UO2F2 - ANSWM 2009
- 1. Criticality Benchmark Analysis of Water-Reflected Uranium Oxyfluoride Slabs Margaret A. Marshall John D. Bess Idaho National Laboratory ANS Winter Meeting November 18, 2009 1
- 2. Outline Purpose of evaluation Background Evaluation process ¤ Uncertainty analysis ¤ Bias analysis Results and Conclusions 2
- 3. Purpose of Evaluation ANSI Standard 8.1 ¤ “Subcritical Limits for Uranium-235 Systems” by Hugh Clark Used “Critical Parameters of Proton- Moderated and Proton-Reflected Slab of U235” by J.K Fox et. al. International Criticality Safety Benchmark Evaluation Project (ICSBEP) Validation & Verification, Criticality Safety, and Cross Section Data 3
- 4. Experiment Background Performed: ¤ 1955-56 ¤ Oak Ridge National Laboratory Critical Experiments Facility. Purpose: minimum critical thickness for infinite slab of UO2F2 Critical Experiments Facility Oak Ridge National Laboratory, 1956 Callihan, A.D., “Critical Experiments and Nuclear Safety At Oak Ridge National Laboratory.” ORNL-2087 (1956) 4
- 5. The Experiment Materials ¤ UO2F2 Solution ¤ Lucite Box ¤ Water Reflected & Moderated Slab Thickness Varied, Critical Height Measured 5 Chris White (INL)
- 6. Water Reflector Lucite Box and Lucite Insert Uranium Oxyfluoride Solution Lucite Inserts 6 Chris White (INL)
- 7. The Experiment Issues ¤ Slab thickness variation due to hydrostatic pressure Extrapolation to Minimum Critical Thickness Results J.K Fox, L.W. Gilley, and J.H. Marable, “Critical Paramters of Proton-Moderated and Proton-Reflected Slabs of U235”, Nucl. Sci. Eng., 3, 694 (1958) ¤ Experimental data allows for extrapolation to minimum slab thickness for infinite height 7
- 8. Benchmark Process Report Sections Section 1 – Experiment Section 2 – Uncertainty Section 3 – Biases Section 4 – Sample Calculations 8
- 9. Uncertainty Assessment Perturbation of Parameters Parameters ¤ Solution & Difficulties Reflector Height ¤ Determining the 1σ uncertainty ¤ Dimensions ¤ “Never-Ending” ¤ Material (always coming Properties up with more uncertainties) 9
- 10. Uncertainty Analysis Results Experiment 105 109 110 111 112 Case 1 2 3 4 5 Parameter U total Weight Fraction 0.00062 0.00020 0.00018 0.00018 0.00018 Specific Gravity 0.00114 0.00107 0.00106 0.00107 0.00106 Temperature 0.00005 0.00005 0.00005 0.00005 0.00005 Enrichment 0.00013 0.00023 0.00022 0.00020 0.00019 U234 Enrichment 0.00211 0.00215 0.00221 0.00203 0.00207 Impurities 0.00023 0.00020 0.00018 0.00022 0.00024 Compounds in Solution 0.00073 0.00065 0.00077 0.00070 0.00060 Lucite Density 0.00021 0.00020 0.00023 0.00020 0.00018 Solution Height 0.00177 0.00055 0.00019 0.00054 0.00015 Reflector Height 0.00005 0.00005 0.00005 0.00005 0.00005 Slab Thickness 0.00155 0.00080 0.00159 0.00161 0.00081 Box Length 0.00002 0.00002 0.00007 0.00002 0.00002 Lucite Thickness 0.00078 0.00074 0.00075 0.00072 0.00075 10 Total 0.00360 0.00281 0.00315 0.00306 0.00268
- 11. Bias Assessment Simplification Simplifications performed of model ¤ No air Find ¤ Insert merged with box in model corresponding Δkeff ¤ No out of solution supports Done ¤ Remove box above reflector height systematically ¤ Remove impurities in solutions ¤ Homogenize supports 11
- 12. Biases Analysis Results Remove No Insert Homo- Total Box above No Air Impuritie Merged genized Simplificati Case Reflector s with Box Supports on Bias b Height Δk Δk Δk Δk Δk Δk 1 -0.00009 0.00013 -0.00005 -0.00011 -- a 0.00024 2 0.00006 0.00037 -0.00002 0.00011 0.00070 0.00100 3 0.00005 0.00028 -0.00003 0.00011 0.00062 0.00114 4 -0.00010 0.00028 -0.00009 -0.00016 0.00049 0.00081 5 0.00003 0.00037 0.00014 0.00011 0.00051 0.00101 a Case 1 has no Lucite supports. b Bias in k eff when all simplifications are made at the same time. 12
- 13. Simple Model 13 Chris White (INL)
- 14. Additional Biases Biases not Homogenized included in the Water Lucite Replaces simplified model. Case Lucite Box Box in Reflector ¤ Replacing Lucite Δk Δk with water 1 -0.02016 -0.01787 2 -0.02213 -0.01960 ¤ Homogenizing 3 -0.02112 -0.01875 4 -0.02135 -0.01897 Lucite into water 5 -0.02234 -0.01991 14
- 15. Other Analysis Thermal Scattering Treatment Thermal scattering Benchm treatment adjusts Case ark Light Watera Polyethyl enea Solid Methanea Free Gasa the neutron cross- keff sections for the upscattering of 1 1.0000 -0.0004 -0.0070 -0.0350 0.0438 thermal neutrons 2 1.0000 -0.0029 -0.0098 -0.0441 0.0450 based on elemental bonds. 3 1.0000 -0.0008 -0.0077 -0.0388 0.0451 Light water 4 1.0000 -0.0010 -0.0077 -0.0408 0.0438 treatment was used 5 1.0000 -0.0031 -0.0098 -0.0462 0.0437 Effects of other Average % treatments were Deviation -0.16% -0.84% -4.10% 4.43% analyzed a All statistical uncertainties were 0.00005. Δk’s are reference to the benchmark keff. ENDF/B.VII.0 library used. 15
- 16. Results Detailed Model Simple Model Case keff uncertainty Case keff uncertainty 1 1.0000 ± 0.0036 1 1.0002 ± 0.0036 2 1.0000 ± 0.0028 2 1.0010 ± 0.0028 3 1.0000 ± 0.0032 3 1.0011 ± 0.0032 4 1.0000 ± 0.0031 4 1.0008 ± 0.0031 5 1.0000 ± 0.0027 5 1.0010 ± 0.0027 16
- 17. Sample Calculations Run with ENDF/B-VI.8 and –VII.0 libraries ENDF/B-VI.8 ENDF/B-VII.0 % Case % # of keff # of σ keff Deviatio Deviation σ n 1 0.9943 -0.57% 1.69 0.9996 -0.04% 0.11 2 0.9915 -0.85% 3.28 0.9971 -0.29% 1.10 3 0.9936 -0.64% 2.16 0.9992 -0.08% 0.26 4 0.9936 -0.64% 2.25 0.9990 -0.10% 0.34 5 0.9914 -0.86% 3.49 0.9969 -0.31% 1.25 17
- 18. Current Efforts Benchmark has been reviewed and improvements to the analysis are being included ¤ Reduction of uncertainty in Lucite thickness and 234U content Revised benchmark to be presented before the ICSBEP technical working group May 2010 in Slovenia. ¤ To be included in the September 2010 edition of the ICSBEP Handbook 18
- 19. Acknowledgments The authors would like to thank the following individuals ¤ J. Blair Briggs – INL ¤ Clinton Gross – Paschal Solutions ¤ Denis Beller – UNLV 19
- 20. Questions? 20