The Advanced Fuel Cycle Initiative Status of Neutronics Modeling

1
The Advanced Fuel Cycle InitiativeStatus of
Neutronics Modeling

• Won Sik Yang
• Argonne National Laboratory
• NEAMS Reactor Simulation Workshop
• May 19, 2009

2
Status of Neutronics Analyses

• Within the current knowledge of physics, theory
  and governing equations are well known
• Boltzmann equation for neutron transport
• Bateman equation for fuel composition evolution
• The coefficients of these equations are
  determined by nuclear data, geometry, and
  composition
• Nuclear data are for the most part relatively
  well known for the most commonly used nuclides
• But still improved data are required to reduce
  design uncertainties
• Geometry and composition have stochastic
  uncertainties and are affected by thermal,
  mechanical, irradiation, and chemical phenomena
• These coupled phenomena are not as well
  described, and they can dominate the analysis
  errors
• The challenge in neutronics analysis is to
  determine the solution efficiently by taking into
  account geometric complexity and complicated
  energy dependence of nuclear data

3
Reaction Rate Traverse Example

• Monte Carlo simulation with MCNP5 (INL)
• Reaction rate tally uncertainties lt 1
• C/E values for U-235 fission rate distribution in
  CIRANO-2A (Blanket) and CIRANO-2B (Reflector)
  experiments

4
Negative Reactivity Transients of PHENIX

• Four unexpected scrams occurred in 1989 - 1990
  due to short negative reactivity transients (200
  ms) with the same signal shape
• Several potential explanations were given, but
  not satisfactory
• Experiments are planned for PHENIX end-of-life
  tests for further investigation

5
Generation IV Target Uncertainties

• Current and Target Uncertainties for sodium
  cooled fast reactors

Parameter Current Uncertainty (SFR) Current Uncertainty (SFR) Targeted Uncertainty
Parameter Input data origin Modeling origin Targeted Uncertainty
Multiplication factor, Keff (?k/k) 1 0.5 0.3
Power peak 1 3 2
Power distribution 1 6 3
Conversion ratio (absolute value in ) 5 2 2
Reactivity coefficients (component) 20 20 10
Control rod worth (total) 5 4 2
Burnup reactivity swing (?k/k) 0.7 0.5 0.3
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Objectives and Requirements

• The final objective is to produce an integrated,
  advanced neutronics code that allows the high
  fidelity description of a nuclear reactor and
  simplifies the multi-step design process
• Integration with thermal-hydraulics and
  structural mechanics analyses to account for
  reactivity feedbacks due to geometry deformation
  accurately
• Required modeling capabilities
• Reactivity and power distribution (coupled
  neutron and gamma heating)
• Non-equilibrium and equilibrium fuel cycle
  analyses
• Refueling, fuel shuffling, and ex-core models
• Perturbation and sensitivity analyses
• Uncertainty analysis and optimization
• Transient analysis (coupled with T/H and T/M
  analyses)
• Reactivity coefficients and kinetics parameters
• Shielding, decay heat, coolant activation and
  dose rate calculations, etc.

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Selected Approaches

• Utilize modern computing power and computational
  techniques
• Meshing, domain decomposition strategies,
  parallel linear solvers, new visualization
  techniques, etc
• Allow uninterrupted applicability to core design
  work
• Phased approach for multi-group cross section
  generation
• Simplified multi-step schemes
• Online cross section generation
• Adaptive flux solution options from homogenized
  assembly geometries to fully explicit
  heterogeneous geometries in serial and parallel
  environments
• Allow the user to smoothly transition from the
  existing homogenization approaches to the
  explicit geometry approach
• Rapid turn-around time for scoping design
  calculations
• Detailed models for design refinement and
  benchmarking calculations

8
Adaptive Flux Solution Options

• Unified geometrical framework
• Unstructured finite element analysis for coupling
  with structural mechanics and thermal-hydraulics
  codes

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Flux Solvers Available in UNIC

• PN2ND
• Second-order, even-parity transport equation (CG
  solve)
• 1-D, 2-D, 3-D Cartesian with general reflected
  and vacuum b.c.s
• Spherical harmonics combined with Serendipity and
  Lagrangian FE
• SN2ND
• Second-order even-parity transport equation (CG
  solve)
• 2-D 3-D Cartesian with general reflected and
  vacuum b.c.s
• Discrete ordinates combined with Serendipity and
  Lagrangian FE
• MOCFE
• First-order transport equation (long
  characteristics)
• 3-D Cartesian with general reflected and vacuum
  b.c.s
• Discrete ordinates combined with Serendipity and
  Lagrangian FE
• NODAL hybrid finite element method for
  structured geometries
• Will replace nodal diffusion and VARIANT options
  in DIF3D
• Use as an multi-grid preconditioner for other
  solvers

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Takeda Benchmark 4
Control Rod In Control Rod Half Control Rod Out
Reference 0.88001 0.00038 0.98340 0.00039 1.09515 0.00040
PN2ND 0.87960 0.98365 1.09599
SN2ND 0.87877 0.98275 1.09494
MOCFE 0.87796 0.98164 1.09353
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ABTR Whole-Core Calculations
Angular Directions Spatial Mesh Approximation Spatial Mesh Approximation Spatial Mesh Approximation Spatial Mesh Approximation Spatial Mesh Approximation
Angular Directions 78243 113873 461219 671219 785801
32 -241 -233 -69 -64 -59
50 -220 -210 -47 -40 -37
72 -225 -217 -51
98 -216 -207 -43
288 -216
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ZPPR-15 Critical Experiments
Flux expansion order Scattering order Eigenvalue
P1 P1 0.99258
P3 P3 0.99640
P5 P3 0.99651
Monte Carlo (VIM) Monte Carlo (VIM) 0.996160.00010
Computational Mesh and Example Flux Solutions of
ZPPR-15 Critical Experiment
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2D OECD/NEA C5G7 Benchmark
Reference 1.18655 0.00010
MOCFE 1.18649
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Parallel Implementation

• The scalability to peta-scale computing resources
  has been demonstrated
• 163,840 cores of BlueGene/P (Argonne)
• 131,072 cores of XT5 (ORNL)
• Over 75 weak scalability

Weak Scaling Study by Angle on BlueGene/P (PHENIX
EOL test)
Cores 4p Angles keff Fission Iters. / Time Total Time (sec) Source Update (sec) Weak Scaling
32,768 32 0.96006 23 / 152 3493 2934 100
49,152 48 0.96004 23 / 152 3510 2933 100
65,536 64 0.96007 23 / 153 3526 2934 99
73,728 72 0.96015 23 / 156 3593 2934 97
131,072 128 0.96019 27 / 156 4209 3437 83
163,840 160 0.96019 27 / 173 4676 3436 75
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Parallel Implementation
Weak Scaling Study by Angle on XT5 (PHENIX EOL
test)
Cores 4p Angles keff Fission Iters. / Time Total Time (sec) Source Update (sec) Effective Weak Scaling
32,768 32 0.96017 25 / 63 1574 851 100
49,152 48 0.96014 22 / 64 1399 746 99
65,536 64 0.96017 22 / 64 1402 745 99
98,304 96 0.96017 25 / 65 1623 847 97
114,688 112 0.96017 26 / 65 1687 882 97
131,072 128 0.96029 28 / 68 1902 948 93
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PHENIX End-of-Life Experiments

• Participating in the PHENIX end-of-life
  experiments
• Whole-core geometry is required (no symmetry)
  using homogenized fuel and explicit control rods
• Space/angle convergence study completed using
  over 4 billion DOF on up to 163,840 cores of Blue
  Gene/P
• Energy discretization study is ongoing

0.4 MeV Max/Min1.78 900 eV Max/Min16.9 2 eV Max/Min84.2
600 eV Flux and Radial Mesh
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ZPR-6 Critical Experiments

• Two ZPR-6 critical experiments are targeted for
  VV in 2009 (Assemblies 6A and 7)
• Explicit fuel plate representation allows direct
  comparison to legacy homogenization methods
• Spatial mesh requirements are large U-235 plates
  are 1/16th in thick
• Preliminary studies performed on BG/P and Jaguar
  up to 130,000 processors indicate that over 10
  billion DOF will be required to resolve the
  space-angle-energy mesh

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ZPR-6 Critical Experiments

14 MeV Flux / Mesh
U-235 Plate Power
19
Advanced Multi-group Cross Section Generation
Code MC2-3

• A modular version has been integrated into UNIC
  for on-line generation of multi-group cross
  sections of each spatial region with given
  material and temperature distribution
• Standalone code to generate ISOTXS datasets for
  legacy tools
• Ultrafine group (2082 groups) transport
  calculations
• Homogeneous mixture, and 1-D slab and cylindrical
  geometries
• Resolved resonance self-shielding with numerical
  integration of point-wise cross sections using
  the narrow resonance (NR) approximation
• Unresolved resonance self-shielding with the
  generalized resonance integral method
• Elastic scattering transfer matrices obtained
  with numerical integration of isotopic scattering
  kernel in ENDF/B data

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Advanced Multi-group Cross Section Generation
Code MC2-3

• 1-D hyperfine group (100,000) transport
  capability
• Consistent P1 transport calculation for entire
  resolved resonance energy range (lt 1 MeV) with
  anisotropic scattering sources
• Optionally used for accurate resolved resonance
  self-shielding and scattering transfer matrix
  generation
• Efficient strategy to generate accurate
  multi-group cross sections for heterogeneous
  assembly or full-core calculations is being
  developed by combining various solution options
• 1-D hyperfine group cell calculation
• 1-D ultrafine group whole-core calculation (with
  homogenized regions)
• 2-D MOCFE calculation in several hundred groups

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MC2-3.0 and Coupling with UNIC
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Reconstructed Pointwise Cross Sections
(ENDF/B-VII.0)
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Hyper-Fine-Group Spectrum Calculation

• Inner core composition of ZPR-6/6A

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Hyper-Fine-Group vs. Ultra-Fine-Group Spectra
25
LANL Criticality Assembly Benchmarks (UFG
Calculation)

• Multiplication factors are in an excellent
  agreement within 0.15 ?? by taking into account
  the anisotropy of inelastic scattering

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MC2-3 vs. VIM for ZPR-6/7 (Standalone UFG
Calculation)
Region VIM MC2-3 (Dk pcm)
Inner Core 1.22945 0.00038 10
Outer Core 1.22482 0.00048 -36
Radial Blanket 0.33513 0.00043 485
Axial Blanket 0.33215 0.00048 440
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ZPPR-15 Critical Experiments
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A Realistic View of ZPPR-15 Double Fuel Column
Drawer
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ZPPR-15 Critical Experiments

• Three loading configurations of ZPPR-15 Phase A
  were analyzed
• Loading 15 initial criticality
• Loading 16 reference configuration for sodium
  void worth measurement
• Loading 20 configuration with an 18 sodium void
  in part of inner core

VIM - Exp DIF3D - Exp
Data Configuration Experiment VIM ?k, pcm DIF3D Sn ?k, pcm
ENDF/B-V.2 L15 1.00046 0.99647 -399 0.99525 -521
ENDF/B-V.2 L16 0.99627 0.99200 -427 0.99104 -523
ENDF/B-V.2 L20 0.99853 0.99529 -324 0.99428 -425
ENDF/B-V.2 Void Worth (pcm) 226 329   324  
ENDF/B-VII.0       L15 1.00046 0.99985 -61 0.99905 -141
ENDF/B-VII.0       L16 0.99627 0.99571 -56 0.99489 -138
ENDF/B-VII.0       L20 0.99853 0.99742 -111 0.99741 -112
ENDF/B-VII.0       Void Worth (pcm) 226 171   252  
Standard deviations of Experiment and VIM 0.00021 Standard deviations of Experiment and VIM 0.00021 Standard deviations of Experiment and VIM 0.00021 Standard deviations of Experiment and VIM 0.00021
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Summary

• An initial version of new multi-group cross
  section generation code MC2-3 has been developed
• Preliminary tests showed significantly improved
  performance relative to MC2-2
• Integrated with UNIC for online cross section
  generation
• Consistent thermal feedbacks
• Account for spectral transition effects
• Second order solvers PN2ND and SN2ND have been
  improved
• SN2ND demonstrated good scalability to gt100,000
  processors
• Working on enhancing the anisotropic scattering
  iteration
• Fixing the load imbalance for reflected boundary
  conditions
• Starting next phase of pre-conditioner
  development
• p-refinement multi-grid and
• Algebraic multi-grid beyond that or possibly
  h-refinement

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Summary

• First order solver MOCFE
• Improving parallel performance with Krylov Method
• Added more elements to ray tracing capabilities
• Adding back projection for parallel
• Started NODAL
• Implement Krylov solution technique to fix some
  convergence problems
• Eliminate memory problems and 1970s architecture
• Will investigate energy parallelization on
  multi-core machines (8-32 cores)

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Backup Slides
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Perturbation Evaluation with MCNP (LANL)

• The MCNP perturbation option was used to
  determine the difference in net neutron
  production in every fuel assembly as a resulting
  of reducing
• Fuel density by 2, cladding density by 5, and
  coolant density by 50
• While the fuel density reduction showed
  reasonable results, the clad and coolant density
  effects still showed significant statistical
  variations
• Observed statistical errors are less than 2 for
  the fuel density perturbation
• However, as large as 41 for the cladding density
  perturbation and 100 for the coolant density
  perturbation
• Direct perturbation calculations showed even
  worse results
• Relative statistical uncertainties of the
  re-converged production rates are often above
  50, and in some cases reach 100
• The re-converged calculation ran 50,000 histories
  per cycle for 160 active cycles, each of which
  took 1000 minutes on a 2.7-GHz Opteron processor

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Convergence of Assembly Power Distribution

• NGNP with 60-degree periodic symmetry
• Core multiplication factor converges relatively
  quickly
• Power distribution converges very slowly

• Asymmetric assembly power distribution is
  observed
• Extremely large number of histories would be
  required for converged pin power distribution

Number of neutron histories Number of neutron histories 100M 20M 5M
Eigenvalue Eigenvalue 1.45598 ? 0.0001 1.45599 ? 0.0002 1.45607 ? 0.0003
CPU time, hr CPU time, hr 1765 360 145
Variation, RMS 0.3 1.6 2.4
Variation, Max 0.6 3.2 5.4
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Depletion with Monte Carlo Method

• DB-MHR benchmark
• Cycle length 540 EFPD
• Total 7 cycles
• 6 burn steps per cycle (90 days interval)
• 50K and 100K neutron histories per burn step
• Note that there are 3 billion fuel particles

• Comparison of whole core depletions performed by
  GA, BNL, and ANL
• MONTEBURNS (MCNP5ORIGEN2)
• Simple cubic lattice model
• CPU time 40 hours for 50K and 100 hours for
  100K histories
• Much larger number of histories are required for
  converged flux solutions

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CEA NEPHTIS Verification Results
Control Rod Position Control Rod Worth Control Rod Worth Control Rod Worth
Control Rod Position TRIPOLI4 38 pcm NEPHTIS, Diff. NEPHTIS, Diff.
Control Rod Position TRIPOLI4 38 pcm Homogeneous Heterogeneous
ARI 18,341 0.90 -1.05
ORI 7,083 0.98 0.64
SRI 5,676 -3.87 -3.35

• APPLO2172-group CP and 28-group MOC calculation
• CRONOS2 8-group diffusion calculation (finite
  element method)

difference in fission rate distributions from
MCNP4C (3D core)
Heterogeneous Element
36
37
Power Distribution of Fuel Block (CR Inserted)
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Effective Multiplication Factors for 2D and 3D
VHTRs with Heterogeneous Fuel Compact
Geometry Control Rod Position MCNP5 20 pcm DeCART , ?? pcm DeCART , ?? pcm
Geometry Control Rod Position MCNP5 20 pcm 190 Group 47 Groups
2D ARO- Standard block 1.46245 187 573
2D ARI 1.09752 14 788
3D ARO- Standard block 1.46379 439
3D ARO 1.45791 123
All Rods In (ARI)
All Rods Out (ARO)
Operating Rods In (ORI)
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2D Power Distributions
ORI
ARO
ARI
39
40
2D Block Power Comparison with MCNP5
ORI
ARO
ARI
40
41
3D Flux Distribution for All Rods Out (ARO) Case
7 eV
1 MeV
0.13 eV
1 eV
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42
3D Flux Distribution for Operating Control Rods
In (ORI)
7 eV
1 MeV
0.13 eV
1 eV
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