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The geometrical complexity and the peculiarities of Atucha-2 PHWR require the adoption of advanced Monte Carlo codes for performing realistic neutronic simulations. Core models of Atucha-2 PHWR were developed using both MCNP5 and KENO-VI codes. The developed models were applied for calculating reactor criticality states at beginning of life, reactor cell constants, and control rods volumes. The last two applications were relevant for performing successive three dimensional neutron kinetic analyses since it was necessary to correctly evaluate the effect of each oblique control rod in each cell discretizing the reactor. These corrective factors were then applied to the cell cross sections calculated by the two-dimensional deterministic lattice physics code HELIOS. These results were implemented in the RELAP-3D model to perform safety analyses for the licensing process.

In the framework of the agreement NA-SA-University of Pisa no. 2”, several technical and research activities are being performed at the GRNSPG of the University of Pisa, in order to analyze the main characteristics of the plant and its behavior during normal and accidental conditions. In this paper, we present the activities performed using the Monte Carlo MCNP5 and KENO-VI codes, or the Atucha-2 full-core model development, some criticality calculations, its use for the RELAP5-3D three-dimensional neutron kinetics model development and validation, and then a result of a transient calculation using the validated RELAP5-3D model.

Atucha-2 is a 693 MWe Siemens designed PHWR under construction in the Republic of Argentina (see Figure

Atucha-2 NPP layout.

After the definition of a relevant core status with fuel at the burnup equilibrium, a set of neutron cross section libraries were calculated by the lattice physics code HELIOS. These data were used for the setting up of an RELAP5-3D neutron kinetic (NK) model of the core that was then coupled with an RELAP5-3D thermal-hydraulic (TH) model of the whole plant. The TH model is based on 280 Fuel Channels (FCs) and a 3D moderator tank nodalization. The 3D NK model is representing all the FCs, the reflectors, and the oblique Control Rods (CRs). The boundary conditions for the reconstruction of the Boron clouds, injected in the moderator tank by the shut-down emergency system, were derived by previously executed Computational Fluid-dynamics (CFD) analyses by the CFX code [

The evolution of the Boron concentration of the clouds was then reconstructed in the 3D TH moderator tank, using an automatic routine and several time-dependent junctions.

All these data were used as a boundary and initial conditions (BICs) for the steady state and transients calculations.

The geometrical complexity of this design (e.g., oblique CR, each one divided in to an upper and lower sections, 451 independent FCs, etc.) required the adoption of 3D Monte Carlo transport models (see Figure

Atucha-2 KENO-VI CR model.

Two independent, full-core, pin-by-pin models were developed for the MCNP5 [

Atucha-2 MCNP5 3D model, planar and axial view.

Atucha-2 KENO-VI and MCNP5 models, ten levels of axial detail.

These model were successfully used for CZP criticality calculation. Further development of these models consider 10 levels of axial discretization to take into account the axial differences in temperature and density.

Preliminary criticality calculations were run at cold zero power (CZP), and sensitivities analyses were performed assessing the effects of several geometrical details on the results. The effects of initial source distribution and of different continuous energy (e.g., ENDF/B-VIv8, ENDF/B-VII) and multigroup cross sections libraries were also investigated. Results with low variance were obtained running about 100 million of active neutron histories. Finally, reference criticality calculations were produced simulating CZP conditions for the core at the beginning of life (BOL).

Several cases were simulated to investigate the effects of control rod insertion, different Boron concentration, flux distribution, and beta delayed factors. In Table

Criticality results, CZP in ARI case from KENO-VI and MCNP5 core.

Boron concentration [ppm] | MCNP | KENO-VI | Differences (KENOVI − MCNP5) [pcm] | ||
---|---|---|---|---|---|

0 | 1.08294 | 5 | 1.08753 | 6 | 459 |

16 | 0.96727 | 6 | 0.97153 | 6 | 426 |

Results from the Atucha-2 MCNP5 3D model-thermal Flux distribution, planar and axial view.

Results from the Atucha-2 MCNP5 3D model-thermal and fast Flux distribution.

Differences of the order of hundreds pcm were found from comparison between MCNP and KENO-VI codes. Such differences are due to the different Xsec library used, or the ENDF/B-VI.6 continuous energy (CE) Xsec by MCNP5 and the 289 energy groups Xsec libraries derived from ENDF/B-VI.8 by KENO-VI.

The MCNP5 CZP results were used in the validation process of the Atucha-2 RELAP5-3D [

A further application of the developed Atucha-2 MCNP5 model was the stochastic volume calculations of the CRs [

As it can be easily understood from Figure

Sketch of a CR and its crossing with 3D NK hexagonal cells.

The developed procedure was the following. The CR volume to be measured was enclosed in a sphere, and an inward spherical distribution of neutron particles was employed for flooding the objects, that is, the CR and the intersected hexagonal prisms. A flux tally got the resulting volume calculation (see Figure

Stochastic cell volume procedure by MCNP5 tally.

In order to get a low variance on each flux (i.e., volume) tally, an automatic C routine was developed for calculating the optimal dimension of the enclosing sphere. Moreover, 100 million of neutron histories were employed to minimize statistical fluctuations.

This volume calculation procedure underwent a validation process comparing volumes calculated by MCNP5 with volumes calculated by the Autodesk AUTOCAD model, developed for a single CR (see Figure

A C/PERL routine allowed to automatically create the several MCNP5 input files for the calculations of all the possible CR volumes resulting from the intersection of the 18 CRs with 3D NK hexagonal meshes. Actually, symmetry considerations allowed to reduce the number of CRs intersections to be investigated to 10 CRs, thus resulting in 10*40 = 400 volumes calculations. In a successive step, the obtained values were integrated in another procedure for the NESTLE CR cross section weighting.

The MCNP5 core model was also applied for the calculations of corrective factors for the CR cross sections libraries. These libraries were developed using the two-dimensional lattice physics code HELIOS, that can not take into account the three-dimensional geometrical effects (i.e., the oblique CR) [

2D HELIOS and 3D MCNP5 models.

The developed procedure allowed us to evaluate the effects on a cell macroscopic cross sections (namely, the absorption and the fission cross sections) by the three-dimensional geometry (see Figure

Equivalent NESTLE composition in MCNP5 core model, axial view.

These averaged rates were obtained calculating with MCNP5 the reaction rate

Thus, the averaged macroscopic cross section

Atucha-2 has two types of CR, differing by the absorber material (hafnium and stainless steel). For each type of CR, 5 cases were simulated, one considering an MCN5 model equivalent to the HELIOS model (straight CR) and 4 cases using a realistic MCNP5 model (oblique CR). Thus, the effects of possible insertion modes of the CR on the macroscopic cross sections were evaluated.

An example of results can be seen in Figure

3D effects on absorption macroscopic cross sections (gray CR and black CR).

The results obtained by the Monte Carlo codes (i.e., the stochastic volume calculation and the corrective factor for the cross section) were implemented in the RELAP5-3D neutron kinetic model. An application of this validated model is the 0.1 a Large Break LOCA in Cold Leg 2 (CL2), one of the design basis accidents (DBAs) that has to be considered for the Atucha-2 licensing. The transient is initiated by the instantaneous opening (i.e., 3–10 seconds) of the break located between the RPV nozzle and the CL2. Boron injection by the shut-down emergency system starts at +0.63 seconds from the beginning of the transient and terminates at +3.91 seconds. Scram signal is actuated after +0.07 seconds, and the CR are completely inserted after +3.57 seconds. The transient analysis was performed for the first ten seconds. The results are presented in Figures

Reactor power (W) and void fraction in central and hot channel.

Fuel clad temperatures for central and hot channel.

As it is shown in Figure

The complex Atucha-2 geometrical design required the adoption of advanced 3D Monte Carlo calculations. The capabilities of two of the most advanced codes (MCNP5 and KENO-VI) allowed us to perform reference calculations with an unprecedented level of details. Moreover, MCNP5 flexibility was exploited for an automatic calculation of CR weighting factors, allowing for a great simplification of the necessary job for the 3D NK model development. Finally, further applications of these models are envisaged in the near future (e.g., criticality calculations with core at equilibrium burnup).