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

1. Advances in Burnup Credit Criticality Safety Analysis Methods and Applications Jens Christian Neuber, AREVA NP GmbH, PEEA8-G, Criticality Safety and Statistical Analysis International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

2. International Workshop onAdvances in Applications of Burnup Credit for Spent Fuel Storage, Transport, Reprocessing, and Dispositionorganized by theNUCLEAR SAFETY COUNCIL of Spain (CSN) in cooperation with theINTERNATIONAL ATOMIC ENERGY AGENCY (IAEA) Córdoba, Spain, 27 ‑ 30 October, 2009 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

3. Depletion calculations BUC levels- fissiles + U-238- U + Pu only- actinides-only- actinides + fission products National regulations BUC isotopic concentrations Chemical assay data from spent fuel Validation of depletion calculations Burnup profiles Criticality calculations Representative benchmarks- criticals- subcriticals- reactivity measurements Loading curve Validation of criticality calculations Reactor records Quantification and verification of the fuel burn-up before loading In-core measurements Out-of-core measure-ments of- neutron emission-  emission Confirmation of reactor record burnup information International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Key Steps in Burn-Up Credit (BUC) J. C. Neuber

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

5. 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 measurementsand deficiencies in documented design and reactor operating history information. Depletion validation 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) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

6. Measured isotopic concentration Burnup Indicators (e.g. Nd-148),Actinides Isotopic Correction Factor (ICF): Predicted (calculated) isotopic concentration Calculation SNF sample assay Fuel burnup Irradiation history of the SNF sample Choice of the SNF sample Uncertainties Depletion Calculation Validation International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

7. 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 Red colored: Sources of possible correlations of the measured isotopic concentrations • -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 Useful Check:Mass Balance Depletion Calculation Validation Sources of measurement uncertainties (measurement) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

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

9. Uncertainty in measured concentrations Uncertainty in burnup Uncertainties and correlations of calculated concentrations 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) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

10. Observation: Hierarchy of Uncertainties Statements on  from data/observations distributions of  Example Uncertaintiesin Measured Isotopic Concentrations (E) Uncertaintiesin Calculated Isotopic Concentrations (C) Uncertaintyin Parameter set a Uncertaintyin Parameter set b Uncertaintiesin Isotopic Correction Factors (ICF = E/C) Uncertainty in Parameter Set x = x(a,b) Uncertaintiesin the Bias-Corrected Isotopic Concentrations of the Application Case Uncertainty in Parameter Set y = y(x) Uncertaintyin keff Uncertainty in z = z(y) Most powerful tool of bearing the uncertainties from one level to the next one:  Bayesian Monte Carlo hierarchical procedures Application case Benchmarks Depletion Calculation Validation International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

11. x3 Sets of MC sampled parameter values (xs)i = (xs1, xs2, xs3, …)i, i =1,…,κ Monte Carlo (MC) sampling on the parameter region x2 Set of MC sampled parameter values (ys)i = y((xs)i), i =1,…,κ distribution of y x1 • 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 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

12. Generate MC samples xs under the condition of empirical data X: Posterior predictive 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 posterior know-ledge about  Likelihood of X under  prior knowledge about  Bayesian Monte Carlo Sampling at given level For detailed information: Córdoba paper 2.10+2.11 (Neuber, Hoefer) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

13. Depletion Code weaknesses Bias in Nuclear Data Uncertaintiesin Nuclear Data Re-calculation of chemical assays Bias in Isotopic Densities Uncertaintiesin Isotopic Densities Uncertaintiesin assay data Isotopic Correction Factors (ICFs) Uncertainty in ICFs Uncertaintiesin Bias-Corrected Isotopic Densities Application case Criticality calculation Benchmarks Depletion Calculation Validation and Depletion Calculation for Application Case International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

14. Uncertaintiesin Nuclear Data Bias in Nuclear Data Criticality Code weaknesses Recalculation of crits/subcrits Uncertaintiesin design data Bias kBin keff Uncertainty in crits/subcrits data Biases (kB)i for crits/subcrits Uncertainties in Biases (kB)i kB and its uncertainty for application case Uncertaintyin (keff + kB) Application case Uncertaintiesin Bias-Corrected Isotopic Densities Confidence Statementon (keff + kB) Benchmarks Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

15. From first-order perturbation evaluation of keff=keff() (:=nuclear data: cross-sections, fission spectrum, neutrons-per-fission properties, etc): (Broadhead, Rearden et al. / ORNL) Covariance nuclear data Correlation Representativeness(ck 0.9) Sensitivity Sensitivity REBUS reactivity worth measurement Criticality Calculation Validation Representativeness of benchmarks (B) w.r.t. application case (A) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

16. 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 vector of calculation result Covariance matrix with elements cov(, )/() vector of Benchmark values covariance matrix of k = k - m Sensitivity Bias application case Criticality Calculation Validation Estimation of Bias k for application case (A): Data adjustment method International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

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

18. Uncertaintiesin Nuclear Data Bias in Nuclear Data Criticality Code weaknesses Recalculation of crits/subcrits Uncertaintiesin design data Bias kBin keff Uncertainty in crits/subcrits data Biases (kB)i for crits/subcrits Uncertainties in Biases (kB)i kB and its uncertainty for application case Uncertaintyin (keff + kB) Application case Uncertaintiesin Bias-Corrected Isotopic Densities Confidence Statementon (keff + kB) Benchmarks Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system) International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

19. In many cases: “mutually dependent experiments” 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 Space of experimental parameters x of all the experiments Bias vector (kB1, kB2, …,kBn) for all the N experiments i j Bayesian linear regression with this bias vector using adequate explanatory variables m MC sample of the bias kB for the application case MC sampling for application case  kcalc Add to kcalc of application case: (kcalc+kND)+kB MC sampling for application case on kND (TSUNAMI) J.C. Neuber, A. Hoefer,NCSD 2009 Topical Meeting, Sept. 13-17, 2009Paper 33 Empirical distribution of (kcalc+kND+kB) Criticality Calculation Validation International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

20. NuclearBasis data Mean values of BD(En) Covariance matrix of BD(En) Neutron energy Probability density of BD(En) (Multivariate Normal) i+1 i-th MC sample on BD Basic data evaluation codes Point data (continuous cross-sections) Application case Uncertainty of Nuclear Data: Monte Carlo Sampling on Nuclear Data AREVA NP Gmbh, PEEA-G: Installed at present for MCNP criticality calculations International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

21. Information(required for calibration, e.g.) Measurement (n,) Reactor records Confirmation of records Burnup value Quantification and Verification of Fuel Burnup Before Loading NUREG/CR-6998 ORNL/TM-2007/229: Review of Information for Spent Nuclear Fuel Burnup Confirmation Independent confirmation  Independent evaluation of core-following measurements International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 J. C. Neuber

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