Task 1:    Computational and Experimental Benchmarking for Transient Fuel Testing

T. Downar W. Martin  University of Michigan

C. LeeArgonne National Laboratory

K. SunMIT

November 2nd, 2016

Task 1• Objective: A comprehensive evaluation of existing TREAT Facility neutronics data using the next generation reactor core neutronics codes.   This will be performed in accordance with  established guidelines per the International Handbook of Evaluated Reactor Physics Benchmark Experiments (IRPhEP). 

• Neutronics Codes:• Monte Carlo:  

• SERPENT (UM)• MCNP  (UM)• OPENMC (MIT)

• Deterministic:   • PARCS    US NRC   (UM)• PROTEUS   DOE NEAMS  (ANL)

• Benchmarks (UM)• Steady‐State – Two steady state condition benchmarking tests will be selected and studied.• Transient – Two transient condition benchmarking problems will be selected and studied.

Task 1.1 (Steady‐State)  ScheduleTask # Task Title Sub‐Task Owner

1. Neutronics Benchmark Task Lead – T. Downar, UM

1.1 Steady State (SS)

1.1.1 Survey candidate problems T. Downar, UM

1.1.2 Preliminary SS modeling of candidate problems T. Downar, UM

1.1.3 Down‐select to two  problems for benchmark evaluation T. Downar, UM

1.1.4 SS modeling with deterministic U.S. NRC codes PARCS/AGREE T. Downar, UM

1.1.5 SS modeling with deterministic NEAMS code PROTEUS C. Lee, ANL

1.1.6 SS modeling with Monte Carlo code OPENMC  K. Sun, MIT

1.1.7 Comparison of experimental data & model results  T. Downar, UM

1.1.8 Benchmark level evaluation of selected problems T. Downar, UM

1.1.9 Evaluation of uncertainties in selected problems T. Downar, UM

1.1.10Preparation of IRPhEP documentation

T. Downar, UM

1.1.11Submission of SS benchmark for peer review

T. Downar, UM

TREAT BENCHMARK

Benchmark completed and submitted on September 30th

DoE has accepted the benchmark as completion of the milestone requirement for this project.

Formal transmittal this month to IRPhEP Committee

TREAT Steady State BenchmarkBenchmark includes three problems with three different cores  providing complementary types of measurements:

• Minimum Critical Mass (MCM) core• MCM+ core  • M8CAL core

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ConfigurationFuel 

AssembliesControl Rod Assemblies

Zirconium Assemblies

Hodoscope Types of Measurement

Minimum Critical Mass(MCM) 133 8 16 No Temperature

Coefficient

MCM+ 135 8 14 No Flux Distribution

M8CAL 318 20 0 Yes Rod Worth Data

Minimum Critical Core (MCM)

• 133 Standard Fuel Elements• 8 Control Rod Fuel Elements• 16 Zr‐Cladded Dummy Fuel Element

• Control rods are above the upper reflector (completely out of the core)

• Specs from INL/EXT‐15‐35372‐BATMAN report

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Temperature Δk (inhr)

Temperature CoefficientHot (°C) Cold (°C) (inhr/°C) (Δk/°C)

Short Rods 35.0 15.5 131 6.74 1.8 ± 0.2 x 10‐4

Long Rods 37.5 22.0 104.5 6.76 1.8 ± 0.2 x 10‐4

MCM+ Core

• 135 Standard Fuel Elements• 8 Control Rod Fuel Elements• 16 Zr‐Cladded Dummy Fuel Element

• Control rod bank #1 was inserted between 47.5” and 49.5”

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1

MCM+ Core  Measurements

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1

M8CAL Core

• 318 Standard Fuel Elements• 20 Control Rod Fuel Elements (8 C/SR, 8 TR and 4 CR)

• 12 Zr‐Cladded Dummy Fuel Element

• 8 slotted dummy assemblies• 1 slotted and 1 Zr‐cladded half assembly

• C/S Rod are 22in inserted for critical core

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1

M8CAL Core Measurements

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1

TREAT Benchmark Specifications:    Geometry and Compositions  

Detailed Specifications from BATMAN Report

Model from Batman Report1

Infinite Lattice UQBatman Report

Boron impurity study

Iskenderian, H. P. (n.d.). Post criticality studies on the TREAT reactor (p. 7, Tech.). (NTIS No. ANL‐6115) 50 samples total of 1.25g out of 2.6tons of fuel

• Direct average: • μ 7.8 , σ 1.4• Inverse variance weighting:• μ . , .

Boron Contamination:  Chi‐Square weighting

Group No. Sample size Degree of Freedom Probability of getting 0.9≤ ≤1.1

1 8 7 0.145

2 10 9 0.165

3 20 19 0.241

4 12 11 0.183

• wi=∑

• Weighted mean: 7.53ppm• Weighted std: 1.16ppm

Final Benchmark SpecificationsCore Specifications keff

Minimum Critical

7.53ppm Boron59% Graphitization16 Zr Assembly

1.00413 ± 20 pcm

MC+7.53ppm Boron

59% Graphitization1.00171 ± 20 pcm

M8CAL

7.53ppm Boron59% Graphitization

C/S Rod 22 in.CR Rod OutTR Rod Out

1.00394 ± 20 pcm

SERPENT Results:    MCM+ Fission Rate/Flux

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SERPENT Results:  M8CAL Rod Worth

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M8CAL Monte CarloPower Distribution

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IRPhEP Benchmark Experiment DocumentationSection 1 Description of the Experiment

A detailed description of the experiments and all relevant experimental data will be provided in the appropriate subsections of section 1. 

Section 2 Evaluation of Experimental DataMissing data or weaknesses and inconsistencies in published data will be discussed and resolved in the appropriate subsections of section 2. The effects of uncertainties in parameter data on the measurement results will be discussed and quantified. Codes and modelling methods used for calculations of the effects will be specified and the use of data with large uncertainties or data that require assumptions on the part of the evaluator will be justified.

Section 3 Benchmark SpecificationsBenchmark specifications will be provided which will include all the data necessary to construct calculationalmodels that best represent the experiment. 

Section 4 Calculated ResultsCalculated results obtained with the benchmark‐model specification data given in Section 3 will be tabulated in this section. These will be regarded as sample calculation and methodologies used for the sample calculations and any other recommendations for the calculations will be described.

Section 5 References / AppendicesAppendix A will provide a description of the options, cross section data, and an input listing for the codes used in the calculations of the results given in Section 4.

UQ Analysis: Parameters

Table 1. Variable and distribution information summary for minimum critical core model uncertainty analysis

Parameter Distribution Distribution parametersU-234 Content in Graphite Fuel(wt.%) Normal µ = 0.91, σ = 0.008U-235 Content in Graphite Fuel(wt.%) Normal µ = 93.239, σ = 0.026U-236 Content in Graphite Fuel(wt.%) Normal µ = 0.438, σ = 0.008U-238 Content in Graphite Fuel(wt.%) Balance

O:U Ratio in Graphite Fuel Triangular a=1.95, b=2.05, c=2Graphite Fuel B Content (wt.%) Normal µ = 7.53, σ = 1.1619U Mass Content in Fuel (wt.%) Triangular a=0.205, b=0.222, c=0.211

Density of Graphite Fuel (g/cm3 ) Triangular a=1.71, b=1.76, c=1.73Graphite Fuel Graphitization (%) Triangular a=58, b=60, c=59C Mass Content in Fuel (wt.%) Balance

Flat-to-Flat Distance of Graphite Fuel (in.) Triangular a=3.795, b=3.82, c=3.8Al 6063 Composition (wt.% Al) Balance

Al 6063 Density (g/cm3 ) Discrete 2.685/2.7Standard fuel assembly outer radius Triangular a=3.935, b=3.985, c=3.96

Al 6063 Can thickness Triangular a=0.05-1/64, b=0.05+1/64, c=0.05Al 1100 Composition (wt.% Al) Balance

Zr-3 Composition (wt.%Zr)Zr-3 Can thickness

BalanceTriangular a=0.025-1/64, b=0.025+1/64, c=0.025

CP-2 Density (g/cm3 ) Triangular a=1.58, b=1.7, c=1.67

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Samples generated

300 cases:All the parameters listed in Table 11200 cases: The five parameters below300 cases: Boron content in graphite fuel 300 cases: Al-6063 can thickness 300 cases: Zr-3 can thickness300 cases: Standard fuel assembly outer radius 300 cases: Flat-to-flat distance of graphite fuel

The five groups of 300 cases:– each contains a significant factor recognised from single assembly studies.– each contains perturbations on one parameter.– prepared for sensitivity analysis.

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Uncertainty resultsParameter(s) perturbed Sample size Average keff Relative uncertainty

All parameters listed in Table 1 300 1.0073 ± 1.1749E − 5 1273.4 ± 1.2pcmThe five parameters below 1200 1.0069 ± 5.8865E − 6 1171.6 ± 0.6pcm

Boron content 300 1.0044 ± 1.1806E − 5 1093.9 ± 1.2pcmFlat to flat distance of fuel block 300 1.0064 ± 1.1763E − 5 222.7 ± 1.2pcm

Standard fuel assembly outer radius 300 1.0041 ± 1.1770E − 5 30.6 ± 1.2pcmAl-6063 can thickness 300 1.0044 ± 1.1788E − 5 335.6 ± 1.2pcm

Zr-3 can thickness 300 1.0040 ± 1.1845E − 5 894.2 ± 1.2pcm

Table 2. TREAT minimum critical core uncertainty analysis summary

• Reference keff : 1.00413 ±0.0002.• Boron content and Zr-3 can thickness were recognised as the two most significant factors.• Perturbations of flat to flat distance of fuel block caused shift in the mean keff value.

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Sensitivity analysis

Parameter perturbed Sample size Si (estimated) Si (tested)Boron content 300 0.6928 0.7444

Flat to flat distance of fuel block 300 0.0256 0.0310Standard fuel assembly outer radius 300 negligible 5.6169E-4

Al-6063 can thickness 300 0.0937 0.0701Zr-3 can thickness 300 0.1482 0.4974

Table 3. TREAT minimum critical core sensitivity analysis summary

• The column of ”Si (estimated)” contains estimation from results of the 1200 cases which hadperturbations on all parameters. Variance decomposition was applied to estimated the uncertaintycontribution of each parameter.

• The column of ”Si (tested)” contains results calculated directly from the ith 300 cases. For these cases, only one parameter was perturbed, no variance decomposition required.

Sensitivity index: Si = partial variance caused by the ith

parameter and D is the total variance.D

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Task 1.6 MIT: MC+ OpenMC Modeling

MC+ is MC with two additional fuel elements and Control Bank 1 (northeast bank) inserted to maintain criticality

Normal absorber sections (no more shorted B4C section as MC) are used

Control Bank 1 at 48.5 inches

MIT: M8CAL OpenMC Modeling 1 318 Fuel Assemblies – Same as MCM(15 with thermocouples)

20 Control Rod Assemblies (8 Shutdown, 8 Transient and 4 Compensation)

12 Zr‐Cladded Reflector Assemblies

8 Slotted Dummy Assemblies

1 Slotted Half Assembly 

1 Zr‐Cladded Half Dummy Assembly

AA

B B

MIT: M8CAL OpenMC Modeling 2Section A ‐ A Section B ‐ B

Summary of  TREAT Monte Carlo Analysis

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Core SERPENT(UM)

MCNP(UM)

OpenMC(MIT)

MCC 1.00413 ± 20 pcm 1.00380± 20 pcm 1.00533 ± 22 pcm

MC+ 1.00171 ± 20 pcm ‐ 1.00268 ± 24 pcm

M8CAL 1.00394 ± 20 pcm ‐ 1.00535 ± 32 pcm

Deterministic TREAT Modeling

• PARCS• U.S. NRC Nodal Core Simulator• 14 group Cross Sections generated by SERPENT• Core calculation with Diffusion Theory (w/ ADFs)

• PROTEUS• NEAMS Full Core Transport

Deterministic:  PARCS RESULTS

Core SERPENTPARCS

MCM 1.00413 ± 20 pcm 1.00177

MCM+ 1.00171± 20 pcm 0.99769

M8CAL 1.00394 ± 20 pcm 1.04821

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• Cross section generation• Serpent 2.26• 14G • Fuel cross section 

• 2‐D Fuel Assembly unit cell

• Control rod color set

PARCS M8CAL Power Dist.

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Quasi‐Diffusion Equations

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1 , ,· J , , Σ , , , , , ,

• Scalar Flux Equation (integrate transport equation over 4π )

Eddington factor

1 , ,· , , , , Σ , , , , , ,

Ω Ω Ω 

• Current Equation (integrate transport equation over 4π with weight Ω)

Directional Diffusion Coefficients

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• If ignore the off‐diagonal elements, quasi‐diffusion is reduced to

, E, t 3

• Quasi‐diffusion equation is more accurate than conventional diffusion equation, and can be solved with almost same cost.

, E, t 3 3 , E, t 3 , E, t

• In homogeneous region, the previous eqation is equivalent to conventional diffusion with directional diffusion coefficients  

=0

3 , E, t

, E, t =∑

Task 1.1.5    Accomplishments at ANL • Preliminary calculations of TREAT benchmark problems (MinCC and M8CAL) using PROTEUS

• Mesh generation for 2D and 3D MinCC and M8CAL cores using CUBIT + UFmesh (built‐in mesh generation of PROTEUS)

• PROTEUS (MOCEX solver) calculations using 9‐group cross sections (generated from Serpent/GenISOTXS) or the cross section API of PROTEUS (ongoing)

• Discussion with the UM team on• IRPhEP benchmarks and documentation• Serpent (UM) and MCNP (ANL) results on MinCC

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Minimum Critical Core

M8CAL

mesh

Task 1.1.5    Accomplishments at ANL  (cont.)

• Two core configurations (MinCC and M8CAL) of TREAT have been simulated using PROTEUS

• MinCC simulation• Systematic test results showed good agreement in eigenvalue between PROTEUS and Serpent• Further whole‐core calculations using higher angular order (e.g., L15T25) will be performed• Comparison of flux solutions needs to be done

• M8CAL simulation • Calculation results of partial core (9x9 elements with 4 control rod elements and air channel to hodoscope) showed good agreement in eigenvalue between PROTEUS and Serpent

• Preliminary whole‐core calculations were performed. So, further calculations and verification tests will be done with accurate composition assignment

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Task 1.2 (Transient)  Schedule1.2

Transient (TR)

1.2.1 Survey available TREAT TR data for benchmark problem T. Downar, UM

1.2.2 Preliminary TR modeling of candidate problems T. Downar, UM

1.2.3 Down‐select to two  problems for benchmark evaluation T. Downar, UM

1.2.4 Perform TR modeling with deterministic U.S. NRC codes PARCS/AGREE T. Downar, UM

1.2.5 Perform TR modeling with deterministic NEAMS code PROTEUS C. Lee, ANL

1.2.6 Perform TR modeling with Monte Carlo code OPENMC W. Martin, UM

1.2.7 Benchmark level evaluation of selected problems T. Downar, UM

1.2.7 Evaluation of uncertainties in selected problems T. Downar, UM

1.2.8 Preparation of IRPhE Documentation T. Downar, UM

1.2.9 Submission of TR benchmark for peer review T. Downar, UM

Task 1.2.6

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• Transition Rate Matrix Method in OpenMC 0.7.0 (UM On-the-fly Doppler version)

• Verified using sample problem supplied by TRMM author Ben Betzler

• Investigated infinite lattice (3x3 assemblies) benchmark problem (homogeneous fuel)

• Validated fidelity to heterogeneous simulations w/ SERPENT (UM) and OpenMC (MIT)

• Cataloged sensitivity of trace isotopes on k-eff• Homogeneous assemblies required for TRMM

finite core simulations, as matrix size = 30x number of geometric regions

• Initial results for minimum critical core (9x9 TRM Matrix, 13.5 x 13.5 assemblies, vacuum boundary)

Figure 1    0th mode eigenfunction for a test TRMM run on min crit core.

Questions?