Report

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 pa a pb b Uncertainty in Parameter set a Uncertainty in Parameter set b Uncertainty in Parameter Set x = x(a,b) px 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) pz 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 px s X px 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 pX 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