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APOLLO2-A - AREVA's new generation lattice physics code: Methodology and
validation
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PHYSOR 2010 – Advances in Reactor Physics to Power the Nuclear Renaissance
Pittsburgh, Pennsylvania, USA, May 9-14, 2010, on CD-ROM, American Nuclear Society, LaGrange Park, IL (2010)
APOLLO2-A – AREVA'S NEW GENERATION LATTICE PHYSICS
CODE: METHODOLOGY AND VALIDATION
E. Martinolli∗, T.C. Carter, F. Clément, P.M. Demy, M. Leclère, P. Magat,
A. Marquis, V. Marotte, J. Marten1, S. Misu1, M. Schneider, S. Thareau2, L. Villatte
AREVA NP
Plants Sector, Tour AREVA, 92084 Paris La Défense, France
(1)
Fuel Sector, Paul-Gossen-Strasse 100, 91052 Erlangen, Germany
(2)
Fuel Sector, 10, rue Juliette Récamier, 69456 Lyon, France
ABSTRACT
AREVA has developed the ARCADIA® reactor code system including the lattice physics transport
code APOLLO2-A. Based on the APOLLO2 kernel developed by CEA, APOLLO2-A features a
state-of-the-art methodology designed by AREVA for Light Water Reactor industrial applications.
The validation of the code is achieved through comparisons with a comprehensive experimental
database and with Monte-Carlo reference codes. In this paper, the main features of APOLLO2-A,
the methodology and results from the validation base are presented.
Key Words: Neutronics, ARCADIA®, APOLLO2-A, methodology, validation
1. INTRODUCTION
AREVA has developed the deterministic neutron transport code APOLLO2-A [1, 2] designed for lattice
physics calculations as part of the new ARCADIA® [3] reactor code system. It is based on APOLLO2
kernel [4, 5] developed by the French Commissariat à l’Energie Atomique (CEA) with the support of
AREVA and Electricité de France (EdF). APOLLO2 provides the basic physics computation modules for
solving the Boltzmann transport equation in a multi-group scheme and for generic unstructured
geometries. APOLLO2 was adapted by AREVA for Pressurized Water Reactor (PWR) and Boiling Water
Reactor (BWR) industrial applications by implementing a layered computational scheme and a userfriendly and flexible input/output software layer. A comprehensive verification and validation base was
set up. APOLLO2-A will replace APOLLO2-F [6], the lattice physics code of AREVA’s SCIENCE V2
reactor code system [7, 8] currently in production.
The advanced methodology and the flexible software architecture of APOLLO2-A make it suitable for
stand-alone lattice physics analyses, such as fuel assembly design studies, as well as for generating multigroup neutron libraries for core simulators, like AREVA’s PWR and BWR 3D core simulators ARTEMIS
[9] and MICROBURN-B2 [10]. In 2010 a Topical Report for the ARCADIA® system, including
APOLLO2-A, will be submitted to the US NRC, with the focus on PWR applications (including the
EPR™ reactor) and uranium oxide (UOX) fuel. Licensing will be extended later to mixed oxide (MOX)
fuel and BWR applications.
∗
Corresponding author, E-mail: emanuele.martinolli@areva.com
E. Martinolli et al.
The first section presents the main functionalities and the new methodology of APOLLO2-A. The second
section provides results of the verification and validation base including both code-to-code comparisons
against Monte-Carlo reference codes as well as validation of the physical models against experimental
results (critical experiments and spent fuel analysis). A comprehensive extension of the experimental
validation to MOX fuel type and BWR fuel assemblies is on-going.
2. FUNCTIONALITIES AND METHODOLOGY
2.1. Functionalities
The main features of APOLLO2-A, from the user’s point of view, are described in the following
paragraphs. Important aspects like the supported types of calculations, the nuclear data libraries, the
input/output capability, and software architecture are presented.
2.1.1 Supported types of calculations
The following types of calculations are available with APOLLO2-A:
• Single PWR or BWR fuel assemblies with various boundary conditions (reflective, vacuum and
periodic) for design purpose or cross-section generation for core simulators;
• Color-set: 2x2, 3x3, NxN fuel assemblies up to quarter cores;
• 1D-slab calculation for reflector cross-section generation;
• Single fuel cell.
For all these types of calculations, APOLLO2-A provides the capability of computing single state points,
as well as complex depletion histories with varying parameters and branch calculations. Restart points can
be included at any state point and burn-up value. Small cores or critical experiments (KRITZ, EPICURE,
Babcock and Wilcox, etc.) can also be computed through either the single fuel assembly or the color-set
type of calculation.
APOLLO2-A includes, by default, the following assembly-averaged branch parameters for cross-section
library generation:
• Boron concentration (both in parts per million - ppm - and B10 number density);
• Moderator density (or void fraction for BWR);
• Moderator temperature;
• Fuel pellet temperature;
• Xe-135 number density (or any isotope in burnable media);
• Fuel exposure;
• Detector, control rod/blade and burnable absorber insertion (more generally any geometric or isotopic
variation of an individual rod or a set of rods can be used as user-defined state parameter).
In addition to the standard computation mode, APOLLO2-A can carry out the transport computation in a
“reference” mode. The reference mode enables a greater input flexibility (i.e. fuel rods, absorber rods, and
moderator tubes can be placed at any location without constraints on lattice regularity; density and
temperature distributions can optionally be specified) and an enhanced accuracy of the results obtained
through a dedicated reference methodology, in which all optimizations and time saving strategies, such as
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APOLLO2-A - AREVA's New Generation Lattice Physics Code System: Methodology & Validation
energy and space collapsing of the neutron flux, are disabled. The reference mode is recommended for
applications where a very precise assessment of the fuel assembly behavior is needed.
2.1.2 Nuclear data libraries
APOLLO2-A currently supports three multi-group neutron data libraries: the default and recommended
library is based on JEFF3.1.1 [11] international nuclear data evaluation files. As an option, libraries based
on ENDF/B-VII.R0 and JEF2.2 are also supported. As a result of the extensive validation work for
APOLLO2-A, JEFF3.1.1 was shown to be the most accurate for fuel inventory, UOX and MOX
reactivity, plutonium depletion and reactivity coefficients. The JEFF3.1.1-based multi-group library
features all the most important actinides and more than 100 fission products. Moreover, the fine 281group energy mesh developed by CEA (SHEM mesh [12]) was adopted for all the supported libraries. The
benefit of these choices will be explained in the methodology section. Specific libraries for gamma
production and gamma transport are also provided and are fully consistent with the neutron transport
library.
2.1.3 Input/output capabilities
APOLLO2-A was specifically designed to provide the users with a large input flexibility for geometry
description and to support all the main fuel assembly types present in the market. This was achieved
thanks to the APOLLO2 flux solver based on the Method of Characteristics (MOC) [13, 14]. The
following geometries are supported:
• For PWR fuel assemblies: 14x14 up to 18x18, including large rod Combustion Engineering cases and
Palisades;
• For BWR fuel assemblies: various designs from 6x6 to 11x11 including AREVA’s ATRIUM™ design
with square water hole, General Electric’s designs with cylindrical water holes, Westinghouse BWR
designs with diamond-shaped water hole and internal water cross, and any type of channel box
including those with asymmetric reinforced walls;
• For all these fuel assemblies, rod displacements from the regular lattice can be individually specified
for each rod;
• The water gaps around the bundle can vary by side (wide and narrow water gaps).
APOLLO2-A can be linked with an external material database that contains default compositions for fuel
and other materials. In addition, any material can be defined by entering its isotopic composition;
however, fuel has the added capability of being defined with general information (density, uranium
enrichment, gadolinium concentration, plutonium concentration, etc). In other words, APOLLO2-A does
not impose any limitations on material definitions.
APOLLO2-A input is based on a user friendly keyword-based file. Keywords are self-explanatory and
default options are provided where possible. Keywords are grouped in blocks describing various physical
objects (for example a rod, an assembly, a detector, etc.) and an extensive consistency checking is
implemented.
APOLLO2-A features a modern and flexible output capability: results are stored in a tree-structured,
customizable Hierarchical Data Format (HDF) file. HDF [15] is a portable international binary file format
for scientific bulk data, and is used for restart, direct result analysis and coupling with core simulators. In
addition to standard spectral code output data, APOLLO2-A provides extended pin-by-pin data: flux and
reaction rates, isotopic densities for burnable media (ring-by-ring) and optionally cross-sections.
PHYSOR 2010 – Advances in Reactor Physics to Power the Nuclear Renaissance
Pittsburgh, Pennsylvania, USA, May 9-14, 2010
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E. Martinolli et al.
Moreover, a graphic output processor provides the capability of displaying the results with accurate
space-resolution on the very fine MOC solver mesh.
APOLLO2-A provides an embedded generator of input decks for MCNP [16] and TRIPOLI [17, 18]
Monte-Carlo codes: these input decks are fully consistent (as for the geometry and the isotopic
composition), with the data used by APOLLO2-A itself. This feature is currently only available for zero
exposure; an extension is planned for depleted fuel. Monte-Carlo code input decks also include typical
pin-by-pin tallies (fission rate, power). A post-processor for automated data treatment of Monte-Carlo
code results is provided in the package.
2.1.4 Software architecture
APOLLO2-A has a multi-layer modular structure which enables fast code evolution and easy
maintenance as well as the capability of fine tuning of the physical models and solvers for advanced
users. A modern C++ front-end (input/output processor and task-handler) is built above a
Fortran77/Fortran95 programmable kernel.
Cross-section library generation or any calculation including more than one depletion or branch-point set
can be parallelized on many processors by a simple input option. The code automatically divides the state
points in sub-sets and recovers the results which are then combined in a single output file.
2.2. Methodology
APOLLO2-A solves the eigenvalue Boltzmann neutron transport equation, as well as a source gamma
transport equation (where both prompt and delayed gamma sources coupled to neutron transport are
accounted for) and can combine the results for the power distributions.
Based on the most recent numerical and physical models, AREVA has developed, in close partnership
with CEA, a methodology dedicated to industrial LWR applications to reach very good accuracy of the
results even considering complex geometries and demanding physical conditions. This methodology is
based upon the new, state-of-the-art MOC transport solver which can completely handle irregular
(unstructured) geometries. The methodology implemented in APOLLO2-A is generic: it is used for both
PWR and BWR applications regardless of the fuel, absorber and geometry and needs no case-specific or
global correction.
The microscopic cross-sections are first read from the multi-group neutron library based on JEFF3.1.1
nuclear data evaluation (e.g. cross-sections but also fission yields, decay constants, fission energy, capture
energy, delayed neutron data, etc.). The cross-sections are provided for the 281-groups SHEM energy
mesh. This mesh was developed by CEA through an individual isotope-by-isotope optimization analysis
to explicitly describe the most important resonances of the main fission products and actinides. Therefore,
this energy mesh allows avoiding resonance self- and mutual- shielding treatment below 23 eV where
complex resonance overlapping effects are observed, while keeping the number of groups and the
computational burden at reasonable level.
Microscopic cross-sections are then processed to take into account the self-shielding effect of the energy
resonances above 23 eV for all the main resonant isotopes. APOLLO2-A treats the self-shielding of the
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APOLLO2-A - AREVA's New Generation Lattice Physics Code System: Methodology & Validation
following materials: actinides (U, Pu, etc.), absorbers (Gd, Er, Dy, Ag, In, Cd, Hf, etc.), structure
materials (Zr, Fe, etc.), and detector materials (Co, V, Rh, etc.). The spatial dependency of the selfshielded cross-sections and the Dancoff effect are taken into account explicitly by a 2D flux calculation.
This flux calculation uses the Collision Probability (CP) method and interface-current approximation [5]
which yields accurate results with negligible computational burden.
The neutron transport equation is then solved to determine the 2D heterogeneous flux. The direct
computation of this flux distribution in the fine 281-energy group structure of the library and on the fine
spatial mesh is performed by APOLLO2-A only in “reference mode”. For the standard usage mode, the
flux is computed on a coarser energy mesh (35 groups) which is an optimum trade-off between accuracy
and computation speed. Macroscopic cross-sections then need to be collapsed to this coarse energy mesh
with an appropriate weighting flux. This flux is obtained through the intermediate steps described below.
The main principle behind this multi-step methodology is an appropriate decoupling of the energy
description from the spatial description of the flux.
First, fine 281-energy group flux calculations are performed on simplified geometries with the CP solver
(1st level). Dedicated 1D flux calculations for BWR components (water rods, water holes, etc.) are also
performed at this step. The set of CP fluxes is accurate from the energy point of view, but less accurate for
the assembly-range spatial coupling. Thus, to enhance spatial coupling at the full assembly scale, a second
flux calculation (2nd level) is performed with the Integro-Differential Transport method (IDT) solver [19,
20] on a 2D, homogeneous cell geometry with 44-group cross-sections. These cross-sections are obtained
by collapsing the self-shielded cross-sections with the CP fluxes. The two fluxes (1st and 2nd level) are
combined using a reconstruction process [21] to yield a 281-group flux with a cell-scale spatial accuracy
over the whole assembly geometry. This weighting flux is used to collapse the cross-sections to 35 groups
for usage by the MOC solver.
Figure 1. APOLLO2-A MOC geometries for PWR and BWR fuel assemblies
The MOC flux calculation is then carried out on a very fine spatial grid (with thousands of meshes)
representing the true heterogeneous geometry. Examples of MOC geometries for PWR and BWR fuel
assemblies are provided in Figure 1. An automated mesh generator, based on CAD software libraries, is
integrated in APOLLO2-A. It also offers post-processing capabilities at the finest spatial mesh level.
PHYSOR 2010 – Advances in Reactor Physics to Power the Nuclear Renaissance
Pittsburgh, Pennsylvania, USA, May 9-14, 2010
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The spatially accurate flux, resulting from the MOC calculation, is combined with the 281-group
weighting flux to obtain the final result: a 2D flux which is very accurate over the full domain (fuel
assembly or color-set) both in space (MOC mesh) and energy (281 groups).
A critical buckling model is then used for computing a 281-group leakage calculation on the assembly
geometry. The flux is then adjusted by a leakage correction. The final flux is used for depletion and
outputs.
The depletion of the fuel pellets, burnable absorbers, and detector active zones is performed with an
extended isotope chain with 26 actinides and 131 explicit fission products. Each depletable material is
divided into rings and each ring is depleted individually. The depletion solver is controlled by a
“predictor-corrector” mechanism with a quadratic extrapolation of the reaction rates and an automatic
depletion step refinement which ensures accurate treatment of burnable absorbers. Furthermore, the code
offers the capability to perform zero power decay calculations (shutdown cooling).
A gamma transport calculation is also performed with the MOC solver. A 94-group set of gamma sources
is first computed from the reaction rates of all gamma-emitting (prompt and delayed) reactions based on
the fine neutron flux. Then, the gamma transport is computed in 18 energy groups. The resulting gamma
flux is used for evaluating the gamma contribution to the detector response as well as to improve the pinby-pin power distribution.
A detailed energy deposition methodology is implemented to compute pin-by-pin power distributions: in
addition to local energy deposition in the pellet (by fission product kinetic energy and beta energy), the
model separately accounts for neutron kinetic energy loss by slowing-down and gamma energy transport
over the geometry.
The color-set methodology of APOLLO2-A is very similar to the single assembly methodology with one
main difference: the 35-group cross-sections feeding the MOC flux solution over the entire color-set
geometry are generated on each individual fuel assembly of the color-set.
3. VALIDATION BASE
The validation strategy of APOLLO2-A is based both on extensive code-to-code benchmarking (against
Monte-Carlo calculations) and comparisons to experimental results (critical experiments and spent fuel
analyses). All APOLLO2-A and MCNP validation calculations presented in this section use consistent
cross-section libraries based on the same JEFF3.1.1 nuclear evaluation. APOLLO2-A was run in the
standard computation mode.
3.1. Monte-Carlo Benchmarking
3.1.1. Zero burn-up calculations
APOLLO2-A is benchmarked against MCNP at zero burn-up on a wide range of fuel assembly types and
physical conditions representative of existing LWR reactors (more than 350 cases, including PWR and
BWR assemblies with UOX and MOX fuel).
The validation base includes lattice sizes ranging from 14x14 to 18x18 for PWR fuel assemblies and the
prevalent BWR designs. Lattice size for BWR ranges from 8x8 to 10x10 pins. Uranium enrichment
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ranges from 1.49% to 4.95%. The validation base also covers MOX fuel with Pu contents ranging from
1.70% to 12.00%. Several different types of non-removable integral burnable absorbers: gadolinium
(Gd2O3 with concentration up to 10%), erbium (Er2O3), zirconium diboride (ZrB2), removable burnable
absorber rods (Pyrex glass and Wet Annular Burnable Absorber) are accounted for in the validation base.
Several physical conditions are covered, representative of normal reactor operation (from cold zero power
to hot full power) and accident conditions (e.g. low moderator density during main steam line break). For
BWR fuel assemblies, void rate conditions range from 0% to 80%. Calculations are performed for
uncontrolled and controlled assemblies: AIC, B4C and Hf are included.
PWR
UOX
1.5
rms (AP2-A / MCNP - 1) (%)
BWR
Uncontrolled
AIC
MOX
B4C
UOX
MOX
300
350
Hf
1
0.5
0
0
50
100
150
200
250
Case
Figure 2. Relative difference on pin-by-pin fission rate rms between APOLLO2-A and MCNP
The uncertainties (1σ) of the MCNP calculations are low: ±10 pcm for k-inf and 0.3% for pin-by-pin
fission rates. The average discrepancies in PWR and BWR fuel assembly k-inf are -48±124 pcm, 42±325
pcm for uncontrolled and controlled assemblies, respectively. The root mean square (rms) differences for
pin-by-pin fission rates between APOLLO2-A and MCNP are shown on Figure 2. The differences in
fission rate rms are 0.17±0.07% and 0.37±0.21% for PWR and BWR assemblies, respectively.
The entire set of results shows the excellent agreement between the two codes. Some generic
optimizations are underway to further improve the level of accuracy.
3.1.2. Monte-Carlo depletion benchmarks
APOLLO2-A depletion calculations are benchmarked against MCOR. MCOR [22] is an interface code
system (similar to MONTEBURNS [23]) which couples MCNP5 to the depletion code KORIGEN [24].
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The results presented in this section are obtained for two PWR and one BWR UOX fuel assemblies. The
PWR assemblies consist of 17x17 lattices with 3 different enrichments (from 4.65 to 4.95%) and 36 pins
with U/Gd . The two PWR assemblies differ only by their gadolinium content (6% and 10%). The BWR
assembly is an ATRIUM™ 10 design with various enrichment levels (ranging from 2.65% to 4.95%) and
16 pins with 2.5% gadolinium content. The assemblies are depleted under standard hot full power,
uncontrolled conditions, up to 80 GWd/t.
The MCNP calculations reach for each depletion point an uncertainty on k-inf of ±50 pcm at 1σ and of
0.3% at 1σ on pin-by-pin fission rates. The KORIGEN burn- up step size is 0.1 GWd/t until Xenon buildup, 0.5 GWd/t until gadolinium burn-out and 2.5 GWd/t afterwards. Each gadolinium fuel pellet is
depleted with 10 annular rings.
Discrepancies on fission rates (rms) between APOLLO2-A and MCOR calculations are shown in Figure 3
for all the cases. In Figure 4, comparisons of the isotopic contents are shown for one representative fuel
assembly and some isotopes of interest (absorbers and actinides).
All results demonstrate the excellent agreement between the two codes over depletion. Mean
discrepancies on k-inf are -141±157 pcm and -161±189 pcm for the two PWR respectively, and -291±86
pcm for the BWR case. Discrepancies of the most important actinides are below 1.5% all over the
depletion. Other minor actinides which are not shown here are below 10%.
PWR UOX with 6% Gd content (HFP)
PWR UOX with 10% Gd content (HFP)
BWR ATRIUM 10 UOX (HFP at 40%)
rms(AP2-A / MCNP - 1) (%)
0.8
0.6
0.4
0.2
0
0
10
20
30
40
50
Burn-up (GWd/t)
60
70
80
Figure 3. Pin-by-pin fission rate discrepancy (rms) between APOLLO2-A and MCOR
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APOLLO2-A - AREVA's New Generation Lattice Physics Code System: Methodology & Validation
Gd155
Gd157
U235
U236
Pu239
Pu240
Pu241
AP2A/MCOR - 1 (%)
2.0
1.0
0.0
-1.0
-2.0
0
10
20
30
40
Burn-up (GWd/t)
50
60
70
80
Figure 4. Relative discrepancies of the isotopic concentrations between APOLLO2-A and MCOR
PWR UOX assembly with 10% Gd content
3.2 Validation against experimental data
This section documents the capability of APOLLO2-A to accurately calculate reactivity, fission rate
distributions, and spent fuel isotopic inventory in a wide range of conditions as compared to measured
data. The reactivity calculation and fission rate distributions of APOLLO2-A are compared against
measurements for several critical experiment configurations. The isotopic depletion of APOLLO2-A is
validated against measurements from experimental and industrial reactors.
3.2.1 Critical experiments
The analyzed experiments come from several international programs, including Babcock and Wilcox
(B&W) in the US, KRITZ-KWU in Sweden, and two experimental programs – EPICURE and
CAMELEON – from CEA in France. These critical experiments are UO2-fueled experimental reactors
which were selected to support the licensing of the ARCADIA® chain in the US.
The configurations were selected in order to support a wide range of validation; this range includes
several U235 enrichments, absorber materials, guide-tube configurations, void conditions, and
fuel/moderator temperatures. The general characteristics of the experiments are given in Table I. Table II
presents the results for both reactivity (pcm) and fission rate distribution (% rms) comparisons. A total of
43 configurations were analyzed for reactivity. Table II presents the results of the experiments with
measured fission rate distributions.
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Table I. Critical Experiment Characteristics
Experiment
Enrichment (w/o)
Temperature (°C)
Special Characteristics
B&W
2.5 - 4.0
21
Absorbers: Pyrex, B4C, AIC, Gd2O3
(Gd Enrichment = 4.00%)
KRITZ-KWU
3.1
20 - 245
EPICURE
3.7
22
CAMELEON
3.5
22
Temperature Variation
Absorbers: Pyrex, AIC –
Void simulated by Al over-cladding
Absorbers: Hf, Gd2O3 (Gd Enrichment
= 3% with 5.1 w/o U235 and 7% with
0.25 w/o U235)
Table II. Critical Experiment Analysis Results
Experiment
B&W-1970's
B&W-1980's
KRITZ-KWU
EPICURE
CAMELEON
Configuration
C-M (pcm)
% rms
XI_2
215
1.72
XI_6
131
1.51
XI_8
63
1.26
XI_11
156
1
146
1.27
0.64
5
94
0.69
12
89
0.87
14
87
0.76
18
237
0.86
20
227
0.86
U-WH1 229°C
-51
1.08
UH1.2
23
1.75
UH1.2 30% Void
-25
0.62
UH1.2 50% Void
-40
1.00
UH1.2 100% Void
-73
0.95
UH1.4
4
0.53
UH1.4 Pyrex
-25
1.13
UH1.4 SSAIC
-199
1.77
25 Guide Tubes 12 Gd2O3 pins
141
0.73
12 Gd2O3 Pins
113
1.56
13 Gd2O3 Pins
148
1.09
5 Gd2O3 Pins
147
1.25
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The fission rate distributions, both measured and calculated, were normalized so that the average of the
measured locations is equal to 1.0. The mean deviation of the k-eff among all the configurations is 66 ±
139 pcm at 1σ. Only two configurations showed more than 250 pcm of discrepancy. CEA has determined
that the uncertainty, in pcm, of its critical experiments, including measurement and modeling, is between
300 and 400 pcm (1σ). These results clearly show a good agreement well within the overall uncertainty.
All of the results for the fission rate distributions fall within 2σ of the reported measurement uncertainty
(2% at 2σ).
3.2.2 Spent fuel analyses
The isotopic inventory of the spent fuel calculated by APOLLO2-A is compared with the measured
compositions from chemical analyses performed on samples irradiated in experimental and power
reactors. The samples come from several power plants in Germany and France as well as a CEA
experimental reactor, and cover a large range of fuel types, including UOX, Enriched Reprocessed
Uranium (ERU), UO2-Gd2O3 and MOX, as well as a large range of burn-up levels, from 3 to 71 GWd/t.
The UOX, ERU and UO2-Gd2O3 cases were computed with single-assembly calculations, whereas those
cases involving MOX were computed using the color-set capability, in order to account for the spectral
effect of neighboring assemblies. Table III presents the general characteristics of the spent fuel analysis
experiments.
Table III. Isotopic Burn-up Analysis Experiments
Experiment
Fuel Type
Number of
Samples
Burn-up Range
Bugey 3
UOX : 3.1% U235 Enrichment
1
20 GWd/t
Gravelines 2&3
UOX : 4.5% U235 Enrichment
7
26-61 GWd/t
Malibu Program
UOX : 4.3% U235 Enrichment
MOX : 8.1% Plutonium
1
1
71 GWd/t
68 GWd/t
Cruas 4
ERU : 3.1% U235, 1.2% U236
6
13-36 GWd/t
6
2.5-8.5 GWd/t
12
3.5-11.8 GWd/t
Gedeon 1 Program
Gedeon 2 Program
UOX : 3.25% Enrichment
Gd2O3 : 5%
UOX : 0.2% Enrichment
Gd2O3 : 8%
Saint Laurent B1
MOX : 2.9 – 5.6% Plutonium
7
25-45 GWd/t
Dampierre 2
MOX : 6.7% Plutonium
4
52-57 GWd/t
The results for the spent fuel analyses, presented in Figure 5, show that for most of the isotopes and burnup values, APOLLO2-A predicts the isotopic inventory within 5% of the measurement. More than 95% of
the results for isotopes of interest are within 2σ of the total reported uncertainties – up to 7% (1σ)
depending on isotopes and burn-up.
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E. Martinolli et al.
U235
U236
Pu239
Pu240
Pu241
Pu242
10.0
C/E - 1 (%)
5.0
0.0
-5.0
-10.0
-15.0
12
24
36
48
Burn-up (GWd/t)
60
72
Figure 5. Results of spent fuel analyses
4. CONCLUSIONS
AREVA has developed APOLLO2-A, a new lattice physics code for PWR and BWR industrial
applications. APOLLO2-A is a component of the new ARCADIA® reactor code system. Thanks to an
advanced multi-level methodology, based on an advanced MOC solver and a state-of-the-art multi-group
neutron data library based on JEFF3.1.1 evaluation, the code computes highly accurate results and
provides high quality neutronics data for core simulators. Efficient usage of APOLLO2-A is achieved
through its flexible and user-friendly input/output software layer. A comprehensive validation database
was defined to ensure accuracy for current and future applications. Results show excellent agreement with
both reference Monte-Carlo codes and several international experimental programs.
ACKNOWLEDGMENTS
The authors acknowledge the significant contribution of the CEA/SERMA (APOLLO2 kernel, multigroup neutron data library and methodology support) and CEA/SPRC (nuclear data evaluation and
experimental programs). Some of the validation programs were funded in a joint R&D effort of AREVA,
EdF, and CEA. The support by AREVA NP Inc. teams is also acknowledged for code review and
validation aspects.
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