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 “CSSG Tasking 2017-01 Rev.1 Response” (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

𝑐𝑐𝑘𝑘 =cov(𝐴𝐴,𝐵𝐵)

std 𝐴𝐴 std(B)

Figure: ck between Hanford tank waste models and experiments in Whisper database + 122 added by WRPS.

𝑤𝑤𝑟𝑟𝑟𝑟𝑟𝑟 = 𝑤𝑤𝑚𝑚𝑚𝑚𝑚𝑚 + 𝑤𝑤𝑝𝑝𝑟𝑟𝑚𝑚𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝(1 − 𝑐𝑐𝑘𝑘,𝑚𝑚𝑝𝑝𝑚𝑚 )

𝑤𝑤𝑚𝑚 = max 0,𝑐𝑐𝑘𝑘,𝑚𝑚 − 𝑐𝑐𝑘𝑘,𝑝𝑝𝑎𝑎𝑎𝑎

𝑐𝑐𝑘𝑘,𝑚𝑚𝑝𝑝𝑚𝑚 − 𝑐𝑐𝑘𝑘,𝑝𝑝𝑎𝑎𝑎𝑎

𝑀𝑀𝜎𝜎′ = 𝑀𝑀𝜎𝜎 −𝑀𝑀𝜎𝜎𝑆𝑆𝑇𝑇 𝑆𝑆𝑀𝑀𝜎𝜎𝑆𝑆𝑇𝑇 + 𝑀𝑀𝐸𝐸 𝑆𝑆𝑀𝑀𝜎𝜎

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Experiment Design

Variant of TEX-Pu— Planet machine— ZPPR PANN plates— Polyethylene moderator

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Design Optimization

Constrained Bayesian optimization1

Design parameters:— Thickness of polyethylene— Thickness of iron/manganese— Number of layers in stack— Absorber material

Constraints:— MCNP keff = 1 ± 150 pcm— Height/width ratio < 2— Separated stack keff < 0.9— Weight

Figure: Results from constrained Bayesian optimization

1. “Constrained Bayesian optimization of criticality experiments.” 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 2022• CED-2 reviewed and accepted

FY 2021• This project was not funded for FY2021 in favor of other NCSP priorities.

FY 2022• Project Introduction. LANL has indicated that the existing TEX-Pu

experimental Plan can be modified to conduct these experiments.• Procurements and Fabrication. LLNL will procure materials and fabricate the

associated experimental parts.

FY 2023• 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.

1σ = 50 pcm 2σ = 100 pcm 3σ = 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

• Scipy has different root finding algorithms• Which finds critical configuration with minimum MCNP runs?• Perform each along grid of 20 poly thicknesses

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Secant Method to Criticality

Find root of keff – 1 = 0

Converges in 5.3 ± 2.4 simulations

𝑦𝑦 =𝑓𝑓 𝑏𝑏 − 𝑓𝑓 𝑎𝑎

𝑏𝑏 − 𝑎𝑎𝑥𝑥 − 𝑎𝑎 + 𝑓𝑓(𝑎𝑎)

0 =𝑓𝑓 𝑏𝑏 − 𝑓𝑓 𝑎𝑎

𝑏𝑏 − 𝑎𝑎𝑥𝑥 − 𝑎𝑎 + 𝑓𝑓(𝑎𝑎)

𝑥𝑥 = 𝑎𝑎 − 𝑓𝑓(𝑎𝑎)𝑏𝑏 − 𝑎𝑎

𝑓𝑓 𝑏𝑏 − 𝑓𝑓 𝑎𝑎

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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 ‘optimal’ experiments

Differences most significant for epithermal systems— H-X = 0.1: 73% of fissions in intermediate energy range— 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, γ)

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 𝑓𝑓(𝑥𝑥) is a random variable (GP)

Derive as,

Expected Improvement (EI)An Acquisition Function

No improvement if 𝑓𝑓′ �𝐱𝐱 > 𝑓𝑓(𝐱𝐱+)

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What About a Constraint?Probability of Feasibility

Define feasibility indicator Δ 𝐱𝐱— Δ 𝑥𝑥 = 1 if constraint satisfied— Δ 𝑥𝑥 = 0 if constraint not satisfied

Fit GP to constraint function, 𝑐𝑐 𝐱𝐱

Calculate CDF of fitted GP

CDF at �𝐱𝐱 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