1. J. C. Neuber1 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Advances in Burnup Credit Criticality Safety Analysis Methods and Applications Jens Christian Neuber, AREVA NP GmbH, PEEA8-G, Criticality Safety and Statistical Analysis

2. J. C. Neuber2 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Advances in Applications of Burnup Credit for Spent Fuel Storage, Transport, Reprocessing, and Disposition 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

3. J. C. Neuber3 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 calculations BUC 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 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

4. J. C. Neuber4 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 BUC Loading Curve

5. J. C. Neuber5 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 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. Depletion validation

6. J. C. Neuber6 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Depletion Calculation Validation Isotopic Correction Factor (ICF): SNF sample assay Measured isotopic concentration Calculation Predicted (calculated) isotopic concentration Irradiation history of the SNF sample Choice of the SNF sample Burnup Indicators (e.g. Nd-148), Actinides Fuel burnup Uncertainties

7. J. C. Neuber7 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Depletion Calculation Validation 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 colored: Sources of possible correlations of the measured isotopic concentrations Chromatographic separation

8. J. C. Neuber8 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Depletion Calculation Validation Mass spectrometry techniques (TIMS: Thermal Ionization Mass Spectrometry) (ICPMS Inductively Coupled Plasma Mass Spectrometry): (pure elemental fractions required) Sources of measurement uncertainties (measurement) Chromatographic separation Use of isotope dilution techniques: calibration: uncertainty in spikes Use of added standards: calibration: uncertainty in standard separation yields Example of TIMS

9. J. C. Neuber9 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 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

10. J. C. Neuber10 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Observation: Hierarchy of Uncertainties Uncertainties in Measured Isotopic Concentrations (E) Uncertainties in Calculated Isotopic Concentrations (C) Uncertainties in Isotopic Correction Factors (ICF = E/C) Uncertainties in the Bias-Corrected Isotopic Concentrations of the Application Case Uncertainty in k eff Example Uncertainty in Parameter set a Uncertainty in Parameter Set x = x(a,b) Uncertainty in Parameter set b Uncertainty in Parameter Set y = y(x) Uncertainty in z = z(y) Statements on  from data/observations  distributions of  BenchmarksApplication case Most powerful tool of bearing the uncertainties from one level to the next one:  Bayesian Monte Carlo hierarchical procedures Depletion Calculation Validation

11. J. C. Neuber11 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 x1x1 x2x2 x3x3 Monte Carlo (MC) sampling on the parameter region Sets of MC sampled parameter values (x s ) i = (x s1, x s2, x s3, …) i, i =1,…,κ Set of MC sampled parameter values (y s ) i = y((x s ) i ), i =1,…,κ 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

12. J. C. Neuber12 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 prior knowledge about   Generate MC samples x s under the condition of empirical data X: n x m data matrix of n independent identically distributed (iid) m-variate data x i = (x i1,x i2,…,x im )   probability distribution model e.g. normal distribution:  = ( ,  ) parameter  unknown  MC sampling on  under the condition of the data X Likelihood of X under  posterior know- ledge about  Posterior predictive Bayesian Monte Carlo Sampling at given level For detailed information: Córdoba paper 2.10+2.11 (Neuber, Hoefer)

13. J. C. Neuber13 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Depletion Calculation Validation and Depletion Calculation for Application Case Depletion Code weaknesses Bias in Nuclear Data Uncertainties in Nuclear Data Uncertainties in Isotopic Densities Bias in Isotopic Densities Re-calculation of chemical assays Uncertainties in assay data Isotopic Correction Factors (ICFs) Uncertainty in ICFs Uncertainties in Bias-Corrected Isotopic Densities Benchmarks Application case Criticality calculation

14. J. C. Neuber14 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system) Uncertainties in Bias-Corrected Isotopic Densities Criticality Code weaknesses Bias in Nuclear Data Uncertainties in Nuclear Data Benchmarks Application case Bias  k B in k eff Recalculation of crits/subcrits Uncertainty in crits/subcrits data Biases (  k B ) i for crits/subcrits Uncertainties in Biases (  k B ) i  k B and its uncertainty for application case Uncertainty in (k eff +  k B ) Confidence Statement on (k eff +  k B ) Uncertainties in design data

15. J. C. Neuber15 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Criticality Calculation Validation Representativeness of benchmarks (B) w.r.t. application case (A) From first-order perturbation evaluation of k eff =k eff (  ) (  :=nuclear data: cross-sections, fission spectrum, neutrons-per-fission properties, etc): (Broadhead, Rearden et al. / ORNL) Sensitivity Covariance nuclear data Sensitivity Correlation  Representativeness (c k  0.9) REBUS reactivity worth measurement

16. J. C. Neuber16 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Criticality Calculation Validation Estimation of Bias  k for application case (A): Data adjustment method  k eff 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  Covariance matrix with elements cov( ,   )/(    ) Sensitivity covariance matrix of  k = k - m vector of Benchmark values vector of calculation result Bias application case

17. J. C. Neuber17 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 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

18. J. C. Neuber18 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Criticality Calculation Validation and Criticality Analysis of Application Case (SNF management system) Uncertainties in Bias-Corrected Isotopic Densities Criticality Code weaknesses Bias in Nuclear Data Uncertainties in Nuclear Data Benchmarks Application case Bias  k B in k eff Recalculation of crits/subcrits Uncertainty in crits/subcrits data Biases (  k B ) i for crits/subcrits Uncertainties in Biases (  k B ) i  k B and its uncertainty for application case Uncertainty in (k eff +  k B ) Confidence Statement on (k eff +  k B ) Uncertainties in design data

19. J. C. Neuber19 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Criticality Calculation Validation Space of experimental parameters x of all the experiments ij m Monte Carlo sampling on entire x space For each sampled vector x MC calculation of the k eff values (k 1, k 2, …,k N ) for all the N experiments Bias vector (  k B1,  k B2, …,  k Bn ) for all the N experiments Bayesian linear regression with this bias vector using adequate explanatory variables MC sample of the bias  k B for the application case Add to k calc of application case: (k calc +  k ND )+  k B MC sampling for application case  k calc Empirical distribution of (k calc +  k ND +  k B ) In many cases: “mutually dependent experiments” J.C. Neuber, A. Hoefer, NCSD 2009 Topical Meeting, Sept. 13-17, 2009 Paper 33 MC sampling for application case on  k ND (TSUNAMI)

20. J. C. Neuber20 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 Uncertainty of Nuclear Data: Monte Carlo Sampling on Nuclear Data Nuclear Basis 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 (E n ) Covariance matrix of  BD (E n ) Probability density of  BD (E n ) (Multivariate Normal) AREVA NP Gmbh, PEEA-G: Installed at present for MCNP criticality calculations

21. J. C. Neuber21 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 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

22. J. C. Neuber22 International Conference for Spent Fuel Management from Nuclear Power Reactors, IAEA, Vienna 31/05 – 04/06/2010 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