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Advances in Burnup Credit Criticality Safety Analysis
Methods and Applications
Jens Christian Neuber, AREVA NP GmbH, PEEA8-G, Criticality Safety and Statistical Analysis
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
1
International Workshop on
Advances in Applications of Burnup Credit
for Spent Fuel Storage, Transport, Reprocessing, and Disposition
organized by the
NUCLEAR SAFETY COUNCIL of Spain (CSN)
in cooperation with the
INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Córdoba, Spain, 27 - 30 October, 2009
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
2
Key Steps in Burn-Up Credit (BUC)
Depletion calculations
BUC isotopic
concentrations
BUC levels
- fissiles + U-238
- U + Pu only
- actinides-only
- actinides + fission products
National regulations
Validation of depletion calculations
Chemical assay
data from spent fuel
Burnup profiles
Criticality calculations
Loading
curve
Quantification and
verification of the fuel
burn-up before loading
J. C. Neuber
Validation of criticality calculations
Reactor records
Confirmation of
reactor record
burnup information
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Representative
benchmarks
- criticals
- subcriticals
- reactivity measurements
In-core measurements
Out-of-core measurements of
- neutron emission
-  emission
3
BUC Loading Curve
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
4
Availability and Reliability
of Spent Nuclear Fuel (SNF) Chemical Assay Data
 Significantly improved in recent years:
Objectives of this group include
• expanding the SFCOMPO experimental data base of SNF isotopic measurements
• making the data accessible through the SFCOMPO website
• sharing best practices on radiochemical analysis methods
• identifying input data and modelling requirements, and
• evaluating uncertainties and correlations associated with the measurements
and deficiencies in documented design and reactor operating history information.
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Depletion validation
Expert group on assay data under the auspices of the OECD NEA Data Bank
Working Party on Nuclear Criticality Safety (WPNCS)
5
Depletion Calculation Validation
Isotopic Correction Factor (ICF):
ICF 
M
C
Measured isotopic
concentration
Burnup Indicators
(e.g. Nd-148),
Calculation
Predicted (calculated)
isotopic concentration
Actinides
SNF sample
assay
Fuel burnup
Irradiation history
of the SNF sample
J. C. Neuber
Choice of the SNF sample
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Uncertainties
6
Depletion Calculation Validation
Sources of measurement uncertainties (measurement)
Red colored: Sources of possible correlations of the measured
isotopic concentrations
Manipulation (hot cell, glove boxes)
• dissolution strategy (efficiency)
• weighing of sample, fuel, residue,…
• incidental losses of material
-spectroscopy
•
•
•
•
standard used for efficiency calibration
sample preparation
counting statistics
evaluation of -spectrum
-spectroscopy
•
•
•
•
standard used for energy calibration
sample preparation
counting statistics
evaluation of -spectrum
Chromatographic separation
Liquid scintillation counting (LSC) (-, -emitter)
(separated radionuclide pure fraction)
• certified value of reference material for
internal standardization
• volumetric sampling tools (e.g., pipette)
• counting statistics
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Useful Check:
Mass Balance
7
Depletion Calculation Validation
Sources of measurement uncertainties (measurement)
Mass spectrometry techniques (TIMS: Thermal Ionization Mass Spectrometry)
(ICPMS Inductively Coupled Plasma Mass Spectrometry):
(pure elemental fractions required)
Use of isotope dilution techniques:
• calibration:
uncertainty in spikes
Example
of TIMS
Use of added standards:
• calibration:
uncertainty in standard
• separation yields
Chromatographic
separation
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
8
Depletion Calculation Validation
Sources of measurement uncertainties (measurement)
Time of measurement:
Separation date -------------- Analysis date
 Reference date ? (e.g. EOL:= end of life of SNF)
 Uncertainty in decay data (half-lives, branching ratios)

Uncertainty in
measured
concentrations
Uncertainty in
burnup
Uncertainties and
correlations of
calculated
concentrations
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
9
Depletion Calculation Validation
Observation: Hierarchy of Uncertainties
Example
Uncertainties
in Measured Isotopic
Concentrations (E)
Uncertainties
in Calculated Isotopic
Concentrations (C)
Uncertainties
in Isotopic Correction
Factors (ICF = E/C)
Statements on  from data/observations
distributions of 
pa a 
pb b 
Uncertainty
in Parameter
set a
Uncertainty
in Parameter
set b
Uncertainty in
Parameter Set x = x(a,b)
px x 
Application case
Benchmarks


Uncertainties
in the Bias-Corrected
Isotopic Concentrations of
the Application Case
Uncertainty in
Parameter Set y = y(x)
p y y
Uncertainty
in keff
Uncertainty
in z = z(y)
pz z 
Most powerful tool of bearing the uncertainties from one level to the next one:
 Bayesian Monte Carlo hierarchical procedures
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
10
Monte Carlo Sampling at given level  pdf of the succeeding level
x3
Monte Carlo (MC) sampling on the
parameter region
Sets of MC sampled parameter values
(xs)i = (xs1, xs2, xs3, …)i, i =1,…,κ
x2
Set of MC sampled parameter values
(ys)i = y((xs)i), i =1,…,κ
100 000 MCS on lE based on 6 empirical data
3200
3000
distribution
of y
2800
2600
2400
Frequency of occurrence
x1
2200
2000
1800
1600
1400
1200
1000
800
600
400
200
0
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.010
0.011
0.012
0.013
0.014
0.015
0.016
0.017
lE / 1/a
0.018
 MC sampling on a parameter region from the joint probability density function (pdf)
p(x|) of the parameters
 Problem: pdf usually unknown
 Necessary: pdf model derived from empirical data
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
11
0.019
Bayesian Monte Carlo Sampling at given level
For detailed information: Córdoba paper 2.10+2.11 (Neuber, Hoefer)
Generate MC samples xs under the condition of empirical data X:
Posterior
predictive
px s X    px s  p X d
n x m data matrix of
n independent
identically distributed
(iid) m-variate data
xi= (xi1,xi2,…,xim)
 x11

 x 21
 

 x n 1,1
 x
 n ,1
x12

x1,m 1
x 22



x 2,m 1

x n 1, 2  x n 1,m 1
x n,2

x n ,m 1
  probability
distribution model
parameter  unknown
e.g. normal distribution:
 = (,)
condition of the data X
x1m 

x 2m 
 

x n 1,m 
x n ,m 
posterior knowledge about 
J. C. Neuber
MC sampling on  under the
p X  pX p
Likelihood of X
under 
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
prior knowledge
about 
12
Depletion Calculation Validation and
Depletion Calculation for Application Case
Depletion Code
weaknesses
Re-calculation of
chemical assays
Bias in
Nuclear Data
Bias in Isotopic
Densities
Uncertainties
in assay data
Uncertainties
in Nuclear Data
Uncertainties
in Isotopic Densities
Isotopic Correction
Factors (ICFs)
Uncertainty in ICFs
Uncertainties
in Bias-Corrected
Isotopic Densities
Application case
Benchmarks
J. C. Neuber
Criticality
calculation
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
13
Criticality Calculation Validation and
Criticality Analysis of Application Case (SNF management system)
Uncertainties
in Nuclear Data
Uncertainties
in design data
Bias in
Nuclear Data
Criticality Code
weaknesses
Recalculation of
crits/subcrits
Bias kB
in keff
Biases (kB)i for
crits/subcrits
kB and its uncertainty
for application case
Uncertainties in
Biases (kB)i
Uncertainty
in (keff + kB)
Uncertainties
in Bias-Corrected
Isotopic Densities
J. C. Neuber
Uncertainty in
crits/subcrits data
Confidence Statement
on (keff + kB)
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Application case
Benchmarks
14
Criticality Calculation Validation
Representativeness of benchmarks (B) w.r.t. application case (A)
From first-order perturbation evaluation of keff=keff()
(:=nuclear data: cross-sections, fission spectrum, neutrons-per-fission properties, etc):
c k  corr (k B , k A ) 
C BA
C BB  C AA
CBA 
cov(k B , k A )

kB  kA

SB
cov( ,  )
,
   
SA
Covariance
nuclear data
Correlation 
Representativeness
(ck  0.9)
Sensitivity
Scl 

1  k c

l 
k c  l

(Broadhead, Rearden et al. / ORNL)
REBUS reactivity
worth measurement
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
15
Criticality Calculation Validation
Estimation of Bias k for application case (A): Data adjustment method
 keff results obtained for benchmarks with a given nuclear data library are
interpreted as experimental information which increases the information on the
nuclear data 
 Combination of first order perturbation and data adjustment
(ORNL: Generalized Linear Least Squares with Normality assumption)
(CEA: Bayes’ theorem + Normality assumption + Maximum Likelihood
 δξ  R (ξ ) S T (C  C ) 1 δk
kk
mm
ξ
Covariance matrix
with elements
cov(, )/()

k
Sensitivity
covariance
matrix of
k = k - m
δk k  m

k
k
vector of
calculation
result
vector of
Benchmark
values
δk A
δξ
 SA
kA
ξ
Bias application case
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
16
Criticality Calculation Validation
Estimation of Bias k for application case (A): Data adjustment method
Some criticism has to be raised from a physicist’ point of view:
• Developers of method do not really claim that method improves nuclear data – in
contradiction to the assumption that the experimental information increases the
information about the nuclear data
• It has been observed that the adjustment procedure can lead to data values which
are incompatible with physics.
• For this reason a so-called “2-filter” has been introduced in the GLLS procedure
generated by ORNL (code TSURFER)
• However, application of this filter results in exclusion of benchmarks from the
GLLS adjustment procedure, even though these benchmarks were identified as
representative for the application case
• Exclusion of representative benchmarks is not understandable:
Decision criterion for excluding these benchmarks is purely statistical,
whereas representativeness of these benchmarks is based on physics properties
• Fundamental principle:
Benchmarks can safely be discarded only on physical arguments
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
17
Criticality Calculation Validation and
Criticality Analysis of Application Case (SNF management system)
Uncertainties
in Nuclear Data
Uncertainties
in design data
Bias in
Nuclear Data
Criticality Code
weaknesses
Recalculation of
crits/subcrits
Bias kB
in keff
Biases (kB)i for
crits/subcrits
kB and its uncertainty
for application case
Uncertainties in
Biases (kB)i
Uncertainty
in (keff + kB)
Uncertainties
in Bias-Corrected
Isotopic Densities
J. C. Neuber
Uncertainty in
crits/subcrits data
Confidence Statement
on (keff + kB)
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
Application case
Benchmarks
18
Criticality Calculation Validation
In many cases: “mutually
dependent experiments”
Space of experimental parameters x
of all the experiments
i
j
m
MC sampling for
application case 
kcalc
MC sampling for
application case on
kND
(TSUNAMI)
J. C. Neuber
Monte Carlo sampling on entire x space
For each sampled vector xMC calculation of the keff values
(k1, k2, …,kN) for all the N experiments
Bias vector (kB1, kB2, …,kBn) for all the N experiments
Bayesian linear regression with this bias vector
using adequate explanatory variables
MC sample of the bias kB for the application case
Add to kcalc of application case: (kcalc+kND)+kB
Empirical distribution of
(kcalc+kND+kB)
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
J.C. Neuber, A. Hoefer,
NCSD 2009 Topical Meeting,
Sept. 13-17, 2009
Paper 33
19
Uncertainty of Nuclear Data: Monte Carlo Sampling on Nuclear Data
Nuclear
Basis data
Mean values of BD(En)
Neutron
energy
Covariance matrix of BD(En)

ˆ (E )
p ξ BD (E n ) ξˆ (E n ), Σ
n
i+1

Probability density of BD(En)
(Multivariate Normal)
AREVA NP Gmbh, PEEA-G:
Installed at present for MCNP
criticality calculations
i-th MC sample on BD
Basic data evaluation codes
Point data (continuous cross-sections)
Application case
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
20
Quantification and Verification of Fuel Burnup Before Loading
NUREG/CR-6998 ORNL/TM-2007/229:
Review of Information for Spent Nuclear Fuel Burnup Confirmation
Reactor records
Information
(required for
calibration, e.g.)
Confirmation of
records
Measurement (n,)
Burnup value
Independent confirmation  Independent evaluation of core-following measurements
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
21
Conclusions
Significant improvements in
• SNF assay data availability and reliability
• data evaluation methods (uncertainty analysis)
- depletion validation and calculation procedures
- criticality validation and calculation procedure
Hierarchical Bayesian Monte Carlo procedures
 complete calculation routes considering all uncertainties
J. C. Neuber
International Conference for Spent Fuel Management from
Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010
22

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