The Advanced Fuel Cycle Initiative
Status of Neutronics Modeling
Won Sik Yang
Argonne National Laboratory
NEAMS Reactor Simulation Workshop
May 19, 2009
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
May 19, 2009 NEAMS Reactor Simulation Workshop 2
Reaction Rate Traverse Example
Monte Carlo simulation with MCNP5 (INL)
– Reaction rate tally uncertainties 100,000 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
May 19, 2009 NEAMS Reactor Simulation Workshop 30
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)
May 19, 2009 NEAMS Reactor Simulation Workshop 31
Backup Slides
May 19, 2009 NEAMS Reactor Simulation Workshop 32
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
May 19, 2009 NEAMS Reactor Simulation Workshop 33
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 C C C C C
is observed C C
1.05
1.04
0.92
0.91
1.03
1.01
1.03
1.02
1.00
0.99
0.98
0.97 C
1.03 0.91 1.00 1.00 0.97 0.95
– Extremely large number of histories would
0.98 0.92 0.86 0.89 0.82 0.88 0.86 0.93 1.06
0.97 0.92 0.86 0.88 0.81 0.87 0.85 0.92 1.05 C
0.98 0.92 0.86 0.87 0.81 0.86 0.84 0.90 1.03
0.99 0.86 1.05 1.24 1.15 1.14 1.22 1.05 0.86 0.93
C 0.99 0.86 1.04 1.23 1.14 1.12 1.21 1.03 0.85 0.91 C
be required for converged pin power C
1.02
1.02
1.01
0.88
0.88
0.87
1.22
1.22
1.05 1.22 1.13 1.11 1.20 1.00
1.24
1.21
0.83
0.89
0.88
0.88
1.03
1.01 C
1.05 0.90 1.24 1.19 0.85 0.99
distribution C
1.02
1.02
1.06
0.82
0.82
0.85
1.13
1.13
1.16
1.16
1.14
1.11
0.82
0.81
0.79
1.02
1.01
0.99
C
0.92 0.89 1.15 1.14 0.88 0.99
C 0.92 0.89 1.15 1.13 0.87 0.98
0.97 0.93 1.19 1.11 0.87 0.98
1.05 0.86 1.23 1.23 0.86 0.98
Number of neutron 1.05
1.10
0.86
0.90
1.23
1.29
1.22
1.20
0.86
0.85
0.97
0.96
C
100M 20M 5M C
0.92
0.93
1.04
1.04
1.05
1.04
0.93
0.93 C
histories 0.97
0.96
0.86
1.09
1.22 1.23
1.03
0.86
0.92
1.05
C 0.98 0.86 1.22 1.24 0.86 1.05
1.03 0.90 1.27 1.21 0.85 1.03
1.45598 1.45599 1.45607 0.99
1.00
1.03
0.88
0.88
0.91
1.13
1.13
1.16
1.15
1.16
1.13
0.89
0.89
0.88
0.93
0.93
0.92
C
1.02 0.82 1.15 1.13 0.82 1.02
Eigenvalue C 1.03
1.06
1.02
0.82
0.84
0.89
1.15
1.18
1.23 1.22
1.14
1.11
0.88
0.83
0.81
1.02
1.02
1.00
C
0.0001 0.0002 0.0003 C 1.02
1.04
0.92
0.89
0.91
0.86
1.23
1.25
1.04 1.22 1.13 1.15 1.23 1.04
1.23
1.22
0.86
0.89
0.86
0.99
1.03
1.01
C
C 0.92 0.86 1.05 1.23 1.15 1.16 1.25 1.06 0.87 1.00 C
0.94 0.87 1.04 1.21 1.13 1.16 1.23 1.05 0.86 0.98
1.05 0.92 0.86 0.88 0.82 0.89 0.86 0.92 0.97
CPU time, hr 1765 360 145 C 1.05
1.06
0.93
0.93
0.86
0.87
0.89
0.88
0.83
0.82
0.90
0.89
0.87
0.86
0.94
0.92
0.99
0.97
0.97 0.99 1.02 1.02 0.92 1.05
C 0.98 1.00 1.03 1.04 0.94 1.06 C C
0.98 0.99 1.02 1.02 0.92 1.03
Variation, RMS 0.3 1.6 2.4 C C C C C
100 M
% Max 0.6 3.2 5.4
20 M
5M
May 19, 2009 NEAMS Reactor Simulation Workshop 34
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Depletion with Monte Carlo
Method
1.08
DB-MHR benchmark
GA BNL ANL-50K ANL-100K
– Cycle length = 540 EFPD
1.04
– Total 7 cycles
1.00 – 6 burn steps per cycle (90
days interval)
K-eff
0.96 – 50K and 100K neutron
histories per burn step
0.92
Note that there are ~3 billion
fuel particles
0.88
0 540 1080 1620 2160 2700 3240 3780
Burnup, EFPD
Comparison of whole core depletions performed by GA, BNL, and ANL
– MONTEBURNS (MCNP5+ORIGEN2)
– 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
May 19, 2009 NEAMS Reactor Simulation Workshop 35
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CEA: NEPHTIS Verification Results
Control Rod Worth
APPLO2:172-group CP and 28-group Control
Rod NEPHTIS, % Diff.
MOC calculation Position
TRIPOLI4
±38 pcm Homogeneous Heterogeneous
CRONOS2: 8-group diffusion
calculation (finite element method) ARI 18,341 0.90 -1.05
ORI 7,083 0.98 0.64
SRI 5,676 -3.87 -3.35
Homogenous Element
% difference in fission rate distributions from MCNP4C (3D core)
May 19, 2009 NEAMS Reactor Simulation Workshop Heterogeneous Element
36
36
Power Distribution of Fuel Block
(CR Inserted)
k∞ = 0.58326±0.00035 (MCNP5) MCNP5
0.58375 (DeCART) % diff
1.094 1.137
0.02 1.03
0.965 1.048 1.120 1.193 RMS = 0.76 %
0.29 0.18 0.28 0.05 Max. = 3.60 %
0.889 0.986 1.073 1.148 1.226
0.24 0.10 -0.12 0.03 0.19
0.742 0.832 0.939 1.038 1.131 1.215 1.302
-0.23 0.54 0.02 0.13 0.01 0.17 -0.15
0.668 0.758 0.862 0.971 1.074 1.164 1.250 1.343
-0.94 0.13 0.16 -0.05 -0.20 0.13 0.28 -0.16
0.552 0.606 0.692 0.805 0.934 1.046 1.153 1.243 1.335 1.416
-1.11 -0.74 0.08 0.16 -0.18 0.33 0.00 0.21 -0.29 -0.08
0.545 0.614 0.717 0.846 0.969 1.093 1.198 1.287 1.367
-0.60 -0.28 0..04 -0.08 0.78 -0.02 -0.33 -0.23 -0.06
0.473 0.471 0.531 0.629 0.795 0.943 1.076 1.192 1.279 1.360 1.432
-1.69 -0.69 -0.42 0.94 0.11 0.60 0.23 -0.54 -0.16 -0.12 -0.05
0.427 0.442 0.524 0.671 0.853 1.006 1.129 1.230 1.320 1.384
-1.00 -1.43 0.14 0.86 0.12 0.01 -0.03 -0.03 -0.45 -0.39
0.365 0.595 0.823 0.992 1.121 1.228 1.312 1.382
-2.99 1.34 0.59 0.56 0.22 -0.36 -0.26 -0.04
0.353 0.693 0.909 1.058 1.174 1.269 1.346 1.413
-2.55 1.22 0.45 0.57 -0.07 -0.19 -0.15 -0.08
1.343
0.297 0.643 1.062 1.170 1.263 1.410
-0.16
-3.60 2.05 0.38 0.18 0.04 -0.15
1.120 1.220 1.303 1.370
0.27 -0.08 -0.01 0.32
May 19, 2009 NEAMS Reactor Simulation Workshop 37
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Effective Multiplication Factors for 2D
and 3D VHTRs with Heterogeneous Fuel
Compact
MCNP5 DeCART , ∆ pcm
Geometry Control Rod Position
±20 pcm 190 Group 47 Groups
ARO- Standard block 1.46245 187 573
2D
ARI 1.09752 14 788
ARO- Standard block 1.46379 439
3D
ARO 1.45791 123
All Rods Out (ARO) All Rods In (ARI) Operating Rods In (ORI)
May 19, 2009 NEAMS Reactor Simulation Workshop 38
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2D Power Distributions
ARO ARI ORI
May 19, 2009 NEAMS Reactor Simulation Workshop 39
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2D Block Power Comparison with
MCNP5
0.8 1.0 0.5 0.7 0.9 0.6
-0. 2 -0. 2 MC -0. 4 -0. 1 0.6 5 -0. 5
08 50 29 47 8 27
N
% P5
dif
f 1.1 1.1 0.8 1.6 1.0 0.6
1.1 0.8 0.9
0.1 3 0.3 8 -0. 9 -0. 5 0.9 5 0.1 8 -0. 0 0.4 1 -0. 6
9 4 41 40 7 3 20 6 24
1.2 0.8 0.9 2.1 1.2 0.4 1.6 0.9 0.5
0.7 2 0.2 6 -0. 8 0.6 3 0.9 6 -0. 9 -0. 8 0.5 2 -0. 2
0 4 86 9 9 91 08 4 39
1.0 0.9 1.8 0.9 1.3 0.7
0.9 4 -0. 3 0.5 3 0.1 0 0.1 3 0.0 1
2 22 3 4 3 4
1.2 0.8 1.0 1.7 1.0 0.5 1.7 0.9 0.5
0.5 3 0.5 6 -0. 5 -0. 2 0.6 6 -1. 8 -0. 0 0.5 0 -0. 3
52 51 8 45 31 1 68
3 1
1.1 0.8 0.9 0.8 0.7 0.3 1.6 1.0 0.5
-0. 5 0.2 9 -0. 2 -1. 0 -0. 8 -0. 9 -0. 2 0.3 1 -0. 5
19 57 88 14 74 29 2 30
4
0.8 1.0 0.5 0.6 0.9 0.6
-0. 2 -0. 2 -0. 4 -1. 2 0.6 5 -0. 9
08 41 29 12 8 03
RMS 0.38%, Max 0.68%
RMS 0.5%, Max 0.92% RMS 0.82%, Max -1.88%
Homogeneous Fuel, ORI
Heterogeneous Fuel, ARO Homogeneous Fuel, ARI
ARO ARI ORI
May 19, 2009 NEAMS Reactor Simulation Workshop 40
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3D Flux Distribution for All Rods
Out (ARO) Case
1 MeV 7 eV 1 eV 0.13 eV
May 19, 2009 NEAMS Reactor Simulation Workshop 41
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3D Flux Distribution for Operating
Control Rods In (ORI)
1 MeV 7 eV 1 eV 0.13 eV
May 19, 2009 NEAMS Reactor Simulation Workshop 42
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