Uncertainty Estimation of Target System Multiplication Factors with the new COMMARA Covariance Matrix

Transcription

1 Uncertainty Estimation of arget ystem Multiplication Factors with the new COMMARA Covariance Matrix Gerardo Aliberti, Won i Yang, and R. D. McKnight Nuclear Engineering Division Argonne National Laboratory WPEC ubgroup 33 Meeting OECD/NEA Paris May 11, 011

2 Introduction Uncertainty estimation was performed for eff values of the target systems selected for the ubgroup-33 activities using the recent COMMARA covariance matrix. he COMMARA (Covariance Multigroup Matrix for Advanced Reactor Application) covariance matrix was delivered by BNL and LANL on April 1st, 011, following a series of revision/corrections made on the AFCI data that were initially used for uncertainty estimation of fast reactor parameters. he target systems selected for the cross section adjustment to be performed within ubgroup 33 are: FBR ABR OXIDE ARUP CORE ABR MEAL ABR OXIDE RECYCLED CORE

3 New Evaluated Covariance Matrices Versions Release Date Isotope/Reaction updated with respect to the previous version AFCI-1.0 November AFCI-1.1 May 009 Pu39 (only ν), Fe56, Cr50, Ni58, C, O, Na3, B10, Zr90, Mn55 AFCI-1. August 009 AFCI-1.3 April 010 U35 capture, Pu39 ν and structural materials (Cr, Fe, Ni, Pb, Bi); 14 Minor Actinides were updated by Maslov review; Missing correlation matrices were recovered. U33, U34, U35, U36, U38, Np37, Pu38, Pu39, Pu40, Pu41, Pu4, Am43, Cm4, Cm44, Fe54, Fe56, Cr5, Ni58, Na3, Mn55 AFCI-.0 first release October 010 New evaluation AFCI-.0 second release January 011 COMMARA April 011 Pu41 Fission h3, Pu38, Pu40, Pu41, Am41, Am4m, Am43, Cm4, Fe54, Fe56, Cr50, Ni58, Ni60, O16, Pb08, Mg6 and Gd155

4 Pu41 Fission Relative tandard Deviations (%) Gr. Energy [MeV] AFCI-1. AFCI-1.3 AFCI-.0 f.r. AFCI-.0 s.r. COMMARA E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

5 arget ystems elected for the ubgroup-33 Activities RZ Model of the FBR Reactor

6 arget ystems elected for the ubgroup-33 Activities R 8.53 cm (econdary control) R cm (Inner core) R cm (Mixture of primary and secondary) R cm (Middle core) R cm (Primary control) R cm (Outer core) R cm (Reflector) R cm (hield) R cm (Barrel) R 8.53 cm (econdary control) R cm (Inner core #1) R cm (Mixture of primary and secondary) R cm (Inner core #) R cm (Primary control) R cm (Outer core) R cm (Reflector) R cm (hield) R cm (Barrel) hield Reflector Outer core Middle core Upper structure Gas plenum Inner core Lower reflector Grid plate Lower tructure.99 cm 5.44 cm cm cm cm cm 15.4 cm cm Absorber Follower cm 87.9 cm Absorber cm cm cm Gas plenum Core Upper structure Lower reflector hield Reflector Outer core Inner core Gas plenum Upper structure Lower reflector Grid plate Lower tructure 15.4 cm cm cm cm cm cm cm cm Absorber Follower 64.9 cm cm Absorber 0.06 cm cm cm 85.8 cm Lower reflector Core Gas plenum Upper structure Displaced bond Na econdary control Primary control Driver assembly RZ Model of 1000 MWt ABR Oxide Core econdary control Primary control Driver assembly RZ Model of 1000 MWt ABR Metal Core

7 Computational ools ensitivity analysis for the target systems is still under way and calculations are performed with the following deterministic codes: 1)ENDF\B-VII - MC - - VARI3D (diffusion theory); )ENDF\B-VII - ECCO - ERANO. (transport 4 P 1 ). he uncertainty estimation up to now has been performed for FBR, using sensitivities obtained with both VARI3D and ERANO., and for the ABRs Oxide tartup and Metal Cores using sensitivities obtained with VARI3D only. Results for ABRs Oxide tartup and Metal Cores using ERANO and for ABR Recycled core will be available in the coming months. N sensitivity analysis for all experiments selected for the ubgroup-33 studies has been already performed using both VARI-3D and ERANO codes.

8 Adopted Meshes for the patial Calculations FBR R-axis Z-axis Point Dimension [cm] mesh width Point Dimension [cm] mesh width ABR Oxide Core R-axis Z-axis Point Dimension [cm] mesh width Point Dimension [cm] mesh width ABR Metal Core Point R-axis Z-axis Dimension [cm] mesh width Point Dimension [cm] mesh width

9 Multiplication Factor Calculated Values for the arget ystems of ubgroup-33 Parameters ANL DIF3D Diffusion ANL ERANO 4 P 1 (a) Not Available yet FBR ABR Oxide Core tartup ABR Oxide Core Recycled ABR Metal Core (a)

10 Different way to present uncertainty contributions he COMMARA data include only partial correlation data of two different reactions of the same isotope. hus, the variation of the parameter R due to the cross section uncertainties of the isotope i can be written as: where is the sensitivity vector of cross section, V is the covariance matrix associated with the cross section, V l is the covariance matrix of cross sections and l. Uncertainty contributions of the single isotope cross sections will be presented as: For the contribution of two correlated cross sections, the following correlation is given: l l l l i V V R R l l l l l l i V V V R R, i V R R,

11 Different way to present uncertainty contributions Numerical example: case of FBR multiplication factor with COMMARA data Using VARI3D sensitivities: u V Void 1 U 8_ el VU 8_ el U 8_ el U 8_ el 0.08% u V Void U 8_ inel VU 8_ inel U 8_ inel U 8_ inel 0.74% Void u1 V U 8_ el _ inel U 8_ el V U 8_ el U 8_ el V U 8_ el U 8_ el _ inel U 8_ inel U 8_ inel V U 8_ inel U 8_ inel 91.97% he uncertainty on void worth due to U8 elastic and U8 inelastic combined together would be: u1 u1 u1u1 u %

12 Major ingle and wo Correlated Cross ection Contributions (%) to the eff otal Uncertainty of FBR Estimated with the COMMARA Matrix FBR VARI3D ERANO Major ingle Cross ection Uncertainties (%) U38 Fission U38 Nu U38 Capture U38 Elastic U38 Inelastic Pu39 Fission Pu39 Nu Pu39 Capture Pu39 Inelastic Pu40 Fission Pu40 Nu Pu40 Capture Pu40 Inelastic Pu41 Fission Pu41 Nu Pu41 Capture Pu4 Fission Pu4 Capture Fe56 Capture Fe56 Elastic Fe56 Inelastic Ni58 Capture Na Inelastic O Capture O Elastic Major wo Correlated Cross ection Uncertainty Contribution Coefficients (%) U38 Inelastic Elastic otal Uncertainty

13 Major ingle and wo Correlated Cross ection Contributions (%) to the eff otal Uncertainty of ABR Oxide tartup Estimated with the COMMARA Matrix ABR OXIDE ARUP VARI3D Major ingle Cross ectionmuncertainties (%) U38 Fission 0.03 U38 Nu 0.1 U38 Capture 0.8 U38 Elastic 0.06 U38 Inelastic 0.55 Pu39 Fission 0.3 Pu39 Nu 0.07 Pu39 Capture 0.31 Pu39 Inelastic 0.07 Pu40 Fission 0.05 Pu40 Nu 0.08 Pu40 Capture 0.06 Fe54 Capture 0.0 Fe54 Elastic 0.03 Fe56 Capture 0.16 Fe56 Elastic 0.9 Fe56 Inelastic 0.15 Cr5 Elastic 0.06 Na Elastic 0.04 Na Inelastic 0.07 O Elastic 0.03 Major wo Correlated Cross ection Uncertainty Contribution Coefficients (%) U38 Inelastic Elastic Pu39 Capture Fission Pu39 Inelastic Elastic Fe56 Inelastic Elastic 7.17 otal Uncertainty 0.88

14 Major ingle and wo Correlated Cross ection Contributions (%) to the eff otal Uncertainty of ABR Metal Estimated with the COMMARA Matrix ABR MEAL VARI3D Major ingle Cross ection Uncertainties (%) U38 Fission 0.04 U38 Nu 0.15 U38 Capture 0. U38 Elastic 0.09 U38 Inelastic 0.74 Pu39 Fission 0.5 Pu39 Nu 0.08 Pu39 Capture 0.3 Pu39 Elastic 0.0 Pu39 Inelastic 0.09 Pu40 Fission 0.04 Pu40 Nu 0.07 Pu40 Capture 0.03 Fe54 Capture 0.0 Fe54 Elastic 0.04 Fe56 Capture 0.15 Fe56 Elastic 0.47 Fe56 Inelastic 0.16 Cr5 Capture 0.0 Cr5 Elastic 0.11 Cr5 Inelastic 0.0 Na Elastic 0.06 Na Inelastic 0.07 Zr90 Capture 0.0 Zr90 Elastic 0.0 Zr9 Capture 0.0 Major wo Correlated Cross ection Uncertainty Contribution Coefficients (%) U38 Inelastic Elastic Pu39 Inelastic Elastic Fe56 Inelastic Elastic 6.93 otal Uncertainty 1.09