j. c. neuber1 international conference for spent fuel management from nuclear power reactors, iaea,...

J. C. Neuber 1International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010

Advances in Burnup Credit Criticality Safety Analysis Advances in Burnup Credit Criticality Safety Analysis Methods and ApplicationsMethods and Applications

Jens Christian Neuber, AREVA NP GmbH, PEEA8-G, Criticality Safety and Statistical Analysis


International Workshop on

Advances in Applications of Burnup Credit Advances in Applications of Burnup Credit for Spent Fuel Storage, Transport, Reprocessing, and Dispositionfor 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 3

Key Steps in Burn-Up Credit (BUC)

International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010

Depletion calculations BUC levels- fissiles + U-238- U + Pu only- actinides-only- actinides + fission products

National regulations

Validation of depletion calculationsValidation of depletion calculationsBUC isotopic concentrations Chemical assay

data from spent fuel

Criticality calculations

Quantification and verification of the fuel burn-up before loading

Loading curve

Burnup profiles

Validation of criticality calculationsValidation of criticality calculations

Representative benchmarks- criticals- subcriticals- reactivity measurements

Reactor records

Out-of-core measure-ments of- neutron emission- emission

Confirmation of reactor record burnup information

In-core measurements


BUC Loading Curve


Availability and Reliability of Spent Nuclear Fuel (SNF) Chemical Assay Data

Significantly improved in recent years: Expert group on assay data under the auspices of the OECD NEA Data Bank Working Party on Nuclear Criticality Safety (WPNCS)

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.

Dep

leti

on v

alid

atio

n


Depletion Calculation Validation

Isotopic Correction Factor (ICF): C

MICF

SNF sample assay

Measured isotopic concentration

CalculationPredicted (calculated) isotopic concentration

Irradiation history of the SNF sample

Choice of the SNF sample

Burnup Indicators (e.g. Nd-148), Actinides

Fuel burnup

UncertaintiesUncertainties



Sources of measurement uncertainties (measurement)

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

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

Useful Check:Mass Balance

Red

col

ored

: S

ourc

es o

f po

ssib

le c

orre

lati

ons

of th

e m

easu

red

isot

opic

con

cen

trat

ion

s

Chromatographic separation



Mass spectrometry techniques (TIMS: Thermal Ionization Mass Spectrometry) (ICPMS Inductively Coupled Plasma Mass Spectrometry): (pure elemental fractions required)


Chromatographic separation

Use of isotope dilution techniques:• calibration:

uncertainty in spikes

Use of added standards:• calibration:

uncertainty in standard• separation yields

Example of TIMS




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


Observation: Hierarchy of Uncertainties

Uncertaintiesin Measured Isotopic Concentrations (E)

Uncertaintiesin Calculated Isotopic

Concentrations (C)

Uncertaintiesin Isotopic Correction Factors (ICF = E/C)

Uncertaintiesin the Bias-Corrected

Isotopic Concentrations of the Application Case

Uncertaintyin keff

Example

Uncertaintyin Parameter

set a

Uncertainty in Parameter Set x = x(a,b)

Uncertaintyin Parameter

set b

Uncertainty in Parameter Set y = y(x)

Uncertainty in z = z(y)

aap bbp

xxp

yyp

zzp

Statements on from data/observations distributions of

Ben

chm

arks

Ap

plication

case

Most powerful tool of bearing the uncertainties from one level to the next one: Bayesian Monte Carlo hierarchical procedures



x1

x2

x3 Monte Carlo (MC) sampling on the parameter region

Sets of MC sampled parameter values (xs)i = (xs1, xs2, xs3, …)i, i =1,…,κ

Set of MC sampled parameter values

(ys)i = y((xs)i), i =1,…,κ

0

200

400

600

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

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 0.018 0.019

distribution of y

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

Monte Carlo Sampling at given level pdf of the succeeding level


prior knowledge about

Generate MC samples xs under the condition of empirical data X:

n x m data matrix of n independent identically distributed (iid) m-variate data xi= (xi1,xi2,…,xim)

probability distribution model

e.g. normal distribution: = (,)

parameter unknown

MC sampling on under the condition of the data X

pXpXp

Likelihood of X under

posterior know-ledge about

dXpxpXxp ssPosterior predictive

m,n1m,n2,n1,n

m,1n1m,1n2,1n1,1n

m21m,22221

m11m,11211

xxxx

xxxx

xxxx

xxxx

Bayesian Monte Carlo Sampling at given level

For detailed information: Córdoba paper 2.10+2.11 (Neuber, Hoefer)


Depletion Calculation Validation and Depletion Calculation for Application Case

Depletion Code weaknesses

Bias in Nuclear Data

Uncertaintiesin Nuclear Data

Uncertaintiesin Isotopic Densities

Bias in Isotopic Densities

Re-calculation of chemical assays

Uncertaintiesin assay data

Isotopic Correction Factors (ICFs)

Uncertainty in ICFs

Uncertaintiesin Bias-Corrected Isotopic Densities

Benchmarks

Application case

Criticality calculation


Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system)


Criticality Code weaknesses



Benchmarks

Application case

Bias kB

in keff

Recalculation of crits/subcrits

Uncertainty in crits/subcrits dataBiases (kB)i for

crits/subcrits

Uncertainties in Biases (kB)i

kB and its uncertainty for application case

Uncertaintyin (keff + kB)

Confidence Statement on (keff + kB)

Uncertaintiesin design data


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):

(Broadhead, Rearden et al. / ORNL)

Sensitivity

Covariance nuclear data

Sensitivity

Correlation Representativeness(ck 0.9)

REBUS reactivity worth measurement



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

k

δkCCSξR

ξ

δξmmkk

1T )()( k

mk

k

δk

Covariance matrix with elements

cov(, )/() Sensitivity

covariance matrix of k = k - m

vector of Benchmark

values

vector of calculation

result

ξ

δξSA

A

A

k

δk

Bias application case



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


Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system)


Criticality Code weaknesses



Benchmarks

Application case

Bias kB

in keff

Recalculation of crits/subcrits

Uncertainty in crits/subcrits dataBiases (kB)i for

crits/subcrits

Uncertainties in Biases (kB)i

kB and its uncertainty for application case

Uncertaintyin (keff + kB)

Confidence Statement on (keff + kB)

Uncertaintiesin design data



Space of experimental parameters x of all the experiments

i j

m

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

MC sampling for application case

kcalc

Empirical distribution of (kcalc+kND+kB)

In many cases: “mutually dependent experiments”

J.C. Neuber, A. Hoefer,NCSD 2009 Topical Meeting, Sept. 13-17, 2009Paper 33

MC sampling for application case on

kND

(TSUNAMI)


Uncertainty of Nuclear Data: Monte Carlo Sampling on Nuclear Data

NuclearBasis data

Neutron energy

i-th MC sample on BD

Basic data evaluation codes

Point data (continuous cross-sections)

Application case

i+1

Mean values of BD(En)

Covariance matrix of BD(En)

Probability density of BD(En) (Multivariate Normal)

AREVA NP Gmbh, PEEA-G: Installed at present for MCNP criticality calculations


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 Measurement (n,)

Burnup value

Information(required for

calibration, e.g.)

Confirmation of records

Independent confirmation Independent evaluation of core-following measurements


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. neuber1 international conference for spent fuel management from nuclear power reactors, iaea,...

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