Nuclear Data Uncertainty Analysis in Criticality Safety. Oliver Buss, Axel Hoefer, Jens-Christian Neuber AREVA NP GmbH, PEPA-G (Offenbach, Germany)

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2 NUDUNA Nuclear Data Uncertainty Analysis in Criticality Safety Oliver Buss, Axel Hoefer, Jens-Christian Neuber AREVA NP GmbH, PEPA-G (Offenbach, Germany) Workshop on Nuclear Data and Uncertainty Quantification Culham Centre for Fusion Energy January 2012

3 Content! Motivation u Nuclear data uncertainty impact in criticality safety! Methods for estimating Nuclear Data Uncertainty! Monte-Carlo approach to Nuclear Data Uncertainty Estimation u NUDUNA framework u Present issues with available uncertainty information u Results for k eff and depletion! Summary & Outlook NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.3

4 Motivation

5 Motivation! Criticality safety evaluations for (re-) processing, storage, transport and final disposal of nuclear fuel u Small Margins additional to the Regulatory Safety Margin u Regulatory Safety Margin: k eff <0.95, 0.98 or even k eff <1.00! Analyses rely on transport codes! Different types of analytical uncertainties: 1. Geometrical and material data uncertainties 2. Burn-up uncertainties 3. Systematic uncertainties in the transport algorithms (Calc. Bias) 4. Nuclear data uncertainties! Status of nuclear data uncertainty estimation: u USA, France: Demand for estimates of nuclear data uncertainties u Otherwise nuclear data uncertainties considered to be covered by the safety margin (which includes errors not accounted for)! We aim to provide a proper estimate for nuclear data uncertainties u Ensure bounding estimates in safety margins u Reduce conservatism in safety margins NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.5

6 Methods for estimating Nuclear Data Uncertainty

7 1. Perturbation theory Approximation, Fast!! 2. Monte Carlo Retrieve statistics for observable based on distribution of input parameters Cov( A) with α N N 1 1 N ( i) random draw All orders included! Flexible Tool! Approaches to the estimation of Nuclear Data Uncertainty impact A A Cov( A) Cov( αi, α j ) α α N i= 1 A i, j 1 N i j Sensitivities Generate random nuclear 2 data library 2 ( α( i) ) A( α( i) ) N i= 1 Nuclear Data Covariances Store transport result Perform analysis with random input data NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.7

8 Available Codes for Nuclear Data Uncertainty Estimation Approximations Monte Carlo Approach (All Orders) 1. Order Perturbation FAST!! Approximations Measured Data Evaluations Grouped Data TMC (NRG) NUDUNA (AREVA NP) KIWI (LLNL) Flexible, CPU intense XSUSA (GRS) NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.8 TALYS based SCALE Cov based, FAST TSUNAMI (ORNL) TSURFER (ORNL) RIB (CEA) Long History Very good Documentation

9 Monte-Carlo approach to Nuclear Data Uncertainty Estimation

10 Generation of random libraries Random library data bench (XML based) NUDUNA: Program Flow Job card creation Idealized HEU Shell Exp from LA E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= imp:n=0 Automated job card multiplication Idealized HEU Shell Exp from LA E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= imp:n=0 Idealized HEU Shell Exp from LA E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= imp:n=0 Idealized HEU Shell Exp from LA E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= E imp:n= imp:n=0 Parallel execution of jobs: Linux or Windows Cluster Automated Output Analysis: Upper/Lower 95/95, Histograms NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.10

11 NUDUNA: Random input library creation! NUDUNA Scope: u Provide libraries for SCALE and MCNP transport suites u Need to generate AMPX and ACE formatted input files! NUDUNA makes use of: u randomlib by AREVA u NJOY 99 tool by Los Alamos National Lab (LANL) u SMILER/PUFF IV tool by Oakridge National Lab (ORNL) randomlib Reads information encoded in ENDF6 tapes Varies information randomly according to covariance matrices Writes random information to ENDF6 tape NJOY 99 Resonance + background treatment Doppler broadening S(α,β) treatment Resonance self-shielding ACE tape generation or multi group treatment ACE tape ENDF6 tape GENDF tape SMILER (PUFF IV) Converts multigroup format to AMPX AMPX tape MCNP SCALE NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.11

12 NUDUNA: Random ENDF6 tapes! Treated Uncertainties: u File 1: Multiplicities u File 2: Resonances u File 3: Cross Sections u File 4: Angular Distributions 235 U 235 U Restoration of sum rules: Normal or Log-Normal Model m = m + tot prompt m delayed NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.12

13 NUDUNA: Random ENDF6 tapes! Treated Uncertainties: u File 1: Multiplicities u File 2: Resonances u File 3: Cross Sections u File 4: Angular Distributions 235 U, JENDL 4.0 Respect Positivity Bounds for Widths Assume Constant Phases of Amplitudes Dimension Normal or Log-Normal Model NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.13

14 NUDUNA: Random ENDF6 tapes! Treated Uncertainties: u File 1: Multiplicities u File 2: Resonances u File 3: Cross Sections u File 4: Angular Distributions mt Z grid mt Y grid mt X grid Algorithm: 1. Res+BG Summation (via NJOY) 2. Define common energy grid for uncertainty information 3. Average Data on Grid 4. Random Draws for Average Data Scaling Factors for Energy Ranges 5. Rescale original data 6. Restore ENDF6 sum rules NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.14 Energy

15 ! Treated Uncertainties: u File 1: Multiplicities u File 2: Resonances u File 3: Cross Sections u File 4: Angular Distributions NUDUNA: Random ENDF6 tapes JENDL 4, 235 U: Check for Angular Distribution > 0 Normal or Log-Normal Model NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.15

16 Technical Details! RandomLib u Highly modular FORTRAN 2003 u Succesful optimization of matrix operations, e.g. SVD and CHOLESKI Current Limit of Application dim < u Runtime dominated by NJOY! NJOY/PUFF interfaces u Automatic choice of NJOY/PUFF parameters (e.g. σ 0 grids)! User Interfaces in Python u Communication with XML data base u Creation of custom job cards u Distribution of jobs on Cluster NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.16

17 Problems with current ENDF6 encodings of Data Uncertainties! Missing LTY=0 Entries for Files 1&3 u Arbitraryness in restoring sum rules! File 1 phases! Covariances of total and prompt neutron multiplicities must be consistent!! Very large nuclear data errors (e.g. lowenergy resonance errors for 235 U in JENDL4)! Arbitraryness of Distribution Models u Why not distribution model in ENDF6? u Especially problematic for forward-peaked angular distributions (File 4)! Incomplete Information in File 35 u Need for uncertainty of underlying parameters and not of the sum itself NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.17 JENDL4, 235 U JENDL4, 235 U

18 Results

19 Results I Godiva (HEU-MET-FAST-001) Evaluation Transport Suite Average k eff Standard Deviaton due to Nuclear Data Uncertainty [pcm] JENDL 4.0 SCALE Groups JENDL 4.0 MCNP ENDF 7.1β SCALE Groups ENDF 7.1β MCNP Tsunami (SCALE 6): 930 pcm (ENDF/B VII) NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.19

20 Results II: Adding the benchmark loop Evaluate representative Experiments Generate random nuclear data library Perform Transport calculation for application case Extract calc. bias for application case Store transport result Apply order statistics to the database of result+bias Upper confidence limit NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.20

21 Results II: Adding the benchmark loop Simple Pin-Cell Model: UO 2 with 5% enrichment water reflected Bias estimation based on LCT51 experiments c k 0.9 for all experiments Δk b 1 = 18 k bench i= LCT 51.2,..., LCT ( i) k calc eff ( i) Upper 95%/95% NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.21

22 OECD Phase 1b Benchmark, Sample A Results III: Depletion calculations for BUC Impact of U238 XS uncertainty based on TALYS TRITON / SCALE 6.0 Generate random nuclear data library Perform Depletion analysis Store Isotopic Composition Succesful Benchmarks with TMC (NRG) NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.22

23 Summary! NUDUNA provides nuclear data uncertainty impact estimates! Support for continuous and group-wise XS libraries! NUDUNA improves on the perturbation theory methodology! Flexibility of MC easy to embed in hierarchical schemes for uncertainty estimation! Succesful benchmarks for k eff and depletion u Consistent results for MCNP and SCALE u NUDUNA compatible to TSUNAMI (ORNL) u Succesful TMC (NRG) vs. NUDUNA benchmarks for OECD Phase-1b depletion problem! Problems with ENDF6 standard and present evaluations u Strong support by Nuclear Data Community needed NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.23

24 Any reproduction, alteration or transmission of this document or its content to any third party or its publication, in whole or in part, are specifically prohibited, unless AREVA has provided its prior written consent. This document and any information it contains shall not be used for any other purpose than the one for which they were provided. Legal action may be taken against any infringer and/or any person breaching the aforementioned obligations. NUDUNA - Culham Oliver Buss - AREVA NP GmbH Proprietary AREVA - p.24

25 End of presentation NUDUNA Nuclear Data Uncertainty Analysis in Criticality Safety Oliver Buss, Axel Hoefer, Jens-Christian Neuber AREVA NP GmbH, PEPA-G (Offenbach, Germany) Workshop on Nuclear Data and Uncertainty Quantification Culham Centre for Fusion Energy January 2012