IER 519: Final Design of a Plutonium TEX Variant with Iron ...
Transcript of IER 519: Final Design of a Plutonium TEX Variant with Iron ...
LLNL-PRES-819381This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344. Lawrence Livermore National Security, LLC
IER 519: Final Design of a Plutonium TEX Variant with Iron and Manganese Absorbers to Provide NCS Validation Benchmarks to Hanford Tank Farms
Daniel Siefman, C. Percher, A. Kersting, D. Heinrichs
February 23rd, 2021
NCSP Technical Program Review
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Validation of Hanford Tank Waste
Illustration by J. Provost
[1] Erickson, D., 2017 โCSSG Tasking 2017-01 Rev.1 Responseโ (letter to A.S. Chambers)
177 tanks at Hanford Site Criticality safety evaluations credit
neutron-absorbing elements Iron, manganese, and nickel
DOE Criticality Safety Support Group recommends using sensitivity/uncertainty for validation1
MCNP & Whisper
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Hanford Waste Models
Best-Basis Inventory defines 100s of sludge and saltcake layer
Contain Pu, U and absorber elements Fe, Mn, Al, Cr, Ni, Si, Na, Zr
Modeled as infinite, homogeneous Additional Models with single
absorbers and varying H-X ratios
Figure: Mn Single Absorber Sensitivity Profiles
Figure: Fe Single Absorber Sensitivity Profiles
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Waste Characteristics
Tank/Layer Pu Mass (kg) U Mass (kg) Fe Mass (kg) Mn Mass (kg) H-XTX-109/Z 10.48 0 1.800 0 142TX-118/NA 29.15 0 0.7020 0.624 215A-106/SRR 45.08 136,100 4.490 0.241 285AN101/C-102 CWP2 155.9 1,669 6.560 1.130 431SX-155/R2 22.88 147.3 1.370 0.330 333SY-102/Z 134.9 881.0 5.780 1.590 1,590
Table: Characteristics of the tank/waste layer models considered for experimental design.
Figure: Decomposition of variance of keff for different waste/layer models in MCNP.
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Need for New Experiments
No large ck
Design new experiments
๐๐๐๐ =cov(๐ด๐ด,๐ต๐ต)
std ๐ด๐ด std(B)
Figure: ck between Hanford tank waste models and experiments in Whisper database + 122 added by WRPS.
๐ค๐ค๐๐๐๐๐๐ = ๐ค๐ค๐๐๐๐๐๐ + ๐ค๐ค๐๐๐๐๐๐๐๐๐๐๐๐๐๐(1 โ ๐๐๐๐,๐๐๐๐๐๐ )
๐ค๐ค๐๐ = max 0,๐๐๐๐,๐๐ โ ๐๐๐๐,๐๐๐๐๐๐
๐๐๐๐,๐๐๐๐๐๐ โ ๐๐๐๐,๐๐๐๐๐๐
๐๐๐๐โฒ = ๐๐๐๐ โ๐๐๐๐๐๐๐๐ ๐๐๐๐๐๐๐๐๐๐ + ๐๐๐ธ๐ธ ๐๐๐๐๐๐
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Experiment Design
Variant of TEX-Puโ Planet machineโ ZPPR PANN platesโ Polyethylene moderator
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Design Optimization
Constrained Bayesian optimization1
Design parameters:โ Thickness of polyethyleneโ Thickness of iron/manganeseโ Number of layers in stackโ Absorber material
Constraints:โ MCNP keff = 1 ยฑ 150 pcmโ Height/width ratio < 2โ Separated stack keff < 0.9โ Weight
Figure: Results from constrained Bayesian optimization
1. โConstrained Bayesian optimization of criticality experiments.โ D Siefman, C Percher, J Norris, A Kersting, D Heinrichs. Annals of Nuclear Energy 151 (2021)
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Exploring Absorber Materials
Figure: Variations in keff with initial design sets for materials with varying Mn/Fe content
Figure: Variations in ck with initial design sets for materials with varying Mn/Fe content
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Variations with Number of Stack Layers
Figure: Variations in ck and keff as number of layers in the TEX stack varies.
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ck values for Critical Configurations
Figure: Variations in ck and for only critical configurations.
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Planned Experiments
Name Targeted Systems Layers
Fission Fraction (%)EALF (eV)
<0.625 eV 0.625 eV - 100 keV >100 keVfe16 H-X = 0.1, 1 16 33.37 45.05 21.58 62.8
fe14 H-X = 10-1000Tank/Layer 14 52.87 32.11 15.03 7.61
fe11 H-X = 2000, 3000 11 60.33 26.28 13.39 3.69
Name Targeted Systems Layers
Fission Fraction (%)EALF (eV)
<0.625 eV 0.625 eV - 100 keV >100 keVmn21 H-X = 0.1-400 21 28.08 48.04 23.87 118
mn16 H-X = 600-3000Tank/Layer 16 49.95 33.83 16.22 10.6
Name Targeted Systems Layers
Fission Fraction (%)EALF (eV)
<0.625 eV 0.625 eV - 100 keV >100 keVfemn Tank/Layers 10 28.08 48.04 23.87 118
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Application vs Experiment Sensitivity Profiles
Tank waste modeled as infinite and homogenous Heterogeneous TEX cannot match large thermal sensitivities
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USL Conclusions13
For waste inventory (440 solids): No ck > 0.9 266 waste layers have ck > 0.8 328/400 has TEX as ck,max fe14 and mn16 most often ck,max
Original criticality safety calculations have generic USL of 0.913 With TEX, Whisper USLs = 0.937 - 0.955
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As General Benchmark14
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Experiment Schedule
FY 2022โข CED-2 reviewed and accepted
FY 2021โข This project was not funded for FY2021 in favor of other NCSP priorities.
FY 2022โข Project Introduction. LANL has indicated that the existing TEX-Pu
experimental Plan can be modified to conduct these experiments.โข Procurements and Fabrication. LLNL will procure materials and fabricate the
associated experimental parts.
FY 2023โข Experiment Execution. LLNL will work with NCERC personnel to schedule and
conduct the six experiments, hopefully in Q1 or Q2.
DisclaimerThis document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.
Thank You, Questions?
Acknowledgments:This work was supported by the Nuclear Criticality Safety Program under Contract DE-AC52-07NA27344.
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Current Benchmarks in Whisper Calculation
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Margin of Subcriticality
Figure: MOSdata from the GLLS adjustment in Whisper
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Scipy Suite of Root Finding
Method Average Number of Iterations +/- Population Std.
1ฯ = 50 pcm 2ฯ = 100 pcm 3ฯ = 150 pcm
Bisection 12 +/- 0.0 11 +/- 0 11 +/- 0
Brentq 8.6 +/- 3.4 8.0 +/- 3.0 8.0 +/- 3.0
Brenth 7.6 +/- 3.1 7.1 +/- 2.8 7.0 +/- 2.9
Ridder 6.6 +/- 3.3 6.2 +/- 2.9 6.1 +/- 3.0
Toms748 5.9 +/- 3.2 5.5 +/- 2.9 5.5 +/- 2.9
Secant 5.3 +/- 2.4 5.3 +/- 2.5 5.4 +/- 2.7
โข Scipy has different root finding algorithmsโข Which finds critical configuration with minimum MCNP runs?โข Perform each along grid of 20 poly thicknesses
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Secant Method to Criticality
Find root of keff โ 1 = 0
Converges in 5.3 ยฑ 2.4 simulations
๐ฆ๐ฆ =๐๐ ๐๐ โ ๐๐ ๐๐
๐๐ โ ๐๐๐ฅ๐ฅ โ ๐๐ + ๐๐(๐๐)
0 =๐๐ ๐๐ โ ๐๐ ๐๐
๐๐ โ ๐๐๐ฅ๐ฅ โ ๐๐ + ๐๐(๐๐)
๐ฅ๐ฅ = ๐๐ โ ๐๐(๐๐)๐๐ โ ๐๐
๐๐ ๐๐ โ ๐๐ ๐๐
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Critical Gaussian Process
Fit Gaussian Process to critical design parameters
Given poly thickness, returns Fe thickness where keff = 1
Save expensive sensitivity calculations for critical configurations
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Maximum ck with Different Libraries
Find maximum ck for critical experiment and all combinations of design parameters
Done for each set of covariance data
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Optimal Design Parameters with Different Libraries
Different covariance data lead to different โoptimalโ experiments
Differences most significant for epithermal systemsโ H-X = 0.1: 73% of fissions in intermediate energy rangeโ H-X = 3,000: has 98% of fissions in thermal energy range
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Sources of Disagreement: 54Fe
Library Stand. Dev. (pcm)
ENDF/B-VII.1 191
JEFF3.3 1,730
Table: H-X = 0.1 keff uncertainty from 54Fe
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Sources of Disagreement: 239Pu (n, ฮณ)
Library Stand. Dev. (pcm)
ENDF/B-VII.1 225
ENDF/B-VIII.0 1,032
JEFF3.3 950
Table: H-X = 0.1 keff uncertainty from 239Pu
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Of existing observations, which was optimal and what was the input?
Improvement: Use GP for every possible input, how do they improve the optimum relative to f(x+)?
Expected Improvement: Use expected value as ๐๐(๐ฅ๐ฅ) is a random variable (GP)
Derive as,
Expected Improvement (EI)An Acquisition Function
No improvement if ๐๐โฒ ๏ฟฝ๐ฑ๐ฑ > ๐๐(๐ฑ๐ฑ+)
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What About a Constraint?Probability of Feasibility
Define feasibility indicator ฮ ๐ฑ๐ฑโ ฮ ๐ฅ๐ฅ = 1 if constraint satisfiedโ ฮ ๐ฅ๐ฅ = 0 if constraint not satisfied
Fit GP to constraint function, ๐๐ ๐ฑ๐ฑ
Calculate CDF of fitted GP
CDF at ๏ฟฝ๐ฑ๐ฑ is the probability of feasibility
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What About a Constraint?Constrained Expected Improvement
Choose next point by multiplying EI by PoF
PoF eliminates infeasible regions from EI
Choose maximum of constrained expected improvement (EIC)
Calculate EIc over sample of design space and used gradient-based optimization