Comparison of deterministic and Monte Carlo sensitivity analysis

Comparison of deterministic and Monte Carlo sensitivity analysis including SAD/SED Ivo Kodeli, SG 39 Meeting, NEA, Dec. 4, 2015

beff sensitivity comparison SUSD 3 D/SERPENT SG 39, NEA, Dec. 4, 2015

beff sensitivity SUSD 3 D/SERPENT

beff sensitivity SUSD 3 D/SERPENT

beff SAD sensitivity SUSD 3 D/SERPENT

SNEAK-7 A & -7 B sensitivity code benchmark exercise (UAM project) SG 39, NEA, Dec. 4, 2015

V. Mastrangelo, I. Kodeli, E. Sartori, Proposal of a Benchmark for Stochastic and Deterministic Analyses of Nuclear Data Sensitivities and Uncertainties, UAM Workshop, Pisa, April 2006 Fast reactor benchmarks SNEAK-7 A & 7 B (Karlsruhe Fast Critical Facility), re-evaluated using detailed 3 -D models in the framework of the International Reactor Physics Benchmark Experiments (IRPh. E) project, were proposed to test and compare state-of-the-art cross section sensitivity and uncertainty codes. n Reference: NEA/NSC/DOC(2006)1 March 2009 Edition – IRPh. E Handbook (Evgeny Ivanov, IRSN, CNAM, IPN) http: //irphep. inl. gov/handbook/hbrequest. shtml Calculate the sensitivity of keff and beff to the nuclear cross sections and the corresponding uncertainties. Ø Compare and analyse results from different methods and codes for consistency and identify and explain discrepancies. Ø SG 39, NEA, Dec. 4, 2015

SNEAK-7 A and -7 B fast critical experiments (detailed&simplified 3 D models). n SNEAK-7 A core unit cell consisted of one Pu. O 2 -UO 2 pellet (26, 6% Pu. O 2 and 73, 4% UO 2) and one graphite platelet. Radial and axial blankets were loaded with metallic depleted UO 2 plates. n In SNEAK-7 B the graphite platelets were replaced by Unat. O 2 platelet. n The effective core radii of SNEAK-7 A & 7 B were 28. 63 cm and 37. 84 cm. SG 39, NEA, Dec. 4, 2015

beff - 252 Cf source measurements – noise analysis beff – benchmark values 2 3 SNEAK 7 B 0. 00395 ± 5% 0. 00429 ± 5% 0. 00413± 6% 0. 00450± 6% 0. 00395± 5% 0. 00429± 6% SNEAK 7 A Model 1 SNEAK 7 A SNEAK 7 B skeff Detailed 3 D model with stretched platelets 1. 0010 (a) 3 D simplified model with homogenized core regions of fuel elements 0. 9998 (c) RZ two-dimensional model 1. 0038 (c) 0. 0029 skeff 1. 0016 (a) 0. 0029 1. 0001 (c) 0. 0035 0. 0029 1. 0028 (c) 0. 0035 (b) 0. 0035 (a) Measured keff. (b) Combined experimental uncertainty (c) Equal to experimental value + (calculated simplified model – calculated more detailed model) SG 39, NEA, Dec. 4, 2015 (b)

Contributed solutions n n n Winfried Zwermann: XSUSA Manuele Aufiero: SERPENT 2 GPT extended Victor Mastrangelo/W. Zwermann: TSUNAMI 3 D Yannick Peneliau, Cyrille De Saint Jean: PARIS & ERANOS Evgeny Ivanov: MCNP 6 Ivo Kodeli: SUSD 3 D SG 39, NEA, Dec. 4, 2015

Computational Methods and Procedures keff and beff sensitivity: Winfried Zwermann, GRS: n XSUSA/TWODANT, direct perturbation method, 2 D n Cross sections: ENDF/B-VII Manuele Aufiero, LPSC/CNRS: n SERPENT 2 with extended GPT option, 2 D , n Cross sections: JEFF 3. 1. 1, probability tables Ivo Kodeli, IJS Ljubljana n n n Neutronic and sensitivity code: SUSD 3 D with PARTISN/TWODANT/THREEDANT Cross sections: 33 -group ENDF/B-VII. 0, S 8 P 3, processed by NJOY 99 2 D and 3 D models Evgeny Ivanov, IRSN (ongoing) n MCNP 6 keff sensitivity: Victor Mastrangelo (retired from CNAM and IPN-Orsay) n n Neutronic and sensitivity code: TSUNAMI-3 D; Cross sections: 238 -group ENDF/B-VII, P 5 S 8 Yannick Peneliau, Cyrille De Saint Jean, CEA Cadarache n n n Neutronics & sensitivity codes: ERANOS and PARIS; 2 D model Cross sections: Ecco+Sn 2 d with JEFF 3. 1. 1 and ENDF/B-VII (33 groups) Sensitivities to cross-sections, total nu-bar and fission spectra SG 39, NEA, Dec. 4, 2015

SNEAK-7 A & -7 B (SUSD 3 D–TSUNAMI 3 DPARIS/ERANOS-XSUSA–SERPENT-MCNP 5) Model SUSD 3 D (simplified 3 D) SUSD 3 D (2 D, P 5) TSUNAMI 3 D (3 D) SNEAK 7 A SNEAK 7 B keff - direct keff - adjoint 1. 00659 (0. 99839) 1. 00691 1. 00690 1. 00630 1. 00628 1. 0120 1. 00848 ± 8 pcm SERPENT (2 D) 1. 00724 ± 3 pcm not needed MCNP 6 (detailed 3 D) 1. 00237 ± 2 pcm not needed Measured 1. 0010 ± 400 pcm ± 290 pcm SG 39, NEA, Dec. 4, 2015 1. 00666 ± 2 pcm 1. 00330 ± 1 pcm 1. 0016 ± 350 pcm 1. 0019 ± 100 pcm not needed

SNEAK-7 A SAD/SED Sensitivity (k-eff)

CONCLUSIONS • Validation of beta-eff sensitivities calculated by SUSD 3 D and SERPENT: excellent/good agreement for Jezebel, Flattop-Pu and SNEAK-7 A, including SAD/SED sensitivities. • SNEAK-7 A & 7 B inter-comparison exercise of XS sensitivity and uncertainty codes (UAM project). Several solutions were received using deterministic and stochastic codes (SUSD 3 D, XSUSA, SERPENT, ERANOS, PARIS, TSUNAMI, MCNP 6), different modelisation of the geometry (2 D/3 D). Good consistency between the sensitivities, both integral values and sensitivity profiles. • Constrained PFNS sensitivity depends on spectra used, unconstrained should be provided to be used in adjustment • Berenice – in cooperation with CEA. SG 39, NEA, Dec. 4, 2015

Analysed benchmarks from ICSBEP and IRPh. E n n n n - SNEAK-7 A & -7 B: MOX fuel reflected by metallic depleted U. Jezebel: bare sphere of 239 Pu metal, 6. 385 -cm radius Skidoo (Jezebel-23): bare ~98. 1% 233 U sphere; Popsy (Flattop-Pu): ~20 -cm natural U reflected 239 Pu sphere; Topsy (Flattop-25): ~20 -cm natural U reflected 235 U sphere; Flattop-23: ~20 -cm natural U reflected 233 U sphere; Big Ten: 10% enriched U with U-reflector, cylinder r=41. 91 cm, h=96. 428 cm; ZPPR-9: MOX core with sodium cooling, depleted U blanket. I. Kodeli, Sensitivity and uncertainty in the effective delayed neutron fraction (βeff), Nuclear Instruments and Methods in Physics Research A 715 (2013)70 -78 WPEC SG 39, NEA, Issy-les-Moulineaux, May 19, 2015