spectrum hardening: this may be linked to the presence of control rods in theassembly, the increase of the boron concentration, the increase of the moderator
temperature, the presence of MOX fuel assemblies close to the assembly or the presenceof burnable poisons;-a decrease in the irradiation time which, for a given burnup, is associated with anincrease in the specific power;-

an increase in the temperature of the fuel.

The remainder of this paragraph will therefore present:-

first, a description of the physical mechanisms that cause the variations in theconcentrations of certain nuclides when an irradiation parameter varies;-

second, the Working Group recommendations with regard to the irradiation conditions
likely to modify the nuclide concentrations of a used fuel assembly.

It will also address the phenomena associated with the cooling time, along with the coolingtime ranges likely to be used in the studies, even though they do not, strictly speaking, form
part of the irradiation conditions.
3.1.1 ASSOCIATED PHYSICAL PHENOMENA

In the remainder of this paragraph, the physical phenomena that lead to the modification of
the nuclide concentrations obtained after irradiation are described, in particular:-

the influence of the burnup on the nuclide concentrations for the selected nuclides;-

the effect of neutron spectrum hardening;

IRSW

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regarding PWR UOX fuel-the influence of the specific power on the used fuel composition;-

the role of the irradiation history, i.e. the length of the irradiation cycles or the presenceof inter-cycles;-

the effect of the fuel temperature;-

finally, the mechanisms associated with the cooling time in the assemblies at the end of
the irradiation cycle.

3.1.1.1 Influence of the burnup
Generally speaking, the nuclide concentration increases with the burnup for all considered
nuclides, with the exception of the following three:-235

U and 238U, which are initially present, and their concentrations decrease during

irradiation;-

149

Sm, which reaches a maximum concentration, then starts to decrease (the IRSN study

in reference 17 shows that the maximum concentration is all the more delayed since thespecific power is high).
In view of this last point, the conditions for including 149Sm would need to be specified.

3.1.1.2 Effect of neutron spectrum hardening
If the irradiation conditions lead to neutron spectrum hardening, there will be fewer fission
processes on the 235U, while the captures on the 238U will increase. These captures will prompt
an increase in the production of plutonium (followed by a greater proportion of fission
processes on the plutonium isotopes, which will harden the spectrum further).
With regard to the fission products, neutron spectrum hardening will lead to:-a change in the distribution of the fission products, since a greater number of fission
processes will occur on the plutonium isotopes, which do not have the same fission yields
as 235U;-

a smaller number of absorption processes associated with the "thermal" fission products(such as 149Sm, 143Nd and 155Gd) during irradiation.

Finally, the calculations show that the reactivity associated with the used fuel is greater
when the neutron spectrum is harder.

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regarding PWR UOX fuel3.1.1.3 Effect of an increase in the specific power
For a given burnup, an increase in the specific power leads to a reduction in the irradiation
time, which reduces the number of radioactive decay events. It is difficult, at first sight, tounderstand the effect of an increase in the specific power on the final concentration, sincemost of the elements are produced by radioactive decay and neutron absorption, but also
disappear in accordance with these two phenomena.
A study was carried out at IRSN, as part of the work cited in reference document 17, on a fuelinitially enriched at 4.5 wt%; this work presented the variation in the concentration of thedifferent nuclides according to the specific power and the burnup. It emerged that anincrease in the specific power leads to:-a low variation in the concentration of actinides, except 239Pu, 241Pu and 242Pu, whose
concentrations increase when the specific power increases, and 241Am and 238Pu, which
decrease;-a very low variation in the concentrations of 99Tc, 101Ru, 109Ag, 133Cs, 143Nd, 145Nd and153

Eu, and a very high variation in the concentrations of 95Mo, 103Rh, 151Sm, 147Sm, 149Sm,

152

Sm, 155Gd and 155Eu.

3.1.1.4 Irradiation history
The irradiation history is linked to the variation in the specific power during the cycles andthe incorporation of "inter-cycle" periods; according to reference document 18, these periods
may lead to significant changes in the concentrations of certain nuclides.
This is because the presence of a sufficiently long cooling period between cycles favours thecreation of elements from radioactive decay events.
If these elements have a large capture cross-section for spectra that are representative of theneutron flux in the reactor, they will disappear when the irradiation process resumes.
As a result:-

For certain "thermal" absorbent nuclides (in particular 155Gd and 241Am), taking a cooling
period into account after irradiation leads to a creation, due to radioactive decay and,
consequently, the disappearance of their parent nuclides.

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regarding PWR UOX fuel31/114

Alternating between shutdown periods and operating phases may, in certain conditions,-lead to the disappearance of thermal absorbents, without the concentration of theparent nuclides having the time to re-reproduce4.

3.1.1.5 Effect of an increase in the fuel temperature
An increase in the fuel temperature causes the resonance of the capture cross-sections of 238U
to increase, which leads to greater absorption on this nuclide (Doppler effect). Theseabsorptions on 238U prompt an increase in the production of plutonium and, for a given
burnup, a lower consumption of 235U.

3.1.1.6 Cooling time
The IRSN calculations presented in reference document 17 showed that reactivity decreases
until the cooling time reaches 100 years. The figure below is taken from reference
document 17.
0.76
0.75
0.74
0 73
0.72
0.71

—4— Assembly surreundedwith 20cm cf water

keff
07

Storage pool(higher standing assembles)

0.69—D- Storage pool(drepped assembly)

0.68

Storage pool(off-centered assemblies)

0 57
055
0.65
0.64
10

100

1000

Ti me in C.x.-1) years

Figure 9: Effect of the cooling time on the effective multiplication factor after an irradiationof 44 GWd/MTHM (on an assembly initially enriched at 4.5 wt%)
This decrease in reactivity, during the first 100 years following irradiation, is linked to theincrease in 155Gd (whose concentration increases until the cooling time reaches 50 years) andthe decrease in 241Pu (together with the increase in 241Am). The concentrations of 151Sm and238

Pu decrease, which should lead to an increase in reactivity. However, this has no4

The absorbent nuclides 149Sm and 143Nd, in the "thermal" domain, see their concentrations increase by 55% and 3%
respectively during the first year of cooling, following an irradiation period of 44 GWd/MTHM (according toreference document 17). The concentration of 239Pu also increases by 2%. Their concentrations will reduce with theresumption of irradiation.

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regarding PWR UOX fuel32/114predominant effect on reactivity (for cooling times of less than 100 years, only theconcentrations of 241Pu, 241Am, 238Pu and 237Np vary to any significant degree).
For cooling times of more than 100 years (but less than 500 years), the reactivity increases
slightly. This increase is mainly linked to the disappearance of 241Am (which reduces by 14%
during a cooling time of between 100 and 200 years). The number of 241Am atoms decreases,
just as the number of 237Np atoms increases (but this nuclide has a smaller cross-section than
241

Am).

The criticality studies conducted by the ANDRA, to define a concept for irreversibly storing
used fuel assemblies in deep geological layers without prior reprocessing, led EDF/SEPTEN to
conduct a close analysis of changes in reactivity over periods of up to 5 million years (seereference document 19).

— 10 GWd/MTHM
000

20 GWdIMTHM

0,85

0,80

30 GWd/MTHM

0,75■ 40 GWd/MTHM
0,70. 50 GWd/MTHM
0,85

_ _-•

0,60
1E-02

1,E-01

1.E+601,E+02

1E+01

1,E+03

1E+0,1

1E+06

1,E+06

Years of cooling

Figure 10: Changes in the keff value of a storage cask according to the cooling time and burnup
Essentially, the change in the reactivity of the used fuel assemblies without flux consists ofthree main phases.
Between leaving the reactor and around 100 years of cooling, the decay:
241

Pu



241

Am

T1 / 2 14.3 yrs

causes a significant decrease in reactivity.

I RS

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regarding PWR UOX fuelBetween 100 years and around 30,000 years of cooling, the decay:
241

Am



237

Np

T1 / 2  432 yrs
240

Pu



236

U

T1/ 2  6555 yrs

causes a significant increase in reactivity.
Between 30,000 years and around 1 million years of cooling, the decay:
239

Pu



235

U

T1 / 2  24204yrs

causes a decrease in reactivity.
Depending on the nature of the problem, different cooling times will need to be considered:-

For handling or interim storage operations that start during the first few hours afterreactor shutdown, possibly extending over a few decades, a fixed cooling period of
30 days must be taken into account to provide the most penalizing used fuel composition,
particularly through the reaction:
239

Np



239

Pu

T1 / 2 2.35days-

For handling or interim storage operations that start x years after reactor shutdown(x >> 30 days), which may extend over y years (y < 100 years), a maximum cooling periodof x years may be taken into account to take advantage of the fall in reactivity following
an initial cooling phase.

The findings from this study are in line with the results obtained by Parks and Wagner inreference 18.
3.1.2 WORKING GROUP CONCLUSIONS ON THE IRRADIATION CONDITIONS

Initially, the Working Group was interested in PWR UOX fuel, with initial 235U enrichment of
up to 5 wt%, and a burnup less than or equal to 60 GWd/MTHM.
The conclusions below were drawn from the studies conducted at IRSN, EDF, CEA and SGN
and, in particular, from reference documents 17, 21 and 30.

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regarding PWR UOX fuelEffect of neutron spectrum hardening
It appears that the neutron spectrum can be modified by: the presence of control rods, thesoluble boron concentration, the temperature of the moderator, the presence of burnablepoison, or the presence of MOX fuel in the immediate vicinity of the UOX fuel.
The consideration of control rods during irradiation is conservative. Reference documents 8,
20, 21 and 30 show that, for an isolated assembly (with initial enrichment between 3 wt% and5 wt%), the difference between taking account of the control rods and disregarding themleads to an increase in reactivity of up to 5,000 pcm (in k) for a burnup of 40 GWd/MTHM.
Reference document 21 also shows (see Appendix 10) that for an infinite lattice of PWR UO2
assemblies, initially enriched at 4.5 wt% and irradiated at 40 GWd/MTHM, the reactivity
penalty (Δk) due to the full axial insertion of a control rod during a cycle is between 500 pcm(if the control rod is inserted during the first cycle) and 2,100 pcm (if it is inserted during thethird cycle).
The investigations carried out by EDF on around 40,000 assemblies, in five major assembly
families, made it possible to determine the proportion of assemblies that were irradiated in
the presence of control rods, depending on the core management method (see Appendix 10).
The findings from this study show that, regardless of the management method, fewer than 1%of the assemblies can be irradiated with the presence of control rods in all cycles, and around
50% of the assemblies are never irradiated with control rods inserted. It can also be seen thataround 23% of the assemblies were irradiated with control rods inserted during their lastirradiation cycle.
The table below shows the insertion history of the rods, depending on their function.
Table 4: Different control rods used in French reactors

IRSW

Type of rod

Function

Insertion during irradiation

S

Emergency shutdown
rodRods extracted (inserted by 5cm)

R

Control rod(temperature)

Variable (depending on the power level, control
and management of the core)
Represents around 10% of the fissile height at
nominal power

N

Black rod (power)

Variable
Fully extracted at nominal power

G

Grey rod (power)

Variable
Fully extracted at nominal power

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regarding PWR UOX fuelMaximizing the boron concentration maximizes the associated spectrum effect. The studies
conducted at CEA showed that modelling the actual concentration variations during the cycle
had little effect on the concentration of actinides (the difference observed when using theDARWIN package – see paragraph 3.2.2 - to validate PWR MOX fuel was less than 0.5% for theconcentrations of uranium, plutonium, americium and neptunium - see reference 22. Thus, acalculation performed using a constant concentration value equal to the maximum boron
concentration value gives a maximum keff value.
For the moderator temperature, it is conservative to consider the core maximum output
temperature.
The presence of burnable poisons is also likely to lead to a hardening of the neutron
spectrum. A study was conducted at CEA to assess the impact that UOX assemblies irradiatedwith gadolinium rods would have on the kinf value. In France, some core management methods
include fuel assembly reloads containing gadolinium rods.
These gadolinium rods may have a depleted uranium (0.715 wt%) or an enriched uranium(2.5 wt%) support. As an example, the CYCLADES management method for the PWR 900 CP0series includes, out of the 52 reloaded assemblies, 36 assemblies with 12 gadolinium rods
(8 wt% gadolinium) and uranium support equal to 0.715 wt%. HTC1 management (900 CPY
PWR) includes, among the 48 reloaded assemblies, 32 assemblies with 12 gadolinium rods
(8 wt% gadolinium) and 2.5 wt% uranium support, and 16 assemblies with 4 gadolinium rods
(8 wt% gadolinium) and 2.5 wt% uranium support. The GEMMES, GALICE and HTC2
management systems for the 1300 PWR, and the ALCADE method for the 1450 PWR, also
involve reloads with assemblies with gadolinium.
The study therefore involved performing a depletion calculation (using the APOLLO2 code) for
an assembly containing a certain number of gadolinium rods, then recalculating kinf using the
CRISTAL package. The first part of the study showed that the presence of gadolinium rods had
a low impact on the BUC nuclide concentration, with the exception of the plutonium andamericium isotopes, whose concentrations at low burnup increased by a few percent. These
effects diminished with the burnup, reflecting the consumption of the gadolinium (seeAppendix 11).
In the case of an interim storage pond, the presence of UO2-Gd2O3 rods reduced Kinf by
3,000 pcm at 2 GWd/MTHM, due to the presence of gadolinium 155 in the gadolinium rods.
This decrease became less marked as soon as the burnup exceeded 20 GWd/MTHM. In thelight of these results, it is therefore conservative to take account of the fact that the

IRSW

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regarding PWR UOX fuelassemblies were irradiated without gadolinium rods in the depletion calculation diagram forburnup credit.
A study by AREVA-NP showed that for an enrichment of gadolinium rods between 3 wt% and4 wt%, the conclusions are not the same. For example, if the enrichment of rods containing
gadolinium is equal to that of rods that do not contain gadolinium, an assembly withgadolinium that has undergone more than one irradiation cycle will be more reactive than an
assembly that does not contain gadolinium rods with the same burnup.
Furthermore, the studies conducted for the LINGAO nuclear plant (presented in Appendix 12)
revealed distortion in the axial burnup profile due to the presence of gadolinium rods. Thus,
for a burnup of 37.7 GWd/MTHM and initial 235U enrichment of 4.45 wt%, the presence ofeight gadolinium rods during irradiation gives the profile a residual penalty of around 100 pcm
for each gadolinium rod, due to the fact that the gadolinium was not used at the ends.
From the internal NRC document, reference 23, it appears that the burnable poisons used in
the USA can be grouped into two categories:-

burnable poisons in the form of absorbent rods inserted into tubes (BPRs); this type of
poison leads to a more reactive situation after irradiation than when the assembly does
not contain burnable poison (in particular, the neutron spectrum is hardened by thepresence of the absorbent rods, and when these rods are extracted, generally at the endof the first irradiation cycle, this results in a moderating ratio within the fuel that ismore favorable to the chain reaction);-burnable poisons in the "integral" form (IBAs); the absorbent is integrated into thecladding of certain fuel rods (IFBAs) or is mixed with uranium oxide; according to theabove study, the impact of their presence on the effective multiplication factor remains
low and, for assemblies that do not contain IFBAs, leads to a lower reactivity after
irradiation than for assemblies irradiated without burnable poison (this decreasing
reactivity is mainly linked to the insufficient quantity of fissile matter at the beginning oflife).

With regard to the effect of the presence of MOX fuel during irradiation in close proximity to
the UOX fuel, the following points have emerged from the calculations performed by CEA,
which are presented in Appendix 2:-

the presence of four MOX assemblies placed at the four corners of the UOX assembly has
no obvious effect on the concentration of the nuclides selected for our studies;-

the presence of four MOX assemblies, placed opposite the UOX assembly, slightly
modifies the concentrations of 236U, 238U, 240Pu, 103Rh, 133Cs and 143Nd; however, thisIRSW

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regarding PWR UOX fuelconfiguration significantly modifies the concentrations of 235U, 239Pu, 241Pu, 242Pu, 241Am,
237

Np, 149Sm, 151Sm, 152Sm and 155Gd.

From the study presented in reference 21 and detailed in Appendix 2, it was found that thereactivity of a lattice of UOX assemblies in the pool increased when each UOX assembly wasirradiated with a complete MOX environment. This increase ranged from 40 pcm for theassemblies irradiated up to 10 GWd/MTHM to 1,250 pcm for assemblies irradiated at
40 GWd/MTHM.
This latter case corresponds to a very high and unrealistic MOX usage rate, as it would occur
during the entire irradiation process; the effects are therefore enhanced here.
Specific power
It is conservative to adopt the maximum specific power, provided that a particular process isused for the 149Sm, 151Sm and 155Gd.
The findings presented in paragraph 3.1.1.3 show that the hypothesis of a maximum specificpower will maximize the concentrations of the fissile nuclides and will minimize theconcentrations of the "absorbent" nuclides.
However, taking 149Sm and 151Sm into account, with a maximum specific power, is notconservative in principle (since the concentration of these absorbent nuclides decreases when
the specific power reduces). Similarly, the calculation of the concentration of 155Gd, which
depends mainly on the decay of 155Eu, will not be conservative when the specific power isincreased, given the overestimation of the production of 155Eu. Finally, we should insist on thefact that this phenomenon will be particularly sensitive at the ends of the assembly, where
the specific power during irradiation is the lowest. Studies are therefore required todetermine correction factors for the concentrations of the four nuclides mentioned above;these must take account of the overestimation of the concentrations of these nuclides,
combined with the hypothesis of an increased specific power.
Another possible approach would involve reasoning in terms of overall conservative used fuelcomposition rather than in terms of used fuel composition, nuclide by nuclide. The CEA and
IRSN reports in references 21 and 30 show that reactivity has a low sensitivity to the specificpower, particularly within the realistic range of 30-50 W/g. A bounding value could therefore
involve selecting a specific power that is slightly greater than the mean specific power in thereactor.

IRSW

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regarding PWR UOX fuel38/114

Irradiation history
With regard to the effect of the possible presence of inter-cycle periods, and the effect ofvariations in the specific power during the cycles, the study cited in reference 14, together
with a study conducted by the DOE in reference 18, indicates that the consequences of suchvariations on the effective multiplication factors are small5 (about a few hundred pcm).
Moreover, given the conservatisms used, and in order to simplify the calculations, it seems
acceptable to retain only one irradiation cycle.
Fuel temperature
For the mean fuel temperature, it is more conservative to consider a temperature that ishigher than the maximum mean temperature reached during normal operation.
Cooling time
The needs of the different members of the Working Group differ according to the nature of
the studies carried out:-

for transportation and interim pool storage, minimum cooling times are greater than orequal to 6 months;-

for reprocessing, minimum cooling times are greater than or equal to 3 years;-

for pools holding fuels irradiated in the reactor, typical cooling times are between 0 daysand 3 months;-

for in-containment fuel storage, minimum cooling times are greater than 30 or 50 years;-

for storage in deep geological layers, minimum cooling times are greater than 100 years.

Reactivity decreases over a cooling period of 100 years, and then increases over a period ofaround 30,000 years, all things being equal (same geometry, same environment, absence ofcorrosion, etc.).

5

There is a connection between the irradiation history and the cooling time, which plays a part in determining themost penalizing situation. If we consider two irradiation histories, the first involving continuous irradiation without
inter-cycles, and the second having six irradiation cycles with a two-year shutdown before the final cycle, it appears(according to the ORNL document, reference 18) that the concentrations of 155Eu and 241Pu after irradiation decreasein the second case, as well as the concentrations of 155Gd and 241Am. This is because, after irradiation, the 241Pu and155
Eu, which disappeared during the inter-cycle period, did not have the time to reach the values obtained before
the inter-cycle. The 241Am and 155Gd produced during the inter-cycle period are consumed when irradiation resumes.
Thus, for a cooling time of five years, the predominant effect will be the fall in the number of 241Pu atoms: the mostpenalizing case consists of one continuous irradiation cycle. On the other hand, for a cooling time of 200,000 years(over ten times the decay period for 241Pu and 241Am), the predominant effect is the decrease in 155Gd (linked to thedecrease in 155Eu) when an inter-cycle period occurs: the most penalizing case consists of the presence of an intercycle period at the end of irradiation. However, the differences in terms of k remain very small (less than
500 pcm).

IRSW

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regarding PWR UOX fuelConsequently, for operations or configurations in which the cooling time is less than
100 years, is seems that the minimum cooling time guaranteed by the operator may be used(for cooling periods of less than 20 days, consideration should be given to the fact that theconcentration of 239Pu is increased by the concentration of 239Np6). However, when a study
uses a non-zero cooling time, it is essential:-

either to ensure that the operation is specific for a "de facto" cooling time of less than
100 years (such as in the case of transportation);-or, for interim storage operations where the cooling time CT0 used in the criticality
studies is not zero, to guarantee that the reactivity during storage never exceeds thelevel obtained during the cooling time CT0 (see references 19 and 24 together with thestudy described in Appendix 9).

With regard to this last point, for operations or storage subject to a cooling time that could
exceed 100 years, it would be possible to disregard the 241Am and, if necessary, the 240Pu, inthe studies. The study presented in Appendix 9 appears to show that, in general, for handlingorinterimstorage

operations

that

take

place

z

years

after

reactorshutdown(z < 1,000 years), a fixed cooling period of 30 days will guarantee the conservative nature of
the calculation. However, if it can be demonstrated that there is a cooling period of between
30 days and 100 years that can guarantee the penalizing nature of the calculation, then thistime may be used to reduce the calculated reactivity.
For handling or interim storage operations that take place t years after reactor shutdown(t > 1,000 years), an increase in reactivity over and above that recorded initially after 30 daysof shutdown is possible but not systematic (see Appendix 9); the conservative nature of the
hypotheses must therefore be demonstrated, given that the peak in reactivity occurs between
20,000 and 40,000 years.

3.2 CONCENTRATIONS OBTAINED FROM THE DEPLETION CODES
3.2.1 DEPLETION CALCULATION CODES

The calculation of the nuclide concentrations in the used fuel for a given burnup is commonly
known as "depletion calculation". It involves resolving the depletion equations for eachnuclide, taking account of the initial composition of the fuel, its irradiation history (burnup,

6

The 239Np transforms into 239Pu over a period of around 2.5 days.

IRSW

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regarding PWR UOX fuelspecific power, flux spectrum, cooling time, etc.), and nuclear data (cross-sections, decay
constants, decay chains, etc.).
3.2.2 FRENCH CALCULATION CODES

The APOLLO, DARWIN and CESAR codes are the calculation codes used by the Working Groupon burnup credit for the parametric studies. The studies may be conducted with either one ofthe depletion codes, in the knowledge that the concentrations obtained can be modified by acorrection factor, which depends on the validation of the code and the source data used.
The DARWIN V2.0 code is fed by cross-section libraries (Saphyb) from APOLLO 2.5 calculations
with the CEA 93.V6 library. The CESAR V5 code is also fed by cross-section libraries from
APOLLO 2.5 calculations with the CEA 93.V6 library; this is a simplified code which can beused to interpolate tabulated results to determine the concentrations of a used fuel.
The DARWIN (PEPIN 2) and CESAR depletion modules resolve the fuel depletion equation using
cross-sections collapsed into one group for all of the capture reactions. For decay, the CESAR
and DARWIN codes use the values from the JEFF 2.2 evaluation.
The DARWIN code underwent a validation programme, presented in Appendix 3, which was
based on determining the differences between the calculated concentrations and themeasured concentrations ((C-E)/E):-in the used fuel samples taken at the mid-point of the used fuel assemblies;-in "dissolution juices" at La Hague, involving the dissolution of two assemblies at most.

The CESAR code was validated in relation to the DARWIN code.
With regard to this last point, it is important to note that the analyses conducted on"dissolution juices" (providing the mean concentration of a given nuclide C (X ) for the mean
burnup BU ) are only able to validate a "dissolution" approach. As the concentration of thenuclides is not proportional to the burnup, these analyses cannot validate the depletioncalculation code for determining a concentration (C(X)) for a burnup BU (even if BU = BU ).
This basis for validation covers the validation of the used fuel composition for UOX fuels withenrichments of 3.1 wt% to 4.5 wt% for burnups of 10 GWd/MTHM to 60 GWd/MTHM. Reference
document 25 shows that the results were satisfactory for nuclides 234U, 235U, 236U, 239Pu, 240Pu,
241

Pu and 241Am: (C/E)-1  5%. Nuclides 238Pu and 242Pu are underestimated by -11% and -7%

respectively. With regard to the burnup credit fission products, the validation results are
satisfactory for neodymium isotopes 143 and 145, samarium isotopes 147, 150 and 152, andIRSW

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regarding PWR UOX fuelcesium 133. Only the

151

Sm,

153

Eu and155

Gd are significantly overestimated, withcalculation/experiment differences of 13%, 16% and 12% respectively at 60 GWd/MTHM.
For metal fission products, the current analytical results do not provide a conclusion (due toan insolubility problem from 30 GWd/MTHM). However, only silver 109 is highly
underestimated (see Appendix 5).
In order to take account of the burnup credit in criticality studies, correction factors to be
applied to the concentrations of the selected nuclides are currently being defined for the
CESAR and DARWIN depletion codes (see Appendix 7, documents 26 and 27, and articles 28
and 29).
In order to assess the effect of correction factors on the concentration of actinides,
calculations performed by IRSN and reported in reference 30 demonstrated the effect of a 1%
variation in the nuclide concentrations, for a fuel initially enriched at 4.5 wt% and forburnups lower than or equal to 44 GWd/MTHM. The main effects are shown in Table 5 below.
Table 5: Effects (determined from a perturbation calculation) of a 1% variation in theconcentrations of U235, Pu239, Pu241 and Pu240 on the reactivity of a fuel element, with initialenrichment equal to 4.5 wt% and irradiated up to 44 GWd/MTHM, and for a non-perturbed(standard) burnup profile
Nuclide variation

235

of +1%
kU+ 104 pcm

239

Pu

+ 75 pcm

241

Pu+ 29 pcm

240

Pu- 28 pcm

Finally, it should be noted that the DARWIN and CESAR depletion codes provide the final
number of atoms for each nuclide per metric ton of heavy metal. However, in order tocalculate the effective multiplication factor with CRISTAL, we need to know theconcentration of the nuclides in atoms/cm3. Also, it is conservative to use the density of the
fresh fuel applied to the selected nuclides (which means artificially increasing their number
by around 1%).

3.3 CONSERVATIVE CONCENTRATIONS
To conclude, in order to determine the nuclide concentrations using calculation codes such as
APOLLO, CESAR or DARWIN, it is conservative to adopt the irradiation conditions defined in
the previous paragraphs, namely:-

IRSW

the presence of control rods;
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regarding PWR UOX fuel-the presence of an environment of MOX fuel assemblies;-

a boron concentration greater than the mean concentration during the cycle;-

the output temperature of the core for the moderator;-

the maximum mean effective temperature of the fuel;-the maximum specific power during a single irradiation cycle, possibly with, for certain
nuclides (149Sm, 151Sm, 242Pu and 155Gd (child of 155Eu)) the incorporation of correction
factors. However, a study has shown that a specific power that is slightly higher than themean power will not change the keff values significantly.

The values to be used with regard to the geometry of the used fuel remain to be defined.
To ensure conservatism when taking burnup credit into account, the concentration values
obtained by the calculation will be modified by a correction factor, resulting from thevalidation of the version of the depletion calculation code used (APOLLO, CESAR or DARWIN).
Moreover, the density retained for the used fuel, consisting of only those nuclides selected
for the approach, may, conservatively, be taken to be equal to the density of the fresh fuel.
Some of these constraints could be relaxed, as the associated demonstrations are yet to be
developed in each specific case.

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4 METHOD
FACTORFOR

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regarding PWR UOX fuel

CALCULATINGTHE

EFFECTIVE

MULTIPLICATION

The previous chapters have listed the hypotheses that must be used to ensure that thecharacteristics of the modelled used fuel assembly are conservative, particularly with regard
to the irradiation history, the burnup profile and the measurement methods for checking theburnup.
The used fuel assemblies, with their burnup profile and nuclide concentrations, are the input
data for the criticality calculations, which are addressed in this chapter. The paragraphs that
follow describe:-

the calculation methods used to obtain the multiplication factor, based on the burnup
profile and the concentrations associated with each axial zone of the fuel;-the validation of the calculation methods, particularly in view of the consideration offission products;-

the problems associated with the calculation methods used (notably the Monte Carlo
method), given the loose neutron couplings between the two ends of a used fuelassembly, together with the proposed solutions.

4.1 CALCULATION SEQUENCE
The calculation sequence described below is based on the CESAR and DARWIN depletioncalculation codes, together with the CRISTAL criticality package. This description is only one
example of a calculation sequence; other sequences based on the same principles may also be
considered (such as STARBUCS using the ORIGEN code and the SCALE system).
The effective multiplication factor is determined using the CRISTAL V1 package, which was
subject to the specifications in reference 31.
The nuclide concentrations, derived from a CESAR V5 or a DARWIN V2.0 calculation, arecomputed for each burnup value, corresponding to the different axially divided zones
selected.
Concentration

correction

factorsareintroduced

to

take

accountofthecalculation/experiment difference between the used fuel compositions, and also, where
necessary, to correct their cross-sections and take account of the overestimation of certain
absorbent nuclides when a maximum specific power is assumed.

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regarding PWR UOX fuel44/114The effective multiplication factor is calculated using the APOLLO and MORET codes("standard" route) or the TRIPOLI code ("reference" route; in this case, the cross-sections aretaken directly from the libraries used by TRIPOLI and the input data are the nuclide
concentrations for each axial zone). The input files for these codes contain the geometricdescription of the modelled system with, for the used fuel assemblies, a number of zones
with the zone heights defined in advance, based on the burnup profile selected for the study.
All of these stages are represented in Appendix 4 (for the CRISTAL V1 “standard” route).

4.2 VALIDATION OF
CALCULATIONS

THE

CROSS

SECTION

LIBRARIESANDCRITICALITY

The validation of the cross-sections of the fission products used is based on:-

the oscillation experiments conducted in the MINERVE reactor in Cadarache;-the "Fission Products" experiments conducted at the Apparatus B experimental facility in
Valduc.

With regard to the oscillation experiments (see Appendix 6), the central rod oscillation
spectrum is characteristic of "fuel transportation" and "pool storage" in the R1UO2
configuration, and "fuel dissolution" in the R2UO2 configuration; these experiments are able todetermine the reactivity of a sample, with either an inert (alumina matrix) support or auranium oxide support, doped with the examined fission product. By making a comparison
with CRISTAL calculations, it is possible to determine whether the cross-section of the fission
product studied, collapsed into one group on the core energy spectrum used during theexperiment, is known in a satisfactory way. During the Burnup Credit programme associatedwith these experiments, 15 fission products7 were tested.
The interpretation of the oscillation experiments on separate samples of fission products (seereference 32) updated the overestimation of99

Tc and133

Cs (4% in R1UO2). The

calculation/experiment discrepancies are satisfactory with regard to the 153Eu, 109Ag, 152Sm,
145

Nd and 155Gd (underestimation of less than 2%). The 143Nd and 95Mo were underestimated by

4% in R1UO2, and the 149Sm by 6%. For the 103Rh, the interpretation of the oscillation
experiments revealed a considerable overestimation (13% in R1UO2), which would need to bemoderated due to the fact that the dissolving technique induces fairly significant analyticaluncertainties.
7

The 15 fission products are those recommended by the OECD, i.e. the "first" six fission products ( 149Sm, 103Rh, 143Nd,
Cs, 152Sm and 155Gd) together with the following nine fission products: 101Ru, 95Mo, 99Tc, 147Sm, 150Sm, 151Sm, 145Nd,
109
Ag and 153Eu.
133

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regarding PWR UOX fuelNo information or trend could be ascertained in relation to the individual poisoning of
nuclides 147Sm, 150Sm, 151Sm or 101Ru, as the capture of these samples is largely attributable to
the residual 149Sm or the 99Ru with regard to the 101Ru.
Furthermore, it appears that to obtain the above results, the multi-group cross-sections of
the fission products have to be self-shielded.
As for the "Fission Products" experiments conducted at the Apparatus B experimental facility
in Valduc from 1997 to 2004 on installation B, described in references 33, 34, 35, 36 and 37,
these involve the "first" six fission products8 and are divided into three different configuration
types:
the "physical" type experiments: a tank filled with a solution containing a given fission-

product (or a mixture of fission products) is placed in the center of a control lattice ofuranium oxide rods; these experiments are used to validate the cross-sections of eachseparate fission product in spectra similar to those encountered during transportation andin dissolution solutions;the "elementary dissolution" type experiments: a tank filled with a solution containing-

either a given fission product, surrounded by a control lattice of UOX or HTC fuel rods9,
or a mixture of fission products and uranyl nitrate, with a lattice of UOX or HTC fuel rods,
is placed in the center of a lattice of uranium oxide rods; these experiments are used tovalidate the interactions between the cross-sections of the fission product and theactinides and, therefore, to validate the self-shielding models (resonance overlap).
the "global dissolution" type experiments: a tank filled with a lattice of UOX10 or HTC fuel-rods is placed in a solution of depleted uranyl nitrate containing a mixture of the six
fission products; these conditions are very similar to the environment encountered in a
dissolver, with no self-sustained critical reactions in the system.
The experiments were conducted then modelled and used with the CRISTAL package. The
following comments can be made on the results obtained:
in the experiments, the reactivity worth of each fission product (negative reactivity-

provided by the fission product) is high enough to be able to validate its absorption

8

The 95Mo will also be used in the FP experiments described in reference 33.

9

The HTC fuel rods (high burnup fuel rods) were manufactured to contain the quantity of uranium and plutonium
corresponding to uranium oxide initially enriched at 4.5 wt% and irradiated to reach a burnup of
37,500 MWd/MTHM.

10

In the configuration with UOX rods, the solution does not contain any FPs.

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regarding PWR UOX fuel46/114(around 4,000 pcm); only the 133Cs and 143Nd experience a slightly lower negative
reactivity due to their smaller quantities in the solution;from 100 to 400 pcm, the effective multiplication factors obtained by the calculation-(using the CRISTAL V1 "standard" route) are still11 slightly higher than 1, which isconservative;
the propagation of the experimental uncertainty in terms of keff is less than 100 pcm-(1 ).
In addition, the calculations performed in the normal way using the CRISTAL package (theidentification details of which are provided in reference 38) are validated based on themethod described in reference document 39.

4.3 CALCULATION CONVERGENCE AND LOOSE NEUTRON COUPLINGS FOR CODESUSING A MONTE CARLO METHOD
In the used fuel storage or transport configurations, most of the reactivity comes from theends of the fuel assemblies, which are the least irradiated parts. The central part of theassembly, separating the two ends, is particularly large compared to the mean free path of
the neutrons. Furthermore, this zone contains fission products resulting from irradiation,
which are highly absorbing. These two factors (distance from the fissile zones and separationby the absorbing materials) mean that the two ends of an assembly are loosely coupled froma neutron point of view. In other words, the probability of a neutron passing from one fissile
zone to another is relatively low.
With any of the criticality calculation codes using the Monte Carlo method, converging
towards the correct effective multiplication factor value can be problematic when theconfiguration contains loosely coupled fissile units. This is because a Monte Carlo calculation
is iterative, and the source sites of the neutrons simulated during one step are chosen fromthe fission sites stored during the previous step. The calculation bias may thus result from theincorrect initial positioning of the neutrons by the user, an insufficient number of neutrons
simulated at each step of the calculation, or an insufficient number of calculation steps,
culminating in an under-representation, or even the omission, of particularly reactive fissile
zones.
After a calculation has been performed, the fuel zones at the ends of the assemblies must be
checked to ensure that they are "visited" by a sufficient number of neutrons.
11With the exception of the 103Rh (elementary dissolution) for which a slight underestimation of around 300 pcm isobserved.

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regarding PWR UOX fuelTo counter this "source convergence" problem inherent to using the Monte Carlo method for
criticality calculations, different methods for simulating and sampling the source neutrons
from the fission sites have been refined by the teams developing the Monte Carlo computercodes, and have been subsequently tested.
The source convergence problem is being studied by the OECD / NEA "Source Convergence"
Working Group, and the MORET 4 code in the CRISTAL package is being developed, to make iteasier to position the sources and detect poor calculation convergence.
Four simulation methods, which are described in Appendix 13 and presented in reference 40,
are available in the MORET 4 code. The effectiveness of each one is currently being examined
for the "Source Convergence" Working Group.
To describe the distribution of the source neutrons in the first generation of a Monte Carlocalculation, it is currently recommended to proceed as follows:-

use the SUNI option (the source neutrons are distributed in equal number across all of thefissile volumes), which guarantees that all of the fissile volumes will be "visited" during
the first generation, and thus reduces the likelihood of a fissile volume being "forgotten"
throughout the simulation;-

place additional source neutrons at the ends of the assemblies to more accurately
reproduce the supposed spatial distribution of the neutrons.

It is evident that the standard checks, relating to the convergence curve profile and thevariations in the final multiplication factor value if the first steps in the calculation are
removed, are still required.
Finally, it should be noted that, when the fuel is highly irradiated and most of the reactivity
comes from the ends of the used fuel assembly, the initial placement of the sources in thiszone leads to an overestimation of the effective multiplication factor in the first steps in thecalculation (the spatial distribution of the neutrons does not, therefore, take complete
account of the neutron leakage outside these volumes) and, consequently, an overestimationof the final effective multiplication factor. This choice is therefore conservative.

4.4 CONCLUSIONS ON THE CALCULATION METHODSTaking burnup credit into account complicates the criticality calculations and therefore
increases the risk of modelling errors. This problem spurs the need to develop appropriatecomputing sequences to automatically take account of burnup credit in the calculations.

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The Working Group believes that particular attention should be paid to monitoring the data
and assuring the quality of the computing sequences.
By way of example, the new CRISTAL V1 criticality package, for performing automatedcriticality calculations that take burnup credit into account, has been described.
Depletion calculations are first performed to determine the conservative concentrations of
the different nuclides, to which correction factors may be applied, for each elementary axial
zone linked to the discretization of the burnup profile. The keff calculation is then performed
using the CRISTAL package.
The CIGALES code, a component of the CRISTAL V1 interface, is currently coupled with the
CESAR 5 depletion calculation code. A similar coupling with the DARWIN V2.0 package is alsoavailable. The CIGALES code is designed to automatically generate APOLLO2 data files for thecriticality calculations. It allows the user to select and take account of:-correction factors (applied to the actinide and fission product concentrations), which
are determined from the validation of the depletion calculations and the cross-sections;-the assembly axial burnup profile;-the number of axial zones modelled.

The links between the different calculations are shown in the two diagrams below (takenfrom Appendix 4).
The validity of the CRISTAL calculations depends on the validation of the cross-sections of thenuclides taken into account, together with the computer codes for the modelled
configurations. In this regard, the experiments conducted in the MINERVE reactor in
Cadarache, and at the Apparatus B experimental facility in Valduc, will enable us todetermine whether it is necessary to apply correction factors to the concentrations and/or totake account of a calculation bias.
These calculations (taking fission products into account) are currently undergoing validation
for the package “standard” route (APOLLO2-MORET4).
Finally, the modelled configurations involve assemblies whose reactivity is very highly
dependent on the under-irradiation at the ends; but the ends of the fuel assemblies have veryloose neutron couplings, which remains difficult to process in the Monte Carlo calculations.
Consequently, certain precautions must be taken, particularly when initially positioning theneutron sources.

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regarding PWR UOX fuelDepletion calculations performed without the CRISTAL package, based on a burnup profile(with conservatism verified)

C1(X)

BU1
BU2

BUk

C2(X)

Penalizing
historyC3(X)

BU3
DEPLETIONCALCULATION

BU4

C4(X)

Ck(X)
Nuclide X

BU5

C5(X)

Criticality calculations performed with the CRISTAL package, based on data provided by the depletion codes
and modified by correction factors where necessaryCk( X)
C1(X)

Pij

C4(X)

C5(X)

IJ
D
2

C2(X)
C3(X)

1

3

Geometry
description

4

k

MC

5

Keff

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5 CONCLUSIONSThe previous chapters have presented the various steps implemented in a criticality
calculation that takes burnup credit into account. Furthermore, subject to the availability of
information, sensitivity to the parameters involved in each of these steps has also been
discussed. This report covers the domain of PWR UOX fuel with 235U enrichment of less than
5 wt% and a burnup of less than 60 GWd/MTHM.
This approach suggests the following stages:-

determine the burnup profiles;-

discretize the previously selected profiles into N zones with a given burnup;-

for each of the axial zones, compute the concentrations of the selected nuclides using
depletion codes. The first approach studied by the Working Group involved guaranteeing
the conservatism of each stage; these calculations are performed with a penalizing
irradiation history;-

apply correction factors to the concentrations of certain nuclides, bearing in mind thecalculation/experiment discrepancies relating to the used fuel composition, and if
necessary, the cross-sections and the variation in certain nuclides depending on theselected irradiation parameters;-

calculate the effective multiplication factor, adopting an additional margin for thecriteria if necessary, depending on the validation being carried out.

The validity of the method is based on the validation of the burnup profile used for the
calculations. The only validation method examined to date by the Working Group involved
measuring the actual burnup and the axial burnup profile of the assemblies actuallytransported, handled or stored.
In certain cases, where the licensee does not wish to take any measurements, the use of apenalizing profile may be considered. However, the conservatism of the choice of profile
must be provided by other profile validation methods. These will be presented in a revision ofthis document.
Each of these stages is dependent on modelling decisions, some of which have already been
evaluated; the most conservative choices are shown in the table below.

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regarding PWR UOX fuelConservative hypothesis
Presence of a control rod
Boron concentration greater than the mean concentration during the cycle

I
R
R
A
D
I
A
T
I
O
N

Moderator temperature equal to the core maximum output temperature

Fuel temperature equal to the maximum mean effective temperature

Presence of MOX in the environment

H
I
S
T
O
R
Y

Irradiation during one single irradiation cycle

Maximum specific power, with the possible use of correction factors for 149Sm,
Sm, 155Gd and 242Pu or specific power slightly greater than the mean specific
power

151

For cooling times of less than 100 years, the cooling time is taken to be equal tothe minimum guaranteed cooling timeP

Selection of a conservative profile

R
O

Determination of the optimal number of axially divided zones

F
I

Axial discretization, selecting the BUmin for each zone

L
E

Maximum horizontal burnup gradientS

MEASUREMENTSKEFFCALCUL-

Incorporation of measurement uncertainties

Correction factors for the concentrations, from the validation of the used fuelcomposition calculation and the cross-sections of the fission products
Fuel density with the selected nuclides equal to that of the fresh fuel

ATION

Calculations with the Monte Carlo codes, initially placing sources in all of thefissile volumes and additional sources at the ends

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Finally, the conservative approaches studied by the Working Group were found to have an
impact on reactivity compared to the "best estimate" scenario, as shown in the tablebelow:

I
R
R
A
D
I
A
T
I
O
N
H
I
S
T
O
R
Y

PROFILES

Calculation options

Effect on keff (1)Presence of a control rod during irradiation

At most: + 5,000 pcm

Boron concentration equal to 600 ppm (instead of456 ppm)+ 300 pcm approx.
(for a lattice of assemblies in the pool with aflat profile)

Moderator temperature equal to the core maximum
output temperature (330°C instead of 300°C)+ 850 pcm

Fuel temperature equal to the maximum meaneffective temperature (650°C instead of 590°C)+ 150 pcm

Presence of MOX fuel in the environment

At most: + 1,200 pcm

Irradiation during one irradiation cycle (without intercycle)

variation of +/- 500 pcm

Maximum specific power equal to 60 W/g (instead of
30 W/g)+ 450 pcm

For cooling times of less than 100 years, the coolingtime is taken to be equal to the minimum guaranteed
cooling time

Dependent on the actual cooling time, between
0 and 7,000 pcm

Cooling time greater than 100 years

Not quantified (see Appendix 9)

Fuel density with the selected nuclides equal to thedensity of the fresh fuelNot determined

Presence of burnable poisons

Not determined (see Appendices 11 and 12)

Geometry of the used fuelNot determined (ACTION REQUIRED)

Determination of the penalizing profile from the seriesof profiles observed at La Hague

Not determined (ACTION IN PROGRESS)

Use of a penalizing axial burnup profile (due to theinsertion of the control rods throughout the irradiation
process)

Up to + 12,000 pcm< 500 pcm
Use of a penalizing horizontal burnup gradient

Up to + 1,600 pcm for 4 assemblies placed side
by sideMEASUREMENTS

Burnup measurement uncertainties

Not quantified (see Appendix 14)

FISSIONPRODUCTS

Other fission products not taken into account+ 3,000 pcm

KEFF
CALCULATION

Application of correction factors proposed by CEA(used fuel composition + cross-sections)+ 600 pcm (for a lattice of assemblies in thepool, taking a burnup profile into account)(1) Effects expressed in k for an isolated assembly initially enriched at 4.5 wt% and irradiated at 44 GWd/MTHM,
as a result of taking account of the recommendation corresponding to a calculation, without taking therecommendation into account.

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuel6 REFERENCES
1.

Exercice OCDE "BURN-UP CREDIT" - Phase II.B (OECD "BURN-UP CREDIT" Exercise - Phase
II.B) - Report SEC/T/95.382 dated 18 December 1995 – French version only

2.

CEA document

3.

"Burnup Credit Criticality Benchmark - Result of Phase IIA" -JAERI Research 96-003,
NEA/NSC/DOC(96)01

4.

"Burnup Credit Criticality Benchmark - Analysis of Phase IIB Results: Conceptual PWR
spent fuel transportation cask" - IPSN/98-05, NEA/NSC/DOC(98)1

5.

CEA document

6.

"Burnup Credit Criticality Benchmark – Phase II-C: "Impact of the Asymmetry of PWR Axial
Burnup Profiles on the End Effect"

7.

Compte rendu de la réunion du Groupe de Travail sur le Crédit Burnup du 12 mars 2001
(Minutes of the meeting of the Burnup Credit Working Group on 12 March 2001) Document SEC/A/01.136 dated 24 April 2001 – French version only8.

"A conservative approach to consider Burnup Credit in criticality studies" – C. Lavarenne,
J. Raby, V. Rouyer - Proceedings of the IAEA Technical Meeting on Advances inApplications of Burnup Credit to Enhance Spent Fuel Transportation, Storage,
Reprocessing and Disposition (London - August 2005 - p 329)

9.

“Analyse statistique des mesures de taux de combustion d’assemblages EDF réalisées à
COGEMA-La Hague” ("Statistical analysis of the EDF assembly burnup measurements taken
at COGEMA-La Hague") - Report EDF-R&D HI28-06-005A – French version only

10. Compte rendu de la réunion du Groupe de Travail sur le Crédit Burnup du 5/02/2004(Minutes of the meeting of the Burnup Credit Working Group on 5 February 2004) –Document DSU/SEC/A/2004-155 dated 14 June 2004 – French version only
11. "Rapport de stage sur le CREDIT BURNUP" ("BURNUP CREDIT course report") – Report
DSU/SEC/T/2004-318 dated 25 November 2004
12. CEA document

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regarding PWR UOX fuel13. "Estimation des marges de sécurité dues à 6 produits de fission dans les combustibles
irradiés en transport et en stockage sous eau" ("Estimation of the safety margins due tosix fission products in used fuels transported and stored in water") ICNC'91 Oxford 1991,
paper II.3:1 pages II.58 - II.67 – French version only
14. "Proposition d'un protocole de calcul pour les études de criticité de combustible usé"("Proposed calculation protocol for used fuel criticality studies") - Document EDF/DER/
Nuclear Reactor and Heat Exchanger Department/DPRHT-11/99/021/A, October 1999 –French version only
15. "Etude de criticité avec prise en compte du Crédit Burn-up - Mise au point d’une
méthodologie de calcul" ("Criticality study taking account of burnup credit - Developmentof a calculation methodology") - EDF document - CNAM thesis – EDF / SEPTEN, July 1999 –French version only
16. "Topical Report on Actinide-Only Burn-up Credit for PWR Spent Nuclear Fuel packages"
DOE/RW report - 0472 Rev.2 U.S Department of Energy - Office of Civilian Radioactive
Waste Management
17. "Effet de la prise en compte du taux de combustion pour des situations de stockage et detransport" ("Effect of taking the burnup into account for storage and transportconditions") - Report SEC/T/01.093 dated 8 March 2001 – French version only
18. "Parametric Analysis of PWR Spent Fuel Depletion Parameters for Long Term Disposal
Criticality Safety" Oak Ridge National Laboratory - ORNL/TM-1999/99, August 1999
19. "Effet du burn up et du profil d’irradiation sur la réactivité à long terme de combustible
irradié UOX" ("Effect of burnup and the burnup profile on the long-term reactivity ofirradiated UOX fuel") EDF/SEPTEN report - ENPRNC040255, issue A – French version only
20. "A New Method to Take Burn-up into Account in Criticality Studies Considering an Axial
Profile of Burn-up Plus Some Fission Products" - C. Lavarenne et al. - Proceedings of the
ANS 2001 Winter meeting
21. CEA document
22. CEA document
23. Internal NRC document W6479/IIR-01-01

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regarding PWR UOX fuel24. Compte rendu de réunion du groupe de travail sur le Crédit Burnup du 18 octobre 2004
(Minutes of the meeting of the Burnup Credit Working Group on 18 October 2004) –Document DSU/SEC/A/2005-104 dated 23 March 2005 – French version only
25. CEA document
26. CEA document
27. Compte rendu de réunion du groupe de travail sur le Crédit Burnup du 24 avril 2007
(Minutes of the meeting of the Burnup Credit Working Group on 24 April 2007) –Document DSU/SEC/A/2007-217 dated 19 July 2007 – French version only
28. "Recent advances in French validation program and derivation of the acceptance criteriafor UOx fuel" – A. Barreau et al. - Proc. Technical meeting on Advances in Applications of
Burnup Credit to Enhance Spent Fuel Transportation, Storage, Reprocessing andDisposition, London, August Sept 2005
29. "Determination of correction factors for the isotopic composition in Burnup Credit
applications taking into account the depletion codes validation" – J. Raby et al. – Proc.
Int. Conf. on Nuclear Criticality Safety, ICNC2007, St Petersburg, Russia, May 2007
30. "Etudes de différentes méthodes de calculs relatives à la prise en compte du taux decombustion pour des situations de stockage et de transport" ("Studies of different
calculation methods for taking the burnup into account for storage and transportconditions") - Report SEC/T/02.018 dated 4 February 2002 – French version only
31. "Cahier des charges du formulaire CRISTAL Version V1" ("Specifications for the CRISTAL
Version V1 package") SEC/T/01.035 dated 2 February 2001 – French version only
32. CEA document
33. "Exploitation du programme expérimental Produits de Fission – 1ère partie" ("Use of thefission products experiment programme – Part 1") Document DSU/SEC/T/2004-162/DR
Issue A dated 17 November 2004 – French version only
34. "Exploitation du programme expérimental Produits de Fission – 2ème partie " ("Use of thefission products experiment programme – Part 2") - Document DSU/SEC/T/2004-441/DR
Issue A dated 2 September 2005 – French version only

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regarding PWR UOX fuel35. "Exploitation du programme expérimental Produits de Fission – 2ème partie " ("Use of thefission products experiment programme – Part 2") - Document DSU/SEC/T/2004-491/DR
Issue A dated 2 September 2005 – French version only
36. "Exploitation du programme expérimental Produits de Fission – 3ème partie " ("Use of thefission products experiment programme – Part 3") - Document DSU/SEC/T/2004-504/DR
Issue A dated 30 August 2005 – French version only
37. "Exploitation du programme expérimental Produits de Fission – 3ème partie " ("Use of thefission products experiment programme – Part 3") - Document DSU/SEC/T/2004-527/DR
Issue A dated 16 September 2005 – French version only
38. "Notice d'identification de la version 1.1 du formulaire CRISTAL" (“Identification details
for version 1.1 of the CRISTAL package”) - Document DSU/SEC/T/2006-200 Issue A dated
16 April 2007 – CRISTAL-V1/NdI_V1.1/A – French version only
39. "Contribution à la qualification de la voie standard APOLLO2-MORET 4 du formulaire decriticité CRISTAL - Synthèse des résultats de calcul obtenus avec la version V1.1 duformulaire CRISTAL" ("Contribution to the validation of the APOLLO2-MORET 4 “standard”
route in the CRISTAL criticality package - Summary of the calculation results obtainedwith version V1.1 of the CRISTAL package") - Document DSU/SEC/T/2007-1/D.R. – Issue A
dated 26 February 2007 – French version only
40. "Development and comparison of Monte Carlo techniques implemented in the MORET4
code for the calculation of loosely coupled systems" Conference MC (Monte Carlo) 2000 Lisbon 23-26 October 2000

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7 APPENDICESAPPENDIX 1:

Document reference system

Page 58

APPENDIX 2:

Sensitivity study on the effect of the environment

Page 64

APPENDIX 3:

Experimental validation database for depletion codes

Page 67(2005)
APPENDIX 4:

Example of calculation sequencing (using the CRISTAL V1Page 68“standard” route)
APPENDIX 5:

Used fuel inventory experimental validation

Page 69

APPENDIX 6:

Reactivity worth experimental validation

Page 72

APPENDIX 7:

Determination of correction factors

Page 73

APPENDIX 8:

Determination of a burnup profile for the studies based

Page 78on the profiles observed at La Hague
APPENDIX 9:

Issue of cooling time for long-term storage

Page 87

APPENDIX 10:

Impact of the control rod insertion history

Page 90

APPENDIX 11:

Study of poisoned rods for 1300 MWe PWR assemblies

Page 96

APPENDIX 12:

Study of the storage of used fuel assemblies with

Page 102

gadolinium
APPENDIX 13:

Simulation methods available in the MORET 4 code

Page 107

APPENDIX 14:

Uncertainties associated with fuel assembly burnup

Page 108

measurements

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APPENDIX 1
DOCUMENT REFERENCE SYSTEM

This document reference system is structured around seven topics:
1-

General method for taking account of the burnup

2-

Used fuel composition and cross-section validation

3-

Cross-section validation

4-

Burnup profiles

5-

Irradiation and cooling history

6-

Discretization of axial burnup profiles and calculation methods

7-

Burnup credit sequence validation

The various documents relating to each of these topics are listed in the remainder ofthis appendix.

1

General method for taking account of the burnup

1.1 Compte rendu de la réunion du 18 mars 1998 du groupe de travail sur le Crédit Burn-up(Minutes of the meeting of the Burnup Credit Working Group on 18 March 1998)
SEC/A/99.218 dated 24 April 1998 – French version only

1.2 Compte rendu de la réunion du 3 mai 1999 du groupe de travail sur le Crédit Burn-up(Minutes of the meeting of the Burnup Credit Working Group on 3 May 1999)
SEC/A/99.218 dated 1 July 1999 – French version only

1.3 Compte rendu de la réunion du 19 janvier 2000 du groupe de travail sur le Crédit Burn-up(Minutes of the meeting of the Burnup Credit Working Group on 19 January 2000)
SEC/A/00092 dated 13 March 2000 – French version only

1.4 Actinide only Burn-up credit
DOE/RW-0472 Rev2, September 1998

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1.5 Etude d’une méthode de prise en compte dans les études de criticité de la combustion
massique des combustibles à base d’oxyde d’uranium des assemblages de type REP, enconsidérant un profil axial d’irradiation, l’évolution des actinides dans le combustible,
ainsi que la formation des produits de fission (Study of a method for taking account of theburnup of uranium oxide-based fuels in PWR type assemblies in criticality studies,considering an axial burnup profile, actinide depletion in the fuel, and the formation offission products)
SEC/T/02.005/DR dated 4 February 2002 – French version only

2

Used fuel composition and cross-section validation

2.1 CEA document

2.2 CEA document

2.3 CEA document

2.4 CEA document

3

Cross-section validation

3.1 CEA document

3.2 CEA document

3.3 CEA document

3.4 CEA document

3.5 CEA document

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3.6 CEA document

3.7 Programme expérimental de type physique - Evaluation des expériences critiques relatives
à la qualification des sections efficaces d'absorption de 6 PF (103Rh, 133Cs, 155Gd, 152Sm,
143Nd) en solutions nitriques légèrement acides, seuls ou mélangés, dans une cuve deZircaloy au centre d'un réseau pilote de crayons REP UO2 à 4,738 % (poids) 235U modéré etréfléchi par de l'eau (Physical type experimental programme - Evaluation of the criticalexperiments relating to the validation of the absorber cross-sections of six FPs (103Rh, 133Cs,
155

Gd, 152Sm and 143Nd) in slightly nitric acid solutions, alone or mixed, in a Zircaloy tank in

the center of a control lattice of PWR UO2 rods with 4.738% (weight) 235U, moderated andreflected by water)
Document SEC/T/01.01/C.CEA dated 1 January 2001 – French version only

3.8 French Fission Products Burnup Experiments performed in Cadarache and Valduc. Results
Comparison - J. Anno et al – in Proceedings of Int. Conf. on Nuclear Criticality Safety,
ICNC'2003, Tokai Mura, Japan, 20-24 October 2003

3.9 Exploitation du programme expérimental Produits de Fission – 1ère partie – « Expériences detype "Physique" relatives à la qualification des sections efficaces d’absorption de 6 Produits deFission (103Rh, 133Cs, 143Nd, 149Sm, 152Sm, 155Gd) en solutions nitriques légèrement acides, seuls ou
mélangés, dans une cuve de zircaloy disposée au centre d’un réseau pilote, de crayons REP UO 2
enrichis à 4,738 % (poids) en 235U, modéré et réfléchi par de l’eau » (Use of the fission products

experiment programme – Part 1 – "Physical" type experiments relating to the validation of theabsorber cross-sections of six fission products (103Rh, 133Cs, 143Nd, 149Sm, 152Sm and 155Gd) in slightly
nitric acid solutions, alone or mixed, in a Zircaloy tank in the center of a control lattice of PWR
UO2 rods enriched with 4.738% (weight) 235U, moderated and reflected by water)

Report DSU/SEC/T/2004-162/DR Issue A dated 17 November 2004 – French version only

3.10

Exploitation du programme expérimental Produits de Fission – 2ème partie – « Expériencesde criticité de type "Dissolution Elémentaire" : réseaux de crayons REP dans des solutions
légèrement acides empoisonnées ou non par des Produits de Fission » (Use of the fission products

experiment programme – Part 2 – "Elementary dissolution" type criticality experiments: lattices
of PWR rods in slightly acidic solutions, with or without fission product poisoning)

Report DSU/SEC/T/2004-441/DR Issue A dated 2 September 2005 – French version only

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Exploitation du programme expérimental Produits de Fission – 2ème partie - « Expériencesde criticité de type "Dissolution Elémentaire" : réseaux de crayons REP immergés dans des solutions
de gadolinium naturel, de nitrate d'uranyle appauvri empoisonnées ou non par des Produits deFission (PF) » (Use of the fission products experiment programme – Part 2 – "Elementary
dissolution" type criticality experiments: lattices of PWR rods immersed in solutions of natural
gadolinium, of depleted uranyl nitrate with or without fission product poisoning)

Report DSU/SEC/T/2004-491/DR Issue A dated 2 September 2005 – French version only

3.12 Exploitation du programme expérimental Produits de Fission – 3ème partie – « Expériencesde criticité de type "Dissolution dans une grande cuve non ajustée" sur des solutions de nitrated'uranyle appauvri baignant un réseau de crayons UO 2 » (Use of the fission products experiment

programme – Part 3 – "Dissolution in a large non-adjusted tank" type criticality experiments on
depleted uranyl nitrate solutions soaking a lattice of UO 2 rods)

Report DSU/SEC/T/2004-504/DR Issue A dated 30 August 2005 – French version only

3.13 Exploitation du programme expérimental Produits de Fission – 3ème partie – « Expériencesde criticité de type "Dissolution avancée" : réseaux de crayons HTC dans des solutions de nitrated'uranyle appauvri empoisonnées ou non par des produits de fission » (Use of the fission products

experiment programme – Part 3 – "Advanced dissolution" type criticality experiments: lattices ofhigh burnup rods in depleted uranyl nitrate solutions with or without fission product poisoning)

Report DSU/SEC/T/2004-527/DR Issue A dated 16 September 2005 – French version only

4

Burnup profiles

4.1 Etude avec prise en compte du crédit Burn-up - Mise au point d'une méthodologie de calcul(Study taking account of burnup credit - Development of a calculation methodology)
CNAM engineering thesis presented by Mr Maillot and defended on 5 July 1999 – French
version only

4.2 Effet de la prise en compte du taux de combustion pour des situations de stockage et detransport (Effect of taking the burnup into account for storage and transport conditions)
Report SEC/T/01.093 dated 15 May 2001 – French version only

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Irradiation and cooling history

5.1 Proposition d'un protocole de calcul pour les études de criticité du combustible usé(Proposed calculation protocol for used fuel criticality studies)
Report EDF/DER/SNRE/DPR HT-11/99/021/A, October 1999 – French version only

5.2 Effet de la prise en compte du taux de combustion pour des situations de stockage et detransport (Effect of taking the burnup into account for storage and transport conditions)
Report SEC/T/01.093 dated 8 March 2001 – French version only

5.3 Etude de différentes méthodes de calcul relatives à la prise en compte du taux decombustion pour des situations de stockage et de transport (Study of different calculation
methods for taking the burnup into account for storage and transport conditions)
Report SEC/T/02.018 dated 11 February 2002 – French version only

5.4 CEA document

5.5 Etudes de sensibilité des paramètres d’irradiation pour la prise en compte du Crédit
Burnup dans les réacteurs REP-UOX (Effects of burnup and the burnup profile on the longterm reactivity of irradiated UOX fuel)Report EDF/SEPTEN/ENPRNC040255 Issue A dated 2 June 2005 – French version only

6

Discretization of axial burnup profiles and calculation methods

6.1 Une contribution à la prise en compte du taux de combustion dans les études de criticité.
Prise en compte de profil axial de combustion des assemblages combustibles (Acontribution to the consideration of the burnup in criticality studies. Taking account of theaxial burnup profile of fuel assemblies).
Report by Mr Tournade following the course held at SGN, March to July 1998 – French
version only

6.2 Prise en compte du taux de combustion dans les études de criticité (Taking account of theburnup in criticality studies).
INSTN report by Mr Reverdy following the course held at SGN in 1999 – French version only

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7Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelBurnup credit sequence validation

7.1 CEA document

7.2 CEA document

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APPENDIX 2
SENSI TIVITY STUDY ON THE EFFECT OF THE ENVIRONMENT

The purpose of this study is to examine the impact of UOX irradiation with a MOX
environment on a criticality calculation. To do this, depletion calculations are performed
using the DARWIN V2.0 fuel cycle package, followed by a criticality calculation on a poolstorage configuration using the CRISTAL V1 criticality safety package (the chosen criticality
configuration maximized the effects under examination).
To this end, three configurations are modelled in the depletion calculation:
1. Central UOX assembly irradiated without control rods, surrounded by eight UOX
assemblies irradiated without control rods (serving as a reference);
2. Central UOX assembly irradiated without control rods, surrounded by eight MOX
assemblies irradiated without control rods (to study a MOX environment irradiatedwithout control rods);
3. Central UOX assembly irradiated without control rods, surrounded by eight MOX
assemblies irradiated with control rods (to investigate a MOX environment irradiatedwith control rods).
In this study, the used fuel inventory used in the criticality calculations consists of thenuclides selected for the burnup credit studies, as follows: actinides 234U, 235U, 236U, 238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 237Np, 241Am and 243Am;
 the 15 fission products: 103Rh, 133Cs, 143Nd, 149Sm, 152Sm, 155Gd, 95Mo, 99Tc, 101Ru, 109Ag,
145

Nd, 147Sm, 150Sm, 151Sm and 153Eu; with a cooling time equal to zero.

In order to differentiate the used fuel composition problem from the "end effect" problem,the axial burnup profile is considered uniform and equal to the assembly mean burnup.
In the tables below,  is the difference in reactivity defined by the formula:  ρ (case2) - ρ (case1)  Ln

IRSW

K eff (case2)
K eff (case1)

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regarding PWR UOX fuel65/114Comparison between the impact of a MOX environment and a UOX
environment

The presence of MOX around a UOX assembly hardened the neutron spectrum, leading to anincrease in the production of plutonium and, therefore, an increase in the reactivity of the
UOX assembly lattice. This reached 1,250 pcm for a lattice of assemblies irradiated at
40 GWd/MTHM, which were completely surrounded by MOX throughout the entire irradiation
process (see Table 6).
Table 6: Comparison between the effects of irradiation with a MOX environment and a UOX
environment on the reactivity of a UOX lattice2.

BU of UOX assembly lattice (MOX env) -  (UOX env)

10 GWd/MTHM+ 44 pcm

20 GWd/MTHM+ 300 pcm

30 GWd/MTHM+ 672 pcm

40 GWd/MTHM+ 1,251 pcm

Influence of the MOX environment burnup

The impact of an irradiation with a MOX environment at 10, 20 or 30 GWd/MTHM compared toan irradiation with a MOX environment at 15 GWd/MTHM is shown in Table 7.
Table 7: Impact of a MOX environment burnup on the reactivity of a UOX lattice
BU of UOX
assemblylattice (MOX env10GWd/MTHM)  (MOX env15GWd/MTHM)

 (MOX env20GWd/MTHM)  (MOX env15GWd/MTHM)

 (MOX env30GWd/MTHM)  (MOX env15GWd/MTHM)

20 GWd/MTHM- 1 pcm- 23 pcm- 50 pcm

40 GWd/MTHM+ 83 pcm- 117 pcm

- 257 pcm

It can be seen that the reactivity of the UOX lattice surrounded by a MOX environment at
30 GWd/MTHM during the irradiation, is lower than the reactivity of the lattice surrounded
by a MOX environment at 15 GWd/MTHM during the irradiation. This is due to the decreasein the content of the 239Pu in the MOX environment with the increase in its burnup, whichsoftened the neutron spectrum of the UOX assembly.
However, the MOX environment burnup has a relatively low impact on the reactivity of the
UOX fuel lattice.

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelImpact of a MOX environment irradiated with control rods

The MOX assemblies surrounding the UOX assembly are irradiated with inserted control rods
throughout the irradiation process (at up to 15 GWd/MTHM).
The impact of an irradiation with a MOX environment irradiated with and without inserted
control rods is shown in Table 8.
Table 8: Effects on the reactivity of a UOX lattice of an irradiation with a MOX environment
irradiated with and without inserted control rods
BU of UOX assembly lattice (MOX envwith CRs) -  (MOX envwithout CRs)

10 GWd/MTHM- 3 pcm

20 GWd/MTHM+ 3 pcm

30 GWd/MTHM+ 37 pcm

40 GWd/MTHM+ 30 pcm

Surrounding the UOX assembly with a MOX environment irradiated with inserted control rods
leads to a hardened neutron spectrum, and thus to an increase of the reactivity of the UOX
lattice. However, this effect is relatively small compared to the effect on the reactivity of
the MOX environment itself.

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APPENDIX 3
EXPERIMENTAL VALI DAT ION DATABASE FOR DEPLETION CODES (2005)
EXPERIMENT
Experimental
Fuel
Enrichment
Burnupdata
ReactorTihange 1

PWR 15x15
UOX

3.10 wt%

PWR 17x17
UOX

2.10 wt%
3.10 wt%

PWR 17x17
UOX

2.60 wt%

27 to 30
GWd/MTHM

HN, MA, Nd
Radial crossmember of rods

PWR 17x17
UOX

3.10 wt%

45 to 60
GWd/MTHM

HN, MA, Nd, Cs,
Osc UF, sensor

PWR 17x17
UOX

4.50 wt%

25 to 62
GWd/MTHM

HN, MA, Nd, Cs,
BUC, SIMS,
sensor, Osc UF

PWR 17x17
Enriched UOX from
100% recycled
uranium

3.61 wt%
U6/U8 = 1.2 wt%

11 to 34
GWd/MTHM
4th cycle
abandoned

HN, MA, Nd

PWR 17x17
UOX extracted at
5 cycles, reirradiated for6th cycle

4.50 wt%

50 to 70
GWd/MTHM

HN, MA, Nd, Cs,
BUC, SIMS,
sensor, Osc UF

PWR 17x17
UOX re-irradiatedfor 6th and 7th cycle

4.50 wt%

55 to 80
GWd/MTHM

HN, MA, Nd, Cs,
SIMS, sensor,
Osc UF

Sample of 3
zones and 3
BUs
10 to 45
GWd/MTHM

HN, MA, Nd, Cs,
BUC, SIMS,
sensor, Osc UF

40 to 50
GWd/MTHM

HN, Nd

5.2 wt% and6.6 wt%Central zone:
1 to 5 cycles
Median zone:
4, 5 cycles
10 to 53
GWd/MTHM

HN, MA, Nd, Cs,
BUC, SIMS,
sensor, Osc UF

PWR simulation
UO2 doped with U236

U5/U8 = 2.80 wt%
0.1 wt% < U6/U8 <1.2 wt%Central UO2~ 2500
MWd/MTHM

Nuclides filiation,
HN, MA, Nd

PWR simulation
UO2 + cr.
appropriate Gd

UO2 at 3.25 wt%
Gd at 5 wt%

UO2
from 3.0 to 10
GWd/MTHM

HN, Nd, Gd

Mélusine

PWR simulation
UO2 + Gdinteraction

UO2 at 3.25 wt%
Gd at 8 wt%

UO2
from 3.0 to 13
GWd/MTHM

HN, Nd, Gd,
Osc I=UFBWR rods

BWR 9x9

UO2 at 3.95 wt%

40 GWd/MTHM

HN, MA, Nd, BUC,
sensor, Osc UF

1 to 3 startup cycles

Bugey 3
1 to 3 startup cycles

Fessenheim 2
2 startup cycles

Fessenheim 2
4 & 5 cycles

Gravelines 3+2
2 to 5 cycles

Cruas 4 / ERU
1 to 3 cycles

Cruas 2 / Highburnup5 & 6 cycles

Gravelines 5 /High burnup
5, 6 and 7 cycles

Saint Laurent B1
1 to 3 cycles
3 zonesGravelines 4
3 & 4 cycles
Central zone and medianzone

Dampierre 2 /High burnup
1 to 5 cycles
Central zone and medianzone

Sherwood 2
MélusineGédéon 1
MélusineGédéon 2

Gundremmingen

Uapp. 0.22 wt%

PWR 17x17
MOX
3 Pu concentrations

 Pu 
 4.5 wt %
 U  Pu  mean

PWR 17x17
MOX
4th cycle againstreflector

 Pu 
 4.5 wt %
 U  Pu  mean

GWd/MTHM
19 to 38
GWd/MTHM

HN, MA, Nd
Rods in center
HN, MA, Nd, Cs,
BUC, Osc UF
Rods in center

Uapp. 0.22 wt%

Uapp. 0.22 wt%
PWR 17x17
MOX

10 to 40

 Pu : U  Pu  mean

HN = heavy nuclei (U, Pu); MA = minor actinides (Np, Am, Cm); BUC = burnup credit (FP Prog.)O s c U F = o s c i l l a t i o n o f u s e d f u e l s a m p l e s i n M I N E R V E ;  s e n s or = e l e c t r o n i c s e n s o r ,distribution of chemical elements ; SIMS = nuclide distribution

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APPENDIX 4: EXAMPLE OF CALCULATION SEQUENCING (USING THE CRISTAL V1 “STANDARD” ROUTE)

Axial profile
of burnup

Spent FuelI nventory

Conservative
Irradiation■_

Correction
Factors

1
7

r

r
DARWIN
or
CESAR

F(q

CRISTAL}/

Depletion calculation with DARWIN or CESARI RSP]

Criticality calculation with CRISTALCe document est la propriété de l’IRSN et ne peut pas être communiqué, reproduit ou utilisé sans son autorisation écrite préalable.
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APPENDIX 5
USED F UEL INVENTORY EXPERIMENTAL VALIDAT ION

Table 9 to Table 15 present the results from the experimental validation of the used fuelinventory for PWR UOX fuels, calculated using the DARWIN V2.0 fuel cycle package, basedon the CEA93-V6 library, and the APOLLO2.5 and PEPIN2.0 codes.

1.

Uranium isotopes
Table 9: Summary of (C-E)/E biases (%) for the 'uranium' inventory
PWR fuel

BU (GWd/MTHM)

UOX
BUGEY FESSENHEIM
3.1 wt%UOX GRAVELINES
4.5 wt%ERU CRUAS
3.5 wt%2.

234

U/238U235

U/238U

236

U/238U20

2.5  0.6

0.2  1.3

-3.5  1.0

25

5.2  1.1

0.06  2.4-3.1  1.2

40

1.7  0.7

-0.1  2.1-3.2  0.4

50-5.8  1.1

0.2  2.7

-4.1  0.1

60-2.1  2.3

4.2  7.5

-3.9  0.2

30-0.3  0.9-0.8  1.2-3.3  1.0

40

0.2  1.3

-0.4  2.8-3.8  1.1

50-4.6  1.7

1.5  4.1

-4.8  0.7

60

1.4  1.0

1.1  3.1

-4.3  0.3

15

0.3  0.5

-0.2  1.0-0.5  0.4

25

0.2  0.8

0.8  1.7

-0.3  0.3

35-0.4  1.1

0.06  3.1-1.1  0.2

Plutonium isotopes
Table 10: Summary of (C-E)/E biases (%) for the 'plutonium' inventory
PWR fuelUOX
BUGEY FESSENHEIM
3.1 wt%UOX GRAVELINES
4.5 wt%ERU CRUAS
3.5 wt%I RS El

BU(GWd/MTHM)

238

Pu/238U

239

Pu/238U

240

Pu/238U

241

Pu/238U

242

Pu/238U

20-12.6  3.2-0.6  1.1-0.7  1.6-3.6  2.1-6.0  3.9

25-9.5  4.6-0.4  1.5-0.7  2.1-3.2  2.9-5.0  5.0

40-6.9  2.0

2.3  0.9

-1.8  0.8-1.2  1.2-7.5  2.2

50-5.0  1.6

1.9  1.1

-1.1  0.6-0.7  1.2-6.2  1.8

60-9.2  2.5

3.4  2.4

-0.5  0.9-0.1  2.6-8.8  2.9

30-13.1  3.8-1.5  1.1-2.0  1.7-4.9  2.3-6.7  3.9

40-10.8  5.1-0.4  1.8-1.9  2.0-4.2  2.7-6.9  4.8

50-11.1  4.5+1.6  2.1-1.7  1.5-3.1  2.4-8.6  4.3

60-10.5  2.5+2.0  1.4-1.5  0.7-2.6  2.2-7.4  2.2

15-3.4  3.9

1.7  1.2

-2.1  2.6

0.3  3.6

-5.3  5.8

25-3.4  3.4

1.0  1.0

-0.5  2.2-1.8  2.7-5.0  5.1

35-2.3  3.3

1.9  1.0

-0.3  1.7-0.7  1.8-4.3  4.3

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3.

Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelNeptunium 237, americium 241 and 243

Table 11: Summary of (C-E)/E biases (%) for the 'neptunium' and 'americium' inventories
PWR fuel

BU(GWd/MTHM)

UOX
BUGEY FESSENHEIM
3.1 wt%UOX GRAVELINES
4.5 wt%ERU CRUAS

4.

237

Np/238U

241

Am/238U

243

Am/238U

20-10.9  4.4-5.8  3.4-9.8 7.8

25-7.5  4.3-2.9  3.1-10.3 7.5

40-1.5 2.1

-3.2  1.2-4.6  3.4

50-4.1  2.5-13.6  2.6-10.8  2.9

60

2.5  3.1

0.02  2.4-5.5 4.6

30

-1.2  4.7-5.0  2.8-10.1  7.7

40-3.2  4.2-3.5  2.1-8.0  7.0

50-4.5  3.4

/

/

60

-3.7  3.1+1.3  0.6-4.8  3.9

15-4.6  3.2

/

/

25

-0.7  3.1

/

/

35

3.3  3.0

-1.4  2.3-5.1  6.4

Neodymium 143 and cesium 133
Table 12: Summary of (C-E)/E biases (%) for the 143Nd and 133Cs inventories
PWR fuelUOX
BUGEY FESSENHEIM
3.1 wt%UOX GRAVELINES
4.5 wt%ERU CRUAS
3.5 wt%I RS El

BU(GWd/MTHM)

143

Nd/238U

133

Cs/238U

20

0.3  1.3

-2.7  2.0

25

0.3  1.7

-3.9  1.9

40/-8.5  1.8

50

2.4  1.8

-1.3  1.6

60/-2.2  1.5

30/-4.9  2.040

0.5  1.4

-3.3  2.0

50

1.6  1.0

-3.9  1.8

60

1.9  0.4

-3.4  1.2

15

0.0  1.8/25

0.6  1.6/35

0.7  1.2/

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5.

Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelMetallic fission products: technicium 99, molybdenum 95, ruthenium 101,
rhodium 103 and silver 109
Table 13: Summary of (C-E)/E biases (%) for the 'metallic FP' inventory
BU(GWd/MTHM)

PWR fuel
UOX
BUGEY
3.1 wt%UOXGRAVELINES
4.5 wt%6.

99

Tc/238U

95

Mo/238U

101

Ru/238U

103

Rh/238U

109

Ag/238U

20-7.6  3.1-3.7  2.7

2.9  2.9

3.5  2.8

-47.3  4.0

40

4.8  3.0

8.4  2.6

15.2  2.9

13.9  2.6-13.7  3.7

40-0.6  3.1

5.5  2.7

5.0  2.9

3.4  2.7/50

2.6  3.1

2.6  2.6

6.4  2.3

4.6  2.5/60

3.6  3.0

2.1  2.6

0.9  2.9

3.0  2.3/

Gadolinium 155 and europium 153
Table 14: Summary of (C-E)/E biases (%) for the 155Gd and 153Eu inventories
BU(GWd/MTHM)

PWR fuelUOX
BUGEY 3.1 wt%
UOX GRAVELINES
4.5 wt%7.

155

Gd/238U

153

Eu/238U

20-3.1  3.6

6.5  3.040

0.1  4.1

11.8  2.640

4.3  4.1

8.9  3.050

8.1  4.3

11.7  2.8

60

11.9  4.4

16.4  2.5

Samarium isotopes
Table 15: (C-E)/E biases (%) for the 'samarium' inventory
PWR fuelUOX
BUGEY 3.1 wt%
UOX
GRAVELINES
4.5 wt%I RS El

71/114BU(GWd/MTHM)

147

Sm/238U

149

Sm/238U

150

Sm/238U

151

Sm/238U

152

Sm/238U

20-4.9  1.5

4.5  4.7

-3.7  2.6-3.1  1.4

0.4  1.9

40

-5.9  1.0-3.4  23.3

-3.6  2.2

7.3  1.7

1.1  1.7

40

-6.5  1.1-8.6  8.5-3.2  2.3

3.6  1.5

1.4  1.850

-7.0  1.0

5.6  4.9

-4.8  2.1

7.9  1.7

3.5  1.6

60

-7.4  0.9-3.5  10.1

-4.1  1.8

12.8  3.0

5.6 1.7

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuel

APPENDIX 6
REACTIVITY WORTH EXPERIMENTAL VALI DAT ION

Table 16 presents the results from the experimental validation of reactivity worth for PWRUOX fuels, carried out with the CRISTAL V1 criticality safety package, based on the
APOLLO2.5 code and its library, CEA93.V6.
The interpretation of the oscillation experiments on separate samples of fission products
revised the overestimation of99

Tc and133

Cs (4% in R1UO2). The calculation overexperiment biases are satisfactory with regard to the 153Eu, 109Ag, 152Sm, 145Nd and 155Gd(underestimation of less than 2%). The 143Nd and 95Mo are underestimated by 4% in R1UO2,
and the 149Sm by 6%. With regard to the 103Rh, the interpretation of the oscillation
experiments showed a significant overestimation.
No information or trend could be ascertained for the reactivity worth of 147Sm, 150Sm, 151Sm
or 101Ru, as the capture of these samples can be largely attributable to the residual 149Sm
or the 99Ru with regard to the 101Ru.
Table 16: Summary of (C-E)/E biases (%) for 11 burnup credit nuclides
Fission product

R1UO2

R2UO2

143

-4.5  2.5-10.0  3.0

145

Nd

0.4  4.1

-1.9  4.8

149

Sm

-5.7  2.1-9.8  2.5

152

Sm

-0.2  3.2-1.2  4.2

95

Mo-3.6  3.4-7.1  3.8

Rh+13.3  4.0+11.9  3.8

Gd-1.9  2.9-11.0  3.6

Eu-1.6  4.4-3.6  5.1

109

Ag

-1.7  4.0-1.5  3.6

99

Tc

4.2  3.8

-2.2  3.5

4.3  1.9

2.0  2.0

Nd

103
155

153

133

Cs

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APPENDIX 7
DETERMINATION OF COR RECTION F ACTORSI

PREAMBLE

At the Working Group meeting on 19 June 2003, CEA was assigned the task of establishing
an approach to determine the correction factors to be applied to the nuclide
concentrations to take account of the experimental validation of the depletion codes andthe experimental validation of the actinides and fission products cross-sections.
This approach was presented at the Working Group meeting on 5 February 2004 and gave
rise to a number of discussions. The entire approach is currently being analyzed by theWorking Group and is therefore expected to evolve.
It is to note that the described approach does not reflect ongoing work.

II APPROACH PROPOSED BY CEA TO DETERMINE THE CORRECTION FACTORS
1) Approach
Determining the correction factors relies on the experimental validation of the used fuelcomposition (see Appendix 5) and the experimental validation of the reactivity worth (seeAppendix 6), based on the following approach:
The calculation C - experiment E comparison for the total reactivity worth of a nuclide,from an depletion calculation followed by a criticality calculation, represented as (N x ),C 

gives the relation (N x )exp = E x (N x )calc.
Working from the assumption that the calculation - experiment comparison for the usedfuel inventory and the reactivity worth are two independent parameters (the C/E valuesC 

obtained are derived from two strictly different calculations), the ratio E is the productC  and theof the experiment - calculation comparison for the used fuel inventory EBMC  : CE  = CE  x CE  .

reactivity worth E



BM



With regard to the absorbent nuclides, for the criticality studies it is conservative to havean underestimated calculated total reactivity worth, illustrated as follows:C 

C  x CE   1.

(N x )exp  (N x )calc, or E  1, or E

I RS

BM



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regarding PWR UOX fuelC  x CE  < 1, the inventory of the absorbent nuclide is modified by applying acorrection factor equal to E  x E  . If E  x E   1 then the inventory is notCCCC
Thus, if E

BM



BM



BM



modified, and the correction factor is therefore equal to 1.
With regard to the fissile nuclides, for the criticality studies it is conservative to have an
overestimated calculated total reactivity worth, illustrated as follows:C  x CE   1.

C 

(N x )exp  (N x )calc, or E  1, or EBMC  x CE  > 1, the inventory of the fissile nuclides is modified by applying acorrection factor equal to E  x E  . If E  x E   1 then the inventory is notCCCC
Thus, if E

BM



BM



BM



modified, and the correction factor is therefore equal to 1.

2) Determination of correction factorsa)Calculation over experiment bias for the used fuel inventoryE C  BMFor each nuclide, the calculation over experiment bias for the used fuel inventory 
adopted to determine the correction factors corresponds to: either the mean value obtained across all of the results when no C/E-1 divergence isobserved with the burnup, while ensuring a certain level of consistency between the
results (for example, a negative C/E-1 is not taken into account in the mean if the setof results indicates a positive C/E-1);
 or the value that minimises the keff if there is a divergence with the burnup or if notrend is revealed by the set of results. In the case of a fissile nuclide, this corresponds
to the lowest C/E value, and in the case of an absorbent nuclide, it corresponds to thehighest; with regard to the 239Pu, the C/E-1 biases for the used fuel composition tend to beslightly underestimated at low burnup, then overestimated from 30 GWd/MTHM. As thisnuclide has a notable influence on the reactivity value, two correction factors arerecommended: one for a burnup lower than 30 GWd/MTHM and the other for a burnup
of between 30 GWd/MTHM and 60 GWd/MTHM.

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regarding PWR UOX fuelCalculation over experiment bias for the reactivity worthC  adopted

 For each FP, the experiment over calculation bias for the reactivity worth Eto determine the correction factors, corresponds to the C/E values obtained from theR1UO2 measurements, as these are higher than the C/E values obtained from the R2UO2
measurements, and therefore involve a lower keff, which is not conservative.
The reactivity worth of fission products 147Sm, 150Sm, 151Sm and 101Ru could not bevalidated with the oscillation experiments in the MINERVE reactor. For this reason, weused the capture cross-section and resonance integral uncertainty data provided by the
JEF2.2 evaluation for these fission products.
 For each actinide, due to the absence of an experimental programme to validate thereactivity worth, the uncertainty data from the JEF2.2 evaluation are used to estimateCE  : for the fissile nuclides, the estimate was based on the uncertainty data forneutron multiplication  and the fission and absorption cross sections; for the othernuclides, the estimate incorporated the uncertainty data for the capture cross-section
and the resonance integral.

3) Presentation of correction factors
The calculation over experiment biases for the used fuel composition and for the reactivity
worth used to calculate the correction factors, and the correction factors themselves, arepresented in Table 17 for each burnup credit nuclide.

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regarding PWR UOX fuelTable 17: (C/E)-1 biases (%) for the used fuel composition and reactivity worth,with associated correction factors
Reactivity worth(C/E)-1 (%)

Used fuel composition

234

+3 %

+1 %

0.96

235

+1 %

-1 %

1

236

U

+4 %

-4 %

1

238

Pu

+2 %

-11 %

1

239

Pu

-1 %

-1 % if BU  30 GWd/MTHM

1.02 is BU  30 GWd/MTHM+2 % if 60  BU > 30 GWd/MTHM

1 if BU 60  BU > 30 GWd/MTHM

240

Pu

+2 %

-2 %

1

241

Pu

-1 %

-5 %

1.06

242

Pu

+3 %

-7 %

1

237

Np

+3 %

-4 %

1

241

Am

+3 %

+1 %

0.96

243

+3 %

-10 %

1

143

-4 %

+2 %

1

145

Nd

+0.4 %-0.5 %

1

147

Sm

+5 %

-7 %

1

149

-6 %

+6 %

1

150

+4 %

-4%

1

151

+3 %

+13 %

0.86

152

Sm

-0.2 %

+6 %

0.94

95

Mo

-4 %

+4 %

1

Rh

+13 %

+4 %

0.85

Gd

-2 %

+12 %

0.91

Eu

-2 %

+16 %

0.88

109

Ag

-2 %

-14 %

1

99

Tc

+4 %

+4 %

0.92

+30 %

+6 %

0.72

+4 %

-4%

1

Nuclide
U
U

Am
Nd

Sm
Sm
Sm

103
155

153

101

Ru

133

Cs

I RS El(C/E)-1 (%)

Correction factor

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III REMARKS
In 2007 it was agreed that further studies should be conducted, in order to:-

take measurement uncertainties into account;-perform statistical processing on the standard deviation on the C/E scatter plot;-

take the changes in the C/E into account with the burnup;-

assess the validity of compensation between the validation of the used fuelcomposition and the validation of the reactivity worth12.

For example, for 149Sm, the approach described above suggests a correction factor of Fc 1 while: C  E 

 <1.
1
 >1 and 1   C  E   E   E  mat.balance
criticalitycalc. 


12

I RS

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Summary report on the French Burnup Credit Working Group knowledge
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APPENDIX 8
DETERMINATION OF A B URNUP PROFILE FOR TH E STUDIESBASED ON THE PROFILE S OBSERVED AT LA HAGUEIPOSSIBLE APPROACHES

Throughout this appendix, Bi(z) represents the lower limit and Bs(z) represents the upper
limit of the profile range.
Based on the observations made at La Hague, the Working Group chose three options fordetermining the profile to be used in the "generic" studies:
the mean profile Pm(z) of the profile range (P(z)) represented in Figure 11 (bold-solid line), where Pm(z) =

P(z)
N

N

;

a "penalizing" profile within each profile range. However, the penalizing nature of-a profile is difficult to maintain for all transport and storage conditions, etc. This
profile can also be difficult to symmetrize;
either the "bounding" profile, which is lower than the observed profiles, as shown-in Figure 12 (bold dotted line), or Bi(z) as defined above.

B411

Mean profile'Boundine profile

Shape

Shape

factorfactor1

1

1.131 (z)dziH
HProfile range
Profile range
BIM

Height Z

Height Z

over assemblyover assembly

Figure 11:
Mean burnup profile

IRSG]

Figure 12:"Bounding" burnup profile

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regarding PWR UOX fuelIf the measurement methods could precisely determine the burnup then the following
points should be noted:- for a fixed mean burnup of an assembly BUactual, a profile Pactual(z) that is lower at one
end than the mean profile (Pm(z)) of the profile range, could not be processed with ageneric study using the "mean profile" and the burnup BU = BUactual (or BUactual x Pm(z)),
since at one end, the burnup Pactual(z) x BUactual would be lower than that used in the
study; all of the profiles observed within the range can be processed by a criticality
study with the mean profile Pm(z) but with a burnup reduced by the maximum burnup
difference observed between the mean profile and the other profiles, i.e. BU-BU(where  is the maximum difference that exists between Pm(z) and P(z); in fact  = max(Bs(z) - Pm(z)); this is illustrated by a solid grey line in Figure 11;- all of the burnup profiles observed in the range can be processed by a generic study
using the "bounding profile" Bi(z). However, for actual mean burnup profiles BUactual, themean burnup used in the study will then be lower than BUactual (in fact, it will be equal
to BUactual-BUactual, where , represented in Figure 12, has the value B ( z ) dz
i

1-

II

STUDY OF A MEAN PROFILE

1)

Overview

H

H)

For the studies conducted by the Burnup Credit Working Group, COGEMA gave EDF a
database containing the measurements (taken in the T1 burnup pit at the plant at La
Hague) for the axial burnup profile of 644 used fuel assemblies in EDF 1300 MWe reactors,
grouped into two series, named R103 and R202, and reprocessed at La Hague. COGEMA
provided the gross count rates for 137Cs and 134Cs at centimetre intervals along two
opposite sides (named route 1 and route 2 throughout the remainder of this document) of
each of the assemblies and, deduced from these measurements, the mean burnups foreach assembly and each side.
2)

Description of the assemblies in the database

The majority of the assemblies reveals an initial 235U enrichment of 3.10 wt%. The otherassemblies, with an initial 235U enrichment of 1.50 wt%, 1.80 wt%, 2.40 wt% and 2.95 wt%,
are those from the first cores. These are associated with a fuel management with abalance enrichment of 3.10 wt%.

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regarding PWR UOX fuelOver 94% of the assemblies have a burnup of between 30 and 40 GWd/MTHM. The otherassemblies have a burnup of between 10 and 30 GWd/MTHM.
The table below shows the distribution of the assemblies according to their mean burnups,
for each of the two series and each of the two routes.
Table 18: Population of assemblies based on their burnups for the series
and routes studied

Number of assemblies
Series R103

Series R103

Series R202

Series R202

Route 1

Route 2

Route 1

Route 2

BU < 25 GWd/MTHM

10

14

13

13

25 < BU < 30 GWd/MTHM

6

3

7

34

30 < BU < 40 GWd/MTHM

290

289

318

291

BU > 40 GWd/MTHM

0

0

0

0

Total assemblies

306

306

338

338

From the data provided by EDF/DPI/DPN/UNIPE, it can be seen that 33% of the measured
assemblies were irradiated in the final cycle under control rods (R or G) and that 10% were
irradiated under control rods for over two thirds of the time spent in the reactor. The
database therefore contains a large number of assemblies placed under control rods
during the irradiation process.
The representativeness of this database (assemblies with an initial 235U enrichment equal
to 3.1 wt% and a burnup of between 30 and 40 GWd/MTHM) remains to be confirmed, by
providing axial burnup curve measurements for additional assemblies.
3)

Formatting the data and establishing evaluation criteria

In order to compare the axial burnup curves, we formatted the initial data in advance. At
each axial point (at centimetre intervals) of the active height of the assembly, we divided
the local count rate by the total count rate and then multiplied the value by the height of
the assembly to obtain a curve "centered" around the value 1. For each route, after
removing the inconsistent points (negative or close to 0), and for each point, themeasured local burnup was divided by the mean burnup value of the route studied, and by
the number of measurement points.

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regarding PWR UOX fuelThe mean burnup profile, characteristic of each of the two series of assemblies and eachof the routes, was established by calculating an arithmetic mean. The profile for thestudied assembly was then compared to the calculated mean profile.
In order to quantify the level of consistency between an assembly profile and the mean
profile for the series, two additional evaluation criteria were established:A Mean Standard Deviation (MSD) was associated with each burnup profile; this was
defined for each assembly using the following formula: plot  (  ~ )
i

2

i

i

N

where:

 i corresponds to the assembly burnup at point i;
~ corresponds to the mean profile burnup at point i;i

N corresponds to the number of axial points along the total length of the assembly.
The summation is performed for all of the axial profile measuring points (centimetreby centimetre).
This criterion is used to evaluate the overall consistency of an assembly profile inrelation to the mean profile. A profile is considered to be inconsistent with the mean
profile when MSD > 10% (chosen as an arbitrary value).
A Series Mean Standard Deviation (SMSD) can be formulated based on this estimator,
i.e. the mean of the mean standard deviations calculated for all of the assemblies fora series of burnups ranging between 30 and 40 GWd/MTHM.


The Local Relative Deviation (LRDi) is calculated at each axial point of an assemblyand defined at each measuring point using the following formula: i  ~i
LRDi  ~i
The notations used are the same as those defined above.
This criterion is used to evaluate the local consistency, point by point, of an assembly
profile in relation to the mean profile. A point is considered to be inconsistent withthat of the mean profile when LRDi > 20% (chosen as an arbitrary value). It should be
noted that the level of uncertainty of the local burnup measurements, provided by
COGEMA, was in the region of 20%.

IRSG9

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regarding PWR UOX fuelFor some assemblies, the burnup measured on one of the routes was higher than
30 GWd/MTHM, whereas on the other route it was lower than 30 GWd/MTHM. In the firstcase, the profile is taken into account when calculating the mean, while in the second
case, it is rejected.
We were able to check that the inclusion of the profiles associated with mean burnups
ranging between 25 and 30 GWd/MTHM, to produce the mean profile associated with agiven series and route, would have very little effect on this. The MSD between the mean
profile calculated for the assemblies with a burnup between 30 and 40 GWd/MTHM, andfor those with a burnup between 25 and 40 GWd/MTHM, was always 0.2%, regardless ofthe series or the route.
4)

Results from the analysis of series R103

Here we present the results for the assemblies that have a burnup of between 30 and
40 GWd/MTHM on both sides, representing 94.8% of series R103, and amounting to 290
assemblies.
-

The mean standard deviation for route 1 of the series is 4.9%. We observe that,
overall, none of the assemblies vary significantly from the mean profile for series
R103-Route 1 (MSD > 10%). At the local level, three profiles for assemblies with an
initial enrichment of 3.1 wt% and a burnup between 30 and 40 GWd/MTHM, varysignificantly from the mean profile for series R103-Route 1 (with between 11 and 25
points displaying an LRD > 20%), representing 1% of the total number of assemblies
with a burnup between 30 and 40 GWd/MTHM.

-

The mean standard deviation for route 2 of the series is 5.1%. We observe that,
overall, only one of the assemblies vary significantly from the mean profile for series
R103-Route 2 (MSD > 10%). This anomaly is the result of an obvious measuring error. At
the local level, with the exception of the profile affected by the measuring error, twoassembly profiles vary significantly from the mean profile for series R103-Route 2(with between 11 and 25 points displaying an LRD > 20%). It should be noted that theinitial 235U enrichment of one of these two assemblies is 3 wt%.

-

The mean standard deviation between the normalized mean curves obtained forroutes 1 and 2 is close to 1%. Furthermore, for series R103, we observe a mean
relative deviation, or MRD (defined as the arithmetic mean for a series), of 3.6% fromthe relative deviation between the mean burnups for routes 1 and 2 on the sameassembly.

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regarding PWR UOX fuelA low mean standard deviation between the two mean curves, combined with a low
MRD, demonstrates the close correlation between routes 1 and 2.
This close correlation between the results obtained for routes 1 and 2 on each assembly
illustrates that the burnup across assemblies is similar.
5)

Results from the analysis of series R202

Here we present the results specifically relating to the assemblies with a burnup of
between 30 and 40 GWd/MTHM.
-

The mean standard deviation for route 1 (318 assemblies) is 5.6%. We observe that,
overall, none of the assemblies vary significantly from the mean profile for series
R202-Route 1 (MSD > 10%).
Similarly, at the local level, 19 profiles for assemblies with an initial enrichment of
3.1 wt% and a burnup between 30 and 40 GWd/MTHM, vary significantly from themean profile for series R202-Route 1 (with between 11 and 25 points displaying an
LRD > 20%), representing 6% of the total number of assemblies with a burnup between
30 and 40 GWd/MTHM.

-

The mean standard deviation for route 2 (291 assemblies) is 5.8%. We observe that,
overall, two of the assemblies vary significantly from the mean profile for series R202Route 2 (MSD > 10%).
Similarly, at the local level, with the exception of the profile affected by a measuring
error, eight assembly profiles vary significantly from the mean profile for series R202Route 2 (with between 11 and 25 points displaying an LRD > 20%). Among these eightassemblies, two also display a MSD > 10%.

The mean standard deviation between the normalized mean curves obtained for routes 1
and 2 is close to 0.6%. Furthermore, for series R202, we observe a mean relative deviation(MRD) of 4.00% for the burnups for routes 1 and 2.
This close correlation between the results obtained for routes 1 and 2 on each assembly
illustrates that the burnup is similar on at least two sides of the assemblies.
6)

Determination of an axial burnup curve representative of the database

Taking the assumption that the COGEMA database is representative of the vast majority ofassemblies with an initial enrichment of 3.1 wt% and a burnup between 30 and
40 GWd/MTHM from 1300 MWe reactors, a mean curve can be defined.

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regarding PWR UOX fuelThe representativeness of this database remains to be confirmed, by providing axial
burnup curve measurements for additional assemblies
Based on this feedback, we suggest establishing an axial burnup profile representative of
the assemblies contained in the COGEMA database with initial 235U enrichment equal to
3.1 wt% and with a mean burnup of between 30 and 40 GWd/MTHM. To do this, at eachaxial point (totalling 427 for a 1300 MWe PWR assembly) an arithmetic mean is calculated
based on all of the selected profiles, corresponding to assemblies with an initial 235U
enrichment equal to 3.1 wt% and a mean burnup of between 30 and 40 GWd/MTHM. The
mean profile obtained for each assembly is then normalized again.
This profile can be considered as being a mean model of the profiles from the COGEMA
database.
To illustrate the low variability of the studied profiles, Figure 14Figure 14 shows thenormalized mean curve, together with the maximum and minimum overall curves,obtained from each axial point of all of the assemblies with a mean burnup of between 30
and 40 GWd/MTHM.
With regard to the minimum and maximum overall curves, the mean standard deviations
in relation to the mean curve are 18.05% and 17.23% respectively (remembering that themeasurement uncertainty for the local burnups is 20%). For the minimum curve, theseresults were obtained based on 118 measuring points, 64 of which are located over thelast 50cm of either end of the assembly; the mean relative deviation is greater than 20%(bearing in mind that a profile comprises 427 points). For the maximum curve, we took 95
measuring points, 53 of which are located over the last 50cm of either end of theassembly; the mean relative deviation is greater than 20% (bearing in mind that a profile
comprises 427 points).

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▪

Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuelThe table below describes the mean profile obtained, discretized according to
12 zones.
Table 19: Description of the mean profile discretized according to 12 zones.
Zone

Length (cm)Beginning of zone

End of zone

Normalized BU

1

6

0

6

0.457

2

2

6

8

0.543

3

3

8

11

0.653

4

5

11

16

0.747

5

20

16

36

0.919

6

17

36

53

0.977

7

293.8

53

346.8

1.0618

8

35

346.8

381.8

1.014

9

17

381.8

398.8

0.935

10

20

398.8

418.8

0.736

11

5

418.8

423.8

0.545

12

3

423.8

426.8

0.476

1.2 -

—.—Normalized mean axial curve—À—Mea n curve d iscrelized accord i ng to 12 zones
0,2

I- CNI C•7 , . , [ID CD 0 CNI C•7 , Ln ID CD 0 0 I- CNI , Ln ID , CD 0 I- CNI C•7 , ID , CD 0 0 CNI

Axial point (cm)Figure 13: Normalized mean axial curves representative of an assembly with initialenrichment equal to 3.1 wt% and a burnup of between 30 and 40 GWd/MTHM from the
COGEMA database, together with the mean curve discretized according to 12 zones

IRSG]

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regarding PWR UOX fuelNormalized burnup

1,4

0,8

0,6

—à—Minimum overall curve
0,4—.—Normalized mean axial curve
0,2—à—Maximum overall curve

0
0

50

100

150

200

250

300

350

400

450

Axial point (cm)Figure 14: Normalized mean axial curves, and minimum and maximum overall curves,obtained from the assemblies with initial enrichment equal to 3.1 wt% and a burnup of
between 30 and 40 GWd/MTHM from the COGEMA database
This profile is compared to the four mean burnup profiles characteristic of each of the twoseries and two routes (R103-Route 1, R103-Route 2, R202-Route 1 and R202-Route 2). The
MSDs calculated in relation to the mean profile are 1.8%, 1.8%, 1.5% and 1.5%
respectively. It can be seen that the MSDs for the mean profiles for series R202 are lower
than those for series R103, since series R202 contained more assemblies than R103 (338compared to 306), which significantly affect the mean profile.
In conclusion, the statistical analysis of the burnup profiles supplied by COGEMA does notreveal any particular axial deformation attributable to operation with partially inserted
rods. The mean profile obtained is representative of the curves likely to be observed in
French PWR operating modes used currently, or envisaged in the near future, including for
the EPR. This representativeness will be extended to other axial burnup curvemeasurements for fuel assemblies. If there is no significant change in the operating mode
for these reactors, and since the profile obtained is not found to be highly variable, there
does not appear to be any reason why this profile should not be used in the criticality
safety studies that take burnup credit into account. Using the mean profile without
penalties for the criticality studies cannot be considered as a viable approach for taking
burnup credit into account. Safety studies using such a profile will need to incorporate
sufficient margins to ensure the overall conservatism of the approach.

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regarding PWR UOX fuel

APPENDIX 9
ISSUE OF COOLING TIME FOR LONG -TERM STORAGE

Variations in reactivity with the cooling time occur, on the one hand, as a result of changes
in the characteristics of the used fuel composition (competition between the presence offissile actinides, essentially 235U, 239Pu and 241Pu, and absorbent actinides such as 241Am,
240

Pu, 237Np, 236U and 238U), and, on the other hand, due to variations in the neutron

spectrum, which is closely linked to the present nuclides.
Although, on the whole, major trends can be easily ascertained (a significant decrease inreactivity during the first 100 years, an almost identical rise in amplitude over a period of
between 20,000 and 40,000 years, followed by a further decrease over around 1 million
years), the amplitudes of the negative and then positive variations are difficult to predict
without prior calculations. They depend on both the irradiation conditions (i.e. thehypotheses relating to the calculation under flux) and the characteristics of the burnup
profile used (i.e. the level of under-irradiation of the upper part).
For example, an assembly irradiated at between 10 and 20 GWd/MTHM with a flat profile,
without the presence of rods, will be more reactive after 30,000 years of cooling than when
it leaves the reactor. However, above 30 GWd/MTHM (with a flat profile), and all things
being equal, the assembly will be most reactive when it leaves the reactor.

1.

Short cooling times (< 1,000 years)

For handling or interim storage operations that take place during the first 1,000 years after
the assembly has left the reactor, the issue is relatively easy to manage, in the sense thattaking a fixed cooling time of 30 days into account will guarantee the conservative nature of
the results.
However, margins may be determined if necessary, provided that the conservative nature of
the selected cooling hypotheses is checked: if we take a cooling time T, the reactivity
obtained at the time T must be greater than that recorded at the times t1 and t2,
corresponding respectively to the beginning and end of the operations being studied, as
shown in the figures below.

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regarding PWR UOX fuel1 AC

ker (g) > ken fe:) > ken (t 2)1

Keff(30 Baya)---«'----«'-'«'-'—''-'--■__,,....Lro,>ea,:,..„,,,..,..„,..______

e=

u..

Phase of interest

4
0,70

065

060
on,

0.1

10

1

lOct

1000
Ic

Time (years);;

Keff(30 Baya)

Figure 15: Example of use of the ratio keff(t)/keff(30 days)Iker (g) > kerr (i2) > keft ( ti)

,
r

t,

Phase of interest
4

L/7.
on,

0.1

1

Io

loa

Ion

Ti me (years}

Figure 16: Example of use of the ratio keff(t)/keff(30 days)

2.

Long cooling times (> 1,000 years)

For handling or interim storage operations that take place more than 1,000 years after theassembly has left the reactor, the possibility of an increase in reactivity, above that seen
when the reactor was shut down, demands that great care be taken when defining thecooling hypotheses, given that the reactivity peaks after 20,000 to 40,000 years. The use of
a fixed cooling time of 30 days will not guarantee the conservative nature of the results.
It is clear that the characteristics of the used fuel composition after irradiation willcondition the changes in reactivity with the cooling and will, therefore, influence whether
or not the reactivity peaks at a higher level than initially.

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regarding PWR UOX fuelGiven the diversity of the input parameters (enrichment, irradiation, profiles) and the times
in question, we maintain the principle that checking the conservative nature of the cooling
hypotheses will be necessary, as illustrated by the figures below.
1.2
1,15

Low irradiation
under a flat profile

1,1

Or

Strong peaked profile
with significant
under-irradiationin the upper part

Fe 1
-0

i

a
Ÿ cos
....
ô;
E "

.9111111111111M Keff (30,000 yrs)> Keff (30 days) M
ir

E 0.85
W

>e

ne
Eus
0,7

oel

a.,

1

lu

Ion
Time (years}

lcre

loax

Io=

Figure 17: Example of checking the conservative nature of the cooling hypotheses

High irradiation
under a flat profileOr

K eff(ti m e) f K eff(30 d ays)

Weak peaked profile with slightunder-irradiationin the upper part
Keff (30 clays)> Keff (30,000 yrs)

0.1

i

Io

101

.

.

in

10000

11:170;0Time (years}

Figure 18: Example of checking the conservative nature of the cooling hypotheses

It can be ascertained that the transition to one curve or the other occurs at around
20 GWd/MTHM with a flat profile and 40 GWd/MTHM with a "Maillot" type peaked profile(below these values keff (30,000 years) > keff (30 days), and above these values
keff (30 days) > keff (30,000 years)).

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APPENDIX 10
IMPACT OF THE CONTROL ROD INSERTION HISTORYI

FEEDBACK

The diversity of the various plant series operated by EDF, and their associated fuelmanagement systems, means that there is a whole range of fuel assemblies with relatively
dispersed enrichments, especially when the startup cores have been loaded with assemblies
other than those nominally enriched in accordance with the core management.
The table below summarizes some of this diversity.
Table 20: EDF core management
Plant series
Original
management

CP0 (FE & BU)
1/3

CPY
3.25 wt%

1300

3.25 wt%

1/3

/

/

1/3 4.0 wt%
GEMMES

Original
management

Intermediate
management

1/4

3.7 wt%1/3 3.7 wt%
1/4 3.7 wt%
1/3 MOX

Current
management

1/3 4.2 wt%
CYCLADES

1/4 3.7 wt%
MOX hybrid
GARANCE

1/3

3.10 wt%

N4
1/3

3.40 wt%

The use of theoretical loading patterns to perform a statistical probability analysis of thepresence of a control rod (CR)13 during the life of an assembly is delicate, as the assemblies
at the sites are not necessarily associated with a particular core management; switches canbe made from one core management to another through so-called transition plans, which
are different from the equilibrium plans; actual plans can differ from the theoretical plans
depending on the actual availability of the assemblies; unplanned outages can lead theoperator to rearrange the core, etc.
Consequently, rather than analyzing theoretical loading patterns, the statistical study
presented here relates to the 38,821 PWR UOX assemblies supplied to La Hague in early
2005. Overall (with all assemblies combined), the following results are obtained:

51.5% of the population was irradiated with CRs for at least one reactor campaign;

22.8 % of the population was irradiated with CRs during the last reactor cycle.

13

A control rod is taken to mean a fine control rod or a regulating rod; the term does not cover rods associatedwith reactor trip systems.

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regarding PWR UOX fuelA slightly closer analysis could be conducted to reveal the trends associated with aparticular type of assembly.
However, to preserve populations containing a significant number of objects, some of theassemblies are intentionally disregarded, such as those used on the startup cores (1.8 wt%,
2.1 wt%, 2.4 wt%, etc.), those that are too specific (including gadolinium), etc., in order tofocus on the families that could be characterized by the nominal enrichments of thedifferent core managements (3.25 wt%, 3.7 wt%, etc.). The results obtained are summarized
in the table below.
Table 21: Proportion of assemblies with a control rod inserted during irradiation

Plant series

900 PWR
1300 PWR
N4Enrichment

Population(assemblies)% with CR
inserted forat least one
campaign% with CR
inserted inlast cycle% with CR
inserted for
all cycles

3.25 wt%

10,44456.5 %

24.9 %

0.9 %

3.70 wt%

9,375

62.9 %

12.4 %

0.4 %

3.10 wt%

7,445

42.2 %

22.2 %

0.1 %

4.00 wt%

1,263

52.3 %

0%0%3.40 wt%

-

-

-

-

In relation to the overall statistics, although the major tendencies are effectively preserved(around 50% of the assemblies had control rods inserted, which took place during the last
reactor cycle in around 50% of the cases), the following specific observations can be made:

for fewer than 25% of the 3.7% assemblies irradiated with control rods, this occurred
during their last reactor cycle;no assemblies under the GEMMES core management (1300 MWe PWR, E = 4 wt%) were
irradiated with control rods during their last cycle in the reactor;



only a very small number of assemblies were irradiated with control rods during all of
the irradiation cycles (< 1%).

In conclusion, the feedback on the assemblies sent by EDF to La Hague in early 2005 reveals
the following:a very large population was irradiated with control rods during at least one reactor
campaign (around 52% of the assemblies). A close analysis of the results does notreally reveal any particular category of assemblies that do not display thischaracteristic;

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regarding PWR UOX fuelthe percentage of assemblies irradiated with control rods during the last reactor

cycle is significant (around 23%). However, a close analysis of the results reveals
some peculiarities: among the 900 MWe PWR assemblies enriched at 3.7 wt%, lessthan 13% of the population was irradiated with a control rod during the last reactor
cycle, and this percentage was zero for the 1300 MWe PWR assemblies enriched at
4 wt%.
Moreover, when assemblies were irradiated with control rods, in general they were only
inserted partially. The partial insertion of an absorbent rod is likely to have a significant
impact on the results, due to both an under-irradiation effect on the upper part of theassembly, and a neutron spectrum hardening effect, which tends to favor the production of
plutonium locally.

II

IMPACT OF THE CONTROL ROD INSERTION HISTORY

The purpose of this study is to examine the impact on a criticality calculation of theirradiation of UOX assemblies with control rods (comprising 24 absorbent rods) inserted. To
do this, depletion calculations were performed using the DARWIN V2 fuel cycle package,followed by a criticality calculation on a pool storage configuration using the CRISTAL V1
criticality safety package (the chosen criticality configuration maximizes the effects under
examination).
To this end, three configurations are modelled in the depletion calculation:1.

central UOX assembly irradiated without control rods, surrounded by eight UOX
assemblies irradiated without control rods (serving as a reference);2.

central UOX assembly irradiated with control rods inserted, surrounded by eight UOX
assemblies irradiated without control rods (control rod insertion study);

3.

central UOX assembly irradiated with control rods inserted, surrounded by eight MOX
assemblies irradiated without control rods (MOX environment and control rod
insertion study).

In this study, the used fuel composition for the criticality calculation consisted of thenuclides selected for the burnup credit studies, as follows: actinides 234U, 235U, 236U, 238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 237Np, 241Am and 243Am;
 the 15 fission products: 103Rh, 133Cs, 143Nd, 149Sm, 152Sm, 155Gd, 95Mo, 99Tc, 101Ru, 109Ag,
145

Nd, 147Sm, 150Sm, 151Sm and 153Eu; with a zero cooling time.

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regarding PWR UOX fuelIn order to maximize the effect of the control rods, we used the most efficient absorbent,
B4C (it should be noted that in the French 900 MWe PWRs, the rods consist of 24 silverindium-cadmium rods).
In order to separate the used fuel composition problem from the "end effect" problem, theaxial burnup profile was taken to be uniform and equal to the assembly mean burnup.
In the tables below,  is the difference in reactivity defined by the formula:  ρ (case2) - ρ (case1)  Ln

K eff (case2)
K eff (case1)

1) Impact of the FULL axial insertion of control rodsa) In the central UOX assembly surrounded by UOXTable 22 shows the effect of the full axial insertion of control rods on the reactivity of alattice of UOX assemblies, throughout the entire irradiation process or during a part of it,
for each assembly in the lattice.
Table 22: Effect of irradiation on the reactivity of a UOX lattice, in a UOX environment witha full axial insertion of control rods compared to a UOX environment without control rods
 (UOX with CR, UOX env.) -  (UOX w/out CR, UOX env.)
BU of UOX
assembly lattice

UOX with CR
from 0 to 40
GWd/MTHM

UOX with CR
from 0 to 12
GWd/MTHM

UOX with CR
from 12 to 24
GWd/MTHM

UOX with CR
from 24 to 40
GWd/MTHM

10 GWd/MTHM+ 274 pcm

+ 274 pcm--

20 GWd/MTHM+ 1,067 pcm+ 471 pcm

+ 419 pcm-

30 GWd/MTHM+ 2,260 pcm+ 444 pcm

+ 814 pcm

+ 481 pcm

40 GWd/MTHM+ 4,053 pcm+ 516 pcm

+ 675 pcm

+ 2,085 pcm

The presence of control rods during the irradiation of a UOX assembly hardens the neutron
spectrum, leading to an increase in the production of plutonium and, therefore, an increasein the reactivity of the UOX assembly lattice. This increase is all the more considerable
when the control rods are inserted for a long period of time or at a later point during theirradiation process. The maximum increase in reactivity is around 4,000 pcm if the control
rods are fully inserted throughout the entire irradiation (up to 40 GWd/MTHM).

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regarding PWR UOX fuelb) In the central UOX assembly surrounded by MOX
Table 23 shows the effect of the full axial insertion of control rods on the reactivity of alattice of UOX assemblies, throughout the entire irradiation of each assembly.
Table 23: Effect of irradiation on the reactivity of a UOX lattice, in a MOX environment withthe full axial insertion of control rods compared to a MOX environment without control rods
BU of UOX
assembly lattice (UOX with CR, MOX env)  (UOX w/out CR, MOX env.)

10 GWd/MTHM+ 364 pcm

20 GWd/MTHM+ 1,195 pcm

30 GWd/MTHM+ 2,421 pcm

40 GWd/MTHM+ 3,991 pcm

If we compare these values to those in Table 1, it can be seen that the effect of the control
rods insertion is the same.
Table 24 shows the effect of irradiation on the reactivity of a UOX lattice, in a MOX
environment with the full axial insertion of the control rods compared to a UOX environment
without control rods.
Table 24: Effect of irradiation on the reactivity of a UOX lattice, in a MOX environment withthe full axial insertion of the control rods compared to a UOX environment without controlrods (UOX with CR, MOX env.)  (UOX w/out CR, UOX env.)
BU of UOX
assembly lattice

UOX with CR fromUOX with CR from0 to 40 GWd/MTHM

24 to 40 GWd/MTHM

10 GWd/MTHM+ 408 pcm-

20 GWd/MTHM+ 1,494 pcm-

30 GWd/MTHM+ 3,093 pcm-

40 GWd/MTHM+ 5,242 pcm+ 3,280 pcm

When the effects of irradiation with the control rods inserted (Table 1) and a MOX
environment (Appendix 2) are combined, this leads to an increase in reactivity of up to

I RS

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regarding PWR UOX fuel5,200 pcm for a lattice of UOX assemblies irradiated at 40 GWd/MTHM, assuming that all of
the assemblies had the control rods fully inserted throughout the entire irradiation process
in a complete MOX environment (eight MOX assemblies).

2) Impact of the partial axial insertion of the control rods (in the central UOX
assembly surrounded by UOX assemblies)
In reality, control rods are only inserted partially during the operation of French reactors. In
order to quantify the impact of the partial insertion of control rods, we model the insertionof control rods in the upper part of the fuel assembly, to an axial depth of 70 cm, for thecriticality calculation (see Figure 19).

Refiector
B4C

A

Insertion of CR :axial depth= 70 cm

Active heightof assembly= 366 cm

Inventory fromdepietion
calculation with CRv
Fuel

Inventory fromdepietion
calculation without
CR

Refiector(a) Radial insertion(b) Criticality cal cu I ati onof control rod

Figure 19: Illustration of the criticality calculation for the partial insertion of control rods
The impact on an infinite lattice of UOX assemblies, irradiated at 40 GWd/MTHM with apartial insertion (70cm) of the control rods, throughout the irradiation of each UOX
assembly, is around +1,300 pcm (compared to +4,000 pcm with the full axial insertion of thecontrol rods).

I RSG1

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regarding PWR UOX fuel

APPENDIX 11

STUDY OF POISONED RO DS FOR 1300 MWE PWR ASSEMBLIES

1. PRESENTATION OF THE STUDYIn France, certain UOX management methods, such as CYCLADES for the 900 MWe PWRs or
GEMMES for the 1300 MWe PWRs, include assemblies reloads containing gadolinium rods.
As part of the studies on burnup credit, the impact on the used fuel composition, and on theinfinite multiplication factor (outside the reactor), of the presence of gadolinium rods
during the irradiation of a UOX assembly is evaluated.
The case of a 17x17 PWR assembly with four or eight gadolinium rods is studied, with an
initial enrichment of the UO2 rods of 4.1 wt%. The 235U enrichment of the Gd2O3 rods is
0.72 wt% with a Gd2O3 enrichment of 8 wt%, or 2.6 wt% with a Gd2O3 enrichment of 6 wt%.
The positions of the four and eight gadolinium rods in the UOX assembly are shown in
Figure 20.

MMMMMMMMMMMMMMMM

MUMMMMMMMMMUMMUM
MM. MM MM MM.
MUM MMIMMMMMM MM
MMMMMMMMMMMMMMMM
MM MM MM MM MM MM ❑MUMMMMMMMMUMMUMMM
MUMMMMMMMMMUMMUM ❑MM MM MM MM MM MM
MUMMMMMMMMMUMMUM ❑MUMMMMMMMMMUMMUM
MM MM MM MM MM MM
MMMMMMMMMMMMMMMM•

LI 02 'OCIS

4 gadolinium rods
8 gadolinium rads
guide tubes

MUM MMMMMMMMM MM
MM. MM MM ■■■■■
MMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMM

Figure 20: Positions of the four and eight gadolinium rods in the PWR UOX assembly
The depletion calculations are performed using the APOLLO2.5 code and the criticality
calculations are performed with the CRISTAL V1.0 criticality safety package.

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regarding PWR UOX fuel2. IMPACT ON THE USED FUEL INVENTORY
2.1 Four gadolinium rods with 0.72 wt% 235U
Table 25 shows the difference in the used fuel inventory of the BUC nuclides between
irradiation with four gadolinium rods (0.72 wt% 235U) in the assembly and irradiation without
gadolinium rods.
Table 25: Four Gd2O3 0.72 wt% - Observed biases (%) in the used fuel composition
BU(GWd/MTHM)
No cooling

0

2

5

10

20

30

40

50

60

234

-1.5%

-1.6%

-1.7%

-1.8%

-1.9%

-2.0%

-2.1%

-2.2%

-2.2%

235

-1.28%-1.32%-1.39%-1.51%-1.75%-2.06%-2.47%-2.86%-3.24%

-0.1%

-0.2%

-0.3%

-0.6%

-0.7%

-0.8%

-1.0%

-1.1%

-0.108%-0.112%-0.118%-0.122%-0.126%-0.131%-0.135%-0.139%

U
U

236

U

238

-0.107%

U

238

Pu

4.1%

4.1%

3.7%

2.0%

1.2%

0.7%

0.3%

0.0%

239

Pu

2.0%

1.9%

1.7%

0.4%

-0.1%

-0.4%

-0.6%

-0.5%

240

Pu

2.1%

1.8%

2.1%

1.7%

1.2%

0.8%

0.4%

0.1%

241

Pu

4.8%

3.5%

1.8%

1.6%

0.8%

0.3%

0.1%

-0.1%

242

Pu

5.4%

4.5%

3.6%

2.4%

2.1%

1.8%

1.5%

1.1%

237

Np

2.3%

2.2%

1.8%

0.6%

0.1%

-0.2%

-0.4%

-0.6%

241

Am

4.9%

4.1%

3.0%

1.5%

0.9%

0.2%

-0.2%

-0.5%

243

8.1%

7.4%

6.2%

3.2%

2.6%

2.2%

1.8%

1.5%

-0.3%

-0.3%

-0.2%

0.1%

0.1%

0.1%

0.0%

-0.1%

133

Cs

-0.4%

-0.4%

-0.3%

-0.2%

-0.2%

-0.2%

-0.2%

-0.2%

143

Nd

-0.5%

-0.5%

-0.4%

-0.4%

-0.4%

-0.5%

-0.6%

-0.7%

145

Nd

-0.4%

-0.4%

-0.4%

-0.3%

-0.3%

-0.3%

-0.3%

-0.3%

Gd (FP)

0.2%

1.1%

1.2%

0.1%

-0.3%

-0.6%

-1.0%

-0.4%

95

-0.5%

-0.5%

-0.5%

-0.3%

-0.3%

-0.3%

-0.3%

-0.3%

-0.4%

-0.4%

-0.3%

-0.2%

-0.2%

-0.2%

-0.2%

-0.2%

-0.4%

-0.3%

-0.2%

-0.1%

0.0%

0.0%

0.0%

-0.1%

109

Ag

1.1%

1.4%

1.6%

1.6%

1.3%

1.0%

0.8%

0.6%

147

Sm

-0.5%

-0.6%

-0.7%

-0.6%

-0.6%

-0.6%

-0.7%

-0.7%

149

0.3%

1.1%

0.3%

-0.8%

-0.9%

-1.0%

-1.7%

-0.9%

150

-0.4%

-0.3%

0.0%

0.1%

0.1%

0.1%

0.0%

-0.1%

151

-0.4%

-0.2%

0.1%

-0.4%

-0.5%

-0.6%

-0.6%

-0.5%

152

-0.3%

-0.3%

-0.3%

0.1%

0.1%

0.1%

0.1%

0.0%

0.0%

0.4%

0.7%

0.5%

0.4%

0.4%

0.2%

0.1%

Am

103

155

Rh

Mo

99

Tc

101

Ru

Sm
Sm
Sm
Sm

153

I RS ElEu

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regarding PWR UOX fuel2.2 Eight gadolinium rods with 0.72 wt% 235U
Table 26 shows the difference in the used fuel inventory of the BUC nuclides between
irradiation with eight gadolinium rods (0.72 wt% 235U) in the assembly and irradiation
without gadolinium rods.
Table 26: Eight Gd2O3 0.72 wt% - Observed biases (%) in the used fuel composition
BU(GWd/MTHM)
No cooling

0

2

5

10

20

30

40

50

60

234

-3.0%

-3.1%

-3.3%

-3.5%

-3.7%

-3.8%

-3.9%

-4.0%

-4.0%

235

-2.56%-2.64%-2.75%-2.92%-3.24%-3.63%-4.06%-4.45%-4.67%

-0.2%

-0.5%

-0.8%

-1.4%

-1.7%

-1.9%

-2.2%

-2.3%

-0.22%-0.23%-0.24%-0.25%-0.26%-0.27%-0.28%-0.29%

U
U

236

U

238

U

-0.21%

238

Pu

8.7%

8.4%

7.1%

3.4%

1.7%

0.8%

0.2%

-0.3%

239

Pu

4.9%

4.6%

3.9%

1.6%

0.6%

0.2%

0.1%

0.3%

240

Pu

5.0%

4.3%

4.3%

3.6%

2.7%

2.0%

1.5%

1.0%

241

Pu

11.0%

8.7%

5.6%

3.4%

2.0%

1.2%

0.7%

0.6%

242

Pu

11.9%

10.0%

8.0%

5.3%

4.1%

3.3%

2.6%

1.9%

237

Np

4.8%

4.5%

3.5%

0.9%

-0.1%

-0.7%

-1.0%

-1.3%

241

Am

11.1%

9.5%

7.2%

4.0%

2.4%

1.3%

0.7%

0.5%

243

17.6%

15.7%

12.6%

6.8%

5.1%

4.0%

3.1%

2.4%

-0.6%

-0.5%

-0.3%

0.2%

0.3%

0.3%

0.2%

0.1%

133

Cs

-0.9%

-0.9%

-0.8%

-0.5%

-0.5%

-0.4%

-0.5%

-0.5%

143

Nd

-1.0%

-1.0%

-1.0%

-0.9%

-0.9%

-1.0%

-1.0%

-1.0%

145

Nd

-0.9%

-1.0%

-0.9%

-0.8%

-0.7%

-0.7%

-0.7%

-0.7%

Gd (FP)

0.7%

2.9%

3.6%

0.6%

0.1%

-0.2%

-1.3%

0.2%

95

-1.0%

-1.0%

-1.0%

-0.8%

-0.8%

-0.7%

-0.7%

-0.7%

-0.9%

-0.9%

-0.8%

-0.6%

-0.5%

-0.4%

-0.4%

-0.5%

-0.8%

-0.7%

-0.5%

-0.3%

-0.2%

-0.2%

-0.2%

-0.2%

109

Ag

2.6%

3.4%

3.7%

3.4%

2.7%

2.1%

1.7%

1.3%

147

Sm

-1.0%

-1.2%

-1.4%

-1.3%

-1.1%

-1.1%

-1.1%

-1.0%

149

0.8%

2.3%

0.8%

-1.3%

-1.2%

-1.2%

-1.4%

-0.6%

150

-0.9%

-0.6%

-0.2%

0.0%

0.0%

-0.1%

-0.1%

-0.2%

151

-0.7%

-0.3%

0.3%

-0.6%

-0.7%

-0.7%

-0.7%

-0.4%

152

-0.6%

-0.7%

-0.6%

0.1%

0.1%

0.1%

0.0%

-0.1%

0.0%

0.7%

1.2%

0.8%

0.6%

0.5%

0.3%

0.2%

Am

103

155

Rh

Mo

99

Tc

101

Ru

Sm
Sm
Sm
Sm

153

Eu

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regarding PWR UOX fuel2.3 Four gadolinium rods with 2.6 wt% 235U
Table 27 shows the difference in the used fuel inventory of the BUC nuclides between
irradiation with four gadolinium rods (2.6 wt% 235U) in the assembly and irradiation without
gadolinium rods.
Table 27: Four Gd2O3 2.6 wt% - Observed biases (%) in the used fuel composition
BU(GWd/MTHM)
No cooling

0

2

5

10

20

30

40

50

60

234

-0.8%

-0.9%

-0.9%

-1.0%

-1.0%

-1.1%

-1.1%

-1.2%

-1.2%

235

-0.61%-0.62%-0.63%-0.66%-0.76%-0.91%-1.09%-1.27%-1.42%

0.1%

0.0%

-0.1%

-0.2%

-0.3%

-0.4%

-0.4%

-0.5%

-0.071%-0.074%-0.079%-0.081%-0.083%-0.085%-0.087%-0.089%

U
U

236

U

238

-0.069%

U

238

Pu

3.8%

3.7%

3.1%

1.5%

0.8%

0.5%

0.3%

0.1%

239

Pu

1.9%

1.8%

1.4%

0.4%

0.0%

-0.1%

-0.2%

-0.2%

240

Pu

1.9%

1.6%

1.9%

1.3%

0.8%

0.5%

0.3%

0.1%

241

Pu

4.4%

3.0%

1.2%

1.1%

0.6%

0.3%

0.1%

0.0%

242

Pu

4.8%

3.8%

2.7%

1.4%

1.2%

1.1%

0.8%

0.6%

237

Np

2.2%

2.1%

1.6%

0.6%

0.2%

0.0%

-0.1%

-0.2%

241

Am

4.5%

3.7%

2.4%

1.1%

0.7%

0.3%

0.1%

-0.1%

243

7.3%

6.5%

4.9%

1.9%

1.5%

1.2%

1.0%

0.8%

-0.2%

-0.2%

-0.1%

0.2%

0.2%

0.1%

0.1%

0.0%

133

Cs

-0.3%

-0.3%

-0.2%

-0.1%

0.0%

0.0%

-0.1%

-0.1%

143

Nd

-0.4%

-0.4%

-0.3%

-0.2%

-0.2%

-0.2%

-0.3%

-0.3%

145

Nd

-0.4%

-0.3%

-0.2%

-0.1%

-0.1%

-0.1%

-0.1%

-0.1%

Gd (FP)

0.5%

1.6%

1.1%

0.5%

0.2%

-0.1%

-1.1%

-0.01%

95

-0.4%

-0.4%

-0.4%

-0.2%

-0.1%

-0.1%

-0.1%

-0.1%

-0.3%

-0.3%

-0.2%

-0.1%

0.0%

0.0%

-0.1%

-0.1%

-0.3%

-0.2%

-0.1%

0.0%

0.0%

0.0%

0.0%

0.0%

109

Ag

1.0%

1.2%

1.3%

1.1%

0.8%

0.6%

0.5%

0.3%

147

Sm

-0.4%

-0.5%

-0.5%

-0.4%

-0.3%

-0.3%

-0.3%

-0.3%

149

1.1%

1.9%

0.3%

-0.3%

-0.3%

-0.4%

-1.0%

-0.3%

150

-0.5%

-0.3%

0.0%

0.1%

0.1%

0.1%

0.0%

0.0%

151

-0.2%

0.1%

0.3%

0.0%

-0.1%

-0.2%

-0.3%

-0.1%

152

-0.3%

-0.3%

-0.2%

0.1%

0.1%

0.1%

0.1%

0.0%

0.0%

0.3%

0.5%

0.3%

0.3%

0.2%

0.2%

0.1%

Am

103

155

Rh

Mo

99

Tc

101

Ru

Sm
Sm
Sm
Sm

153

I RS ElEu

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Summary report on the French Burnup Credit Working Group knowledge
regarding PWR UOX fuel2.4 Conclusion
The most significant effects observed on the used fuel composition involved the plutonium
and americium isotopes. The increase in the concentration of these nuclides of a few
percent is due to neutron spectrum hardening, which caused an energy increase in the
integrated flux, together with a modification of the capture cross-section integrated into
one group of the 238U and the plutonium isotopes. The increase in the concentration of these
nuclides is even higher due to the gadolinium in the assembly.
This increase lessened as soon as the burnup exceeded 20 GWd/MTHM, reflecting thedepletion of the gadolinium 155 in the gadolinium-poisoned rods.
3. IMPACT ON THE KINF OF A STORAGE POOL
Below we present the differences between the Kinf for an infinite lattice of UOX assemblies
in the pool, irradiated with gadolinium rods, and the Kinf for an infinite lattice of UOX
assemblies in the pool, irradiated without gadolinium rods.
The Kinf is calculated by taking the BUC nuclides into account, namely:

actinides 234U, 235U, 236U, 238U, 238Pu, 239Pu, 240Pu, 241Pu, 242Pu, 237Np, 241Am and 243Am;

the 15 fission products: 103Rh, 133Cs, 143Nd, 149Sm, 152Sm, 155Gd, 95Mo, 99Tc, 101Ru, 109Ag,
145

Nd, 147Sm,

150

Sm,

151

Sm and 153Eu. With regard to theconcentration of the

155

155

Gd, we added the

Gd produced by fission to the concentration of the 155Gd

contained in the gadolinium-poisoned rods.
In order to separate the used fuel composition problem from the "end effect" problem, theaxial burnup profile was taken to be uniform and equal to the assembly mean burnup.
Table 28 shows the differences between the Kinf for an infinite lattice of assemblies in thepool, irradiated with gadolinium rods, and the Kinf for an infinite lattice of assemblies in thepool, irradiated without gadolinium rods. In this case, we do not take account of coolingtimes between the end of irradiation and storage in the pool.

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regarding PWR UOX fuelTable 28: Observed biases in reactivity of the storage pool
[Kinf (UOX-Gd2O3) - Kinf (UOX)] x 105
BU of assembly

lattice

4 Gd2O3
8 Gd2O3
0.72 wt% 235U 0.72 wt% 235U

4 Gd2O3
2.6 wt% 235U

2 GWd/MTHM-2,790-2,800-2,5605 GWd/MTHM-2,550-2,590-2,25010 GWd/MTHM-1,980-2,010-1,74020 GWd/MTHM

-260

-270

-145

30 GWd/MTHM

-300

-430

-220

40 GWd/MTHM

-370

-450

-240

50 GWd/MTHM

-510

-540

-180

60 GWd/MTHM

-470

-480

-350

Table 28 shows that despite the increase in the concentration of plutonium isotopes, theKinf decreases due to the presence of gadolinium 155 in the gadolinium-poisoned rods. Thisdecrease lessens as soon as the burnup exceed 20 GWd/MTHM, reflecting the consumptionof the gadolinium in the gadolinium-poisoned rods.
However, a study showed that cooling has no effect on the impact of the UO2-Gd2O3 rods.

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regarding PWR UOX fuel

APPENDIX 12STUDY OF THE STORAGE OF USED FUEL ASSEMBLIES WITHGADOLINIUM

1. INITIAL COMPOSITION OF THE FUELFor fuel assemblies with gadolinium rods, the only differences from a standard fuel assembly
are the 235U (or fissile Pu) enrichment of the uranium support and the Gd enrichment.
The support is studied to minimise the local power when the odd nuclides, 157Gd and 155Gd,
disappear. For the usual assemblies with gadolinium (8 wt% Gd2O3), this occurs at
10,000 MWd/MTHM locally.
Due to axial leakage and the reduced density of the water in the upper part of theassembly,

thisburnupis

obtained

for

a

mean

assembly

burnupofaround25,000 MWd/MTHM.
This is the period during which the presence of Gd causes additional axial perturbation for
the assembly. Therefore, the detailed examination of the axial distribution of theseassemblies is imperative since it is more penalizing.
2. PARAMETERS OF THE DEPLETION OF THE FUEL
As in the case of fuel that is not poisoned with gadolinium, the final composition of theassemblies containing rods with Gd2O3 depends upon the thermal conditions of the rods andthe moderator:-

fuel temperature;-

water temperature and density;-

power history;-

axial offset of the assembly during depletion;-

radial gradient of the power;-presence or absence of control rods.

3. ESTIMATION OF THE AXIAL BURNUP
For the estimation of the axial burnup, the same approach was used as that adopted by
AREVA-NP for the standard assemblies.

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regarding PWR UOX fuelThe assemblies in the core are currently monitored by calculating the scattering of neutrons
together with the thermal-hydraulics. For AREVA NP – France, the axial mesh used has
between 16 and 20 mesh points. This division is sufficient to monitor the variations in power
without losing important information.
Thus, the axial breakdown used for the criticality calculations, after conducting various
sensitivity analyses, was between 7 and 20 mesh points. The axial homogenisation at eachmesh point may lead to non-conservatism if there is a small number (~ 7) mesh points,
hence the incentive to use the scattering code mesh (of around 20 cm).
4. NUCLIDESThe nuclides concentrations are provided as for the assemblies without gadolinium by
APOLLO2.
To the 30 nuclides (actinides and fission products) we add the depletion of the six
gadolinium isotopes (154Gd to 160Gd). This approach corresponds to that proposed by theOECD, with a conservatism of around 6% to 10% for the negative reactivity of the used fuel,by not taking account of the minor fission products.
5. UNCERTAINTIES TAKEN INTO ACCOUNTThe uncertainties include the following:-technological uncertainties (enrichment, geometry, mass) relating to the componentsof the assembly studied, and to the storage structure;-

the local burnup uncertainty, calculated by the core distribution code or measured;-

the APOLLO2 calculation of the used fuel composition;-

the spectral effect due to the presence of the rods;-

the METHOD uncertainty, representing the C/M deviation from the MC code used inrelation to the critical experiments on which it was validated;-

the statistical uncertainty of the MC code.

For the assemblies with Gd, the additional uncertainty is related to the concentration ofresidualodd

nuclides

of

Gd

in

the

case

of

fairlylowassembly

burnups(<25,000 MWd/MTHM). Beyond this limit, only the even nuclides of Gd influence the keff and,in this case, the uncertainty is very low given the residual effectiveness of these nuclides.

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regarding PWR UOX fuel6. CRITICALITY CALCULATION
The lattice studied is generally conservative based on the part of the pool taken into
account in the MC simulation. The most penalizing is obviously the infinite lattice of cells.
An intermediate configuration is used at AREVA NP, with the simulation of the largest
module consisting of around 100 cells. The gain is due to the fact that the inter-modulewater level is taken into account. The pool configuration with regions I and II is alsomodelled to study the impact of the interface between the two storage regions.
An important parameter for the reliability of the keff obtained is the stabilisation of thefission sources in the volume studied. This leads to very long calculations, such as in thecase of an "entire pool" simulation.
7. EXAMPLES OF UO2 WITH GADOLINIUM RODS
The minimum mean burnup observed in the balanced cycle is 37.7 GWd/MTHM for an
assembly with eight gadolinium rods and 38.5 GWd/MTHM for an assembly without
gadolinium rods.
An initial analysis is carried out to compare the 2D and 3D approaches.
Table 29 below shows that this burnup is at the limit with regard to the conservatism of the
2D method, thus without axial leakage. This leakage is found to have an impact on keff ofabout 300 pcm. Taking the axial burnup into account results in perfect equality(keff = 0.9400).
The same burnup but with eight gadolinium rods and a new axial burnup leads to a slightdecrease in reactivity. This configuration is equivalent, in terms of the keff value, to an
assembly at 38.5 GWd/MTHM without gadolinium, studied in 3D with its own axial burnup
profile.
Table 29: keff for UO2 with 4.45 wt% 235U
Case

Mean burnup

Axial burnup

Model

Number ofgadolinium rods

Keff

1

37.7 GWd/MTHM

No

2D

0

0.94

2

37.7 GWd/MTHM

No

3D

0

0
0.93

3

37.7 GWd/MTHM

Yes

3D

0

8
0.94

4

37.7 GWd/MTHM

Yes

3D

8

0
0.93

5

38.5 GWd/MTHM

Yes

3D

0

5
0.93
4

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These results were obtained for a burnup characteristic of a 1/3 management method andan 235U enrichment limited to 4.45 wt%.
This situation is very different for EPR management methods with 5.0 wt% 235U and for whichassemblies with 24 gadolinium rods are frequently used. The axial profile is modified alongwith the residual penalty for the even nuclides. For these assemblies, we therefore expect
to see significant differences between the five cases shown in the table above.
Table 30 below shows the differences between the axial profiles for three assemblies
containing 0, 8 and 24 gadolinium rods. The profile with 24 gadolinium rods displays low
values in the upper and lower parts, which should result in a significant difference inreactivity between the three configurations with the same mean burnup.
Table 30: Axial burnup profile for UO2 with 5.0 wt% 235U
Axial mesh

UO2 - 0 Gd

UO2 - 8 Gd

UO2 - 24 Gd

18 (upper)

0.626

0.613

0.583

17

0.891

0.894

0.886

16

0.967

0.996

1.008

Central mesh points

1.079

1.076

1.080

3

1.071

1.069

1.060

2

1.000

0.989

0.965

1 (lower)

0.726

0.700

0.654

8. ORDERS OF MAGNITUDE
Here are some of the typical values for the storage of used fuel assemblies with gadolinium
currently used:-

residual negative reactivity of the even gadolinium isotopes ~ -75 pcm / Gd rod;-axial burnup penalty between 1,000 and 2,000 pcm for a high mean burnup(> 45 GWd/MTHM);

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-

spectral effect of the control rods ~ +300 pcm;-

enrichment uncertainty ~ +800 pcm / +0.1 wt% U235 (5.0 wt% to 5.1 wt%);-

region II storage lattice pitch ~ 500 pcm /mm (lattice 240cm);

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regarding PWR UOX fuel-calculated mean burnup ~ 4%;-

nuclide concentration calculated with APOLLO2 ~ 500 to 1,000 pcm;-

uncertainty method ~ 1,100 pcm.

9. SUMMARY
No specific differences are observed between the storage of the used fuel assemblies withgadolinium and standard storage in region II.
The uncertainties used for the storage of fuel without gadolinium are therefore renewed.
The residual even gadolinium nuclides has a limited effect and the impact of theiruncertainties (cross-sections - concentrations) on the keff is low.
However, particular care is required for the axial modelling of the fuel.
The axial burnup profile is dependent on the mean burnup and the number of gadolinium
rods in the studied assembly. This parameter can generate great differences in reactivity,
despite the residual presence of the even gadolinium nuclides: at equal mean burnup, theeffect of the axial burnup can prevail over the residual penalty of the even gadolinium
nuclides.
The used fuel with gadolinium must therefore be represented with the maximum number ofaxial meshes possible (> 10).

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APPENDIX 13
SIMULATION METHODS AVAILABLE IN THE MORET 4 CODE
The natural or conventional or analogous (to reality) method: this is the method that is
usually available and used in the Monte Carlo criticality codes; the number of neutrons
produced in a volume, divided by the total number of neutrons produced in the system,
represents the proportion of neutrons to be emitted from this volume during the nextstage.
The stratified method: this does not allow the number of source neutrons to be generated
in a fissile volume to be zero when the number of neutrons, sources potentially emitted inthis volume (Pv), is less than 0.5. (Production in this volume is divided by the sum of thesystem entire production.) In this case, (Pv<0.5) with the previous method, no neutrons
would be generated in the volume in question, whereas with the stratified method, asource neutron is generated with a weight equal to the actual number of source neutrons;
the aim of this strategy is to guarantee that every fissile zone (that has very little
interaction with the rest of the system) contains, with each generation, at least one
source neutron with a weight possibly less than 1.
The kij method: this is a simulation option that uses the eigenvector associated with thehighest eigenvalue in the kij matrix to estimate the distribution of the source neutrons in
the following stage, with the aim of accelerating the convergence of the sources; thismethod is very similar to the stratified method, apart from the use of the eigenvector
associated with the highest eigenvalue in the kij matrix to renormalize the distribution of
the source neutrons at every stage "Freq" (Freq is an integer specified by the user); the kijmatrix gives the number of neutrons emitted by fission in the volume i from a neutron
emitted in the volume j; the highest eigenvalue in this matrix is equal to the system
multiplication factor, and the associated eigenvector corresponds to the distribution of theneutrons in the different volumes.
The "super-history" method: this is a simulation option used to monitor a source neutron
and its descendants over L generations in order to avoid recalculating the distribution of
the sources for each generation; for all methods other than the "super-history" method,
the number of neutrons simulated with each generation is constant; it was shown that thisnormalization was the cause of a bias on the calculated keff value and its variance; this was
because by considering a constant number of neutrons for each generation, smaller zones
were likely to be favoured; this method allows the population of neutrons to vary over L
generations; normalization is only performed after these L generations.

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APPENDIX 14
UNCERTAINTIES ASSOCIATED WITH FUEL ASSEMBLY BURNUP
MEASUREMENTSI

PURPOSEThe purpose of this appendix is to summarise the major tendencies in terms of
uncertainties associated with a burnup measurement, depending on the measuring devices
used and the types of assemblies measured.
This appendix summarises the various physical principles on which the various burnup
measurement methods and devices are based, before addressing the uncertainties
associated with these methods.

II

PHYSICAL PRINCIPLES FOR BURNUP MEASUREME NT

Measuring burnup may require the use of two different types of measurements:
gamma spectrometry;

passive neutron measurement.

These two methods are associated with gamma spectrometry measurement: the absolutemeasurement of 137Cs and the Cs ratio method (134Cs/137Cs).

1) Absolute measurement of 137Cs
This radionuclide is a direct fission product. It has no precursor and has a small capture
cross-section. Due to the link between the burnup and the number of fissions, the 137Cs is
produced proportionally to the burnup and decays according to its half-life. Furthermore,
its thermal fission yields for both 235U and 239Pu are identical. Therefore, the quantity of137

Cs (or its activity) is independent of the initial quantity of

235

U, and thus theenrichment. Finally, it is not sensitive to variations in the irradiation history (IH) due to its
long period of decay, of around 30 years.
Its mass or its gamma activity, expressed as Cs137, takes the following form:

Cs137   BU exp( Cs137 CT )where:

α is a coefficient of proportionality
BU represents the burnup

Cs137 denotes the radioactive decay constant of the 137Cs
CT represents the cooling time

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regarding PWR UOX fuelThe method is therefore a measurement of the 662 keV ray of the 137Cs, which is directly
proportional to the burnup.

2) Cs ratio method (134Cs/137Cs)
The main production route of 134Cs is shown in the figure below:( n , )
133
133
134
fission 
133I 


Xe




Cs




Cs
20.8 hrs
5.2 daysstableFigure 21: Production of 134Cs
It can be seen that this production requires two neutron interactions. Therefore, unlike
the 137Cs, the fact that the 134Cs needs two neutrons to be produced means that it develops
proportionaly to the square of the burnup. Moreover, this nuclide decays according to its
approximately two-year half-life and it is independent of the enrichment for the same
reasons as the 137Cs. However, due to its short half-life and the length of the fuel cycles(around one year), this radionuclide is sensitive to the irradiation history (IH).
Therefore, its mass or gamma activity, expressed as 134Cs, follows the law below:

Cs134   BU 2 exp( Cs134 CT ) f ( IH )
 is a coefficient of proportionality

where:

BU represents the burnup

Cs134 denotes the radioactive decay constant of the 134Cs
CT represents the cooling time
f is a function of the irradiation history (IH)
The cesium activity ratio (134Cs/137Cs) thus follows a law that is proportional to the burnup
but dependent on the irradiation history. This method therefore requires to know the fuelirradiation history (the mean power or burnup for each irradiation cycle and the dates ofthese cycles).

3) Neutron method
First of all, neutron emission is mainly caused by the production of curium 244 forstandard burnups for assemblies irradiated in light water reactors (however for very low
burnups of UNGG type reactors, plutonium is the main neutron emitter). For light water
reactors, 244Cm is the predominant neutron emitter and decays according to its half-life ofaround 18.1 years. This makes it insensitive to the irradiation history but it has a

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regarding PWR UOX fueldependency according to the burnup, based on the nature of the fuel. This is because for a
UOX fuel, 244Cm will be produced from the 238U after a long capture chain.
For MOX fuels, the capture chain starts predominantly from the 239Pu, a nuclide located ata shorter "relationship distance" from the 244Cm, involving fewer neutron reactions.
Therefore, while the total neutron emission for a UOX depends on BU where  varies
between 4 and 5, the total neutron emission for a MOX depends on BU2.
Furthermore, for a UOX, if the 235U enrichment increases, then less 239Pu is produced, as itcomes mainly from the capture of 238U, which is in a smaller quantity. This leads to adecrease in the quantity of 244Cm produced. This highlights the dependence of neutron
emission on enrichment for a UOX fuel. As far as MOX fuels are concerned, due to the link
between the initial quantity of Pu and the production of 244Cm, the neutron emission has adependence on the Pu content, expressed as c_Pu.
This measurement requires the use of an actinide depletion calculation code for actinides,
ranging from 235U to 244Cm. This is the reason why this method was the latest to be used inindustry.
The neutron emission (EN), linked to the production of the radionuclide 244Cm, anddepending on the nature of the fuel, is expressed in the following two forms:
For a UOX fuelEN UOX   BU  exp( Cm244 CT ) g ( ENR)
 is a coefficient of proportionality

where:

BU represents the burnup

 varies between 4 and 5
Cm244 denotes the radioactive decay constant of the 244Cm
CT represents the cooling time
g is a function of the enrichment (ENR)
For a MOX fuelEN MOX   BU 2 exp( Cm244 CT ) h(c _ Pu )where:

 is a coefficient of proportionality
BU represents the burnup

Cm244 denotes the radioactive decay constant of the 244Cm
CT represents the cooling time
h is a function of the plutonium content

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regarding PWR UOX fuelNeutron emission is therefore a power function of the burnup and depends on the initial
composition of the fuel.

III

MEASUREMENT METHODS

1) Ionization chamber
An ionization chamber can be used to count all of the gammas emitted by a fuel assembly.
When the fuel cooling time is longer than a few months, the number of gammas emitted isgenerally proportional to the burnup. With this type of measurement, a method similar to
the absolute measurement of 137Cs can be used, but with a greater level of uncertainty due
to the incomplete linearity of the method. This detector is used to track the burnup
profile in the PYTHON system.

2) CZT gamma spectrometry
A cadmium telluride (Cd-Zn-Te) detector is used to perform a gamma spectrometry
analysis with a medium resolution (peak width of around 2%). This type of semi-conductor
detector has the advantage of being able to operate at ambient temperature andaccurately extracts the 134Cs peak at 796 keV and the 137Cs peak at 662 keV. However, themeasurement uncertainty will be slightly higher than with a germanium detector. Thisdetector is used in the SMOPY system.

3) Gamma spectrometry with a germanium detector
The germanium detector operates at -200°C and therefore requires a cooling system.
However, it has an excellent resolution (<0.2%). This type of detector is used on thepermanently installed systems in workshops T1 and R1 at the La Hague plant. With thissystem, the counting uncertainties are negligible.

4) Fission chamber
The fission chamber has an enriched uranium deposit. The thermal neutrons create fissions
in the chamber and the resulting fission products ionize the gas inside it, generating an
associated count rate.
If this method is used in water, the neutrons are thermalized and a bare fission chamber
can be used. At the La Hague plant, measurements are taken in an air environment; thefission chambers are therefore surrounded by polythene to thermalize the neutron flux
exiting the assembly.

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regarding PWR UOX fuelIV UNCERTAINTIES OF THE VARIOUS METHODS AND MEASURIN G
SYSTEMSThe measuring systems installed in the T1 and R1 workshops at the La Hague plant include
gamma spectrometry and fission chamber neutron measurement. This is the most effective
system with the minimum level of uncertainty. First details of this system are provided,
then the sources of uncertainty associated with the other measuring systems aredescribed.

1) Measuring system installed at La Hague
Thanks to operation feedback, we were able to compare the expected neutron activities
and emissions with the measurements. These values are shown in the table below.
Cs134 uncertainty

Cs137 uncertainty

Neutron uncertainty

Minimum

-6.9%

-5.1%

-12.7%

Maximum

8.8%

8.1%

34.7%

Mean

-0.2%

0.8%

1.3%

2 sigma

6.1%

4.7%

13.4%

The observed discrepancies combine three different aspects as follows:

the measurement uncertainties;the uncertainties related to the values provided by the reactor (irradiation history);

uncertainties related to the use of the CESAR code to evaluate the correlation
functions between a measured parameter and the burnup.

For the 137Cs, the measurement uncertainties and the uncertainty relating to the use of
CESAR are negligible.

2) Minimum uncertainties associated with a measuring system
Under measuring conditions, the uncertainty inherent to the measurement calibration
coefficient must also be added to the uncertainties discussed in the paragraph above. Thisadditional uncertainty has a minimum value of 5%. Thus for gamma spectrometry, thetotal uncertainty value is around 10%.
For neutron measurement, the total uncertainty is therefore around 20%.

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regarding PWR UOX fuel3) Additional tendencies depending on the measurement methoda) Gamma spectrometry
The 137Cs method is an absolute method and is therefore sensitive to the measuring
parameters. For example, the assembly moves in front of the detector at a certain speed.
The uncertainty associated with this speed has a direct impact on the measurement.
Similarly, if the assembly is repositioned, this also affects the measurement. However,these parameters do not affect the Cs ratio method as there is a compensation
phenomenon. Ultimately, the Cs ratio method is more accurate.
If a CZT detector is used, the lack of precision associated with the evaluation of the net
areas must also be added, amounting to a few additional percent.
The precision of the absolute 137Cs method can, therefore, be estimated at around 15% to25%, depending on the type of detector and the mechanical precision of the measuringsystem (speed, positioning, acquisition time, etc.).
The 134Cs/137Cs ratio method is a little more accurate, from 10% to 15%, depending on thetype of detector and the acquisition time.

b) Neutron measurement
Like the 137Cs method, neutron measurement is also an absolute approach.

4) Tendencies based on the types of assemblies measureda) 137Cs method
The 137Cs method is independent of the irradiation history, and the production of 137Cs islinear with the burnup. The 137Cs half-life of 30 years also makes the level of uncertainty
stable, even for long cooling times (if this duration is known). The uncertainty of thismethod is relatively stable, based on variations in the assembly characteristics.

b) Cs ratio method (134Cs/137Cs)
The 134Cs is produced by double neutron capture and, as a result, there is very little 134Cs
with a low burnup. The uncertainty of this method therefore increases at low burnup(when the assembly has been through only one irradiation cycle).
The 134Cs half-life of two years makes the method inapplicable when the cooling times arevery long, and particularly when the burnup is low. However, at the La Hague plant, for

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regarding PWR UOX fuelstandard burnups (three to four reactor cycles), measuring an assembly with a cooling timeof 20 years is still possible.

c) Neutron measurement
Assemblies with a low burnup have an even higher impact on neutron measurement
uncertainties due to the production of a very small amount of 244Cm at the start ofirradiation. The neutron method is only applicable to assemblies with a burnup above
10,000 MWd/MTHM. The higher the burnup, the lower the uncertainty of this method.
Compared to the gamma measurement method, this approach also has the advantage ofbeing representative of the entire assembly. This is because with gamma spectrometry,the measured energies are lower than 800 keV and, consequently, the measuring systemsees only the first three rows of rods.

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