EMERALD1: A Systematic Study of Cross Section
Library Based Discrepancies in LWR Criticality
Calculations
Jaakko Leppänen
Technical Research Centre of Finland
VTT PROCESSES / Nuclear Energy
VTT TECHNICAL RESEARCH CENTRE OF FINLAND
Outline
• Background
• Calculations, tools and methods
• Example results
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Background
•
•
•
•
•
The MCNP Monte Carlo transport calculation code is routinely used at
VTT for various reactor physics calculations.
A few years ago, some validation calculations on newly acquired cross
section libraries showed relatively large cross section library based
differences in criticality calculations.
It was decided to look into these differences more thoroughly, in order to
find out what kind of uncertainties can be expected in common LWR
calculations.
The main conclusions of a literature survey and preliminary comparison
calculations were that the differences can be: 1) large, 2) systematic.
The study was continued and the differences investigated in a systematic
manner.
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Calculations
• Instead of using realistic geometry models, an infinite LWR pin-cell lattice
was chosen as the starting point for various reasons:
– The simplicity allows straightforward and systematic study of the most
significant sources of discrepancies.
– The system parameters can be varied easily and the impacts on the
results assessed.
– Most of the comparison calculations encountered in the literature
used realistic models – there was no need to duplicate the results.
• Since the differences seemed to be strongly dependent on flux spectrum,
fuel-to-moderator ratio was chosen as the main free parameter in the
system.
• Various modifications of the basic lattice were also studied (finite lattice
with leakage, burnable and control absorber pins, high-burnup fuel, etc...).
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Calculation tools
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The comparison calculations were carried out using MCNP version 4C.
Burnup calculations were carried out using Monteburns 1.0
(MCNP-ORIGEN coupling).
The cross section data libraries were generated using the NJOY-99
nuclear data processing system from five evaluated nuclear data files:
1.
2.
3.
4.
5.
ENDF/B-VI.8 (USA 2001)
JEFF-3.0 (NEA Databank 2002)
JENDL-3.3 (Japan 2002)
JEF-2.2 (NEA Databank 1993)
JENDL-3.2 (Japan 1994)
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Calculation methods
• In addition to a direct comparison of multiplication factors, an analytic
method based on the detailed neutron balance of the system was used
(next slide).
• Only the most significant isotopes in the fuel were included in the study:
– U-235, U-238 and O-16 in the regular lattice.
– Gd isotopes in the modified lattice with burnable absorber pins.
– Boron, Ag, In and Cd isotopes in the modified lattice with control rods.
– U-236, the most significant plutonium and minor actinide isotopes and
fission products in the regular lattices with high- and low-burnup fuel.
• Various sensitivity studies were also performed on the results (fuel
enrichment, fuel and moderator temperature, chemical shim, level of
heterogeneity, unresolved resonance probability treatment).
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Calculation methods
generation rate
F
• The multiplication factor can be written
k

as a function of simple source and sink
loss rate
S F  S C  S M ( L)
terms.
G
• Each term consists of group-wise


F   VF  F   mg  gf ,m   2gn ,m 
reaction rates that can be easily
g 1 
m

calculated using MCNP.
• The impact of small differences in the
k
group-wise reaction rates can be
k  Rx
Rx
assessed by linearising k.
• Four energy groups were used in the calculations (thermal, resonance,
unresolved/slowing-down, fast fission).
• Various significant contributions were separated from the overall
differences.
• The total differences were predicted correctly by summing up the individual
terms.


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Example results
Figure 1: Total reactivity differences between the libraries.
Comparison to ENDF/B-VI.8.
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Example results
Figure 2: The most significantly contributing terms. Results of
JEF-2.2 compared to ENDF/B-VI.8.
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Example results, summary
• The essential results can be summarised as follows:
– There are significant cross section library based discrepancies in
LWR criticality calculations.
– These discrepancies are systematic and strongly dependent on the
level of neutron moderation.
– The most significant contributors are the fission and the radiative
capture rates of U-235 and U-238, especially in the resonance region.
– The compatibility between two libraries depends mostly on how well
the individual discrepancies cancel each other out.
– The differences are not particularly dependent on small deviations in
system parameters (except fuel enrichment).
– These discrepancies should be taken into account in all calculations
as an additional source of uncertainty.
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Thank you for your attention !