Modélisation neutronique des réacteurs à lit de boulets dans le code APOLLO2. (Neutronic modeling of pebble bed reactors in APOLLO2)

In this thesis we develop a new iterative homogenization technique for pebble bed reactors, based on a "macro-stochastic" transport approximation in the collision probability method. A model has been developed to deal with the stochastic distribution of pebbles with different burnup in the core, considering spectral differences in homogenization and depletion calculations. This is generally not done in the codes presently used for pebble bed analyses, where a pebble with average isotopic composition is considered to perform the cell calculation. Also an iterative core calculation scheme has been set up, where the low-order RZ SN full-core calculation computes the entering currents in the spectrum zones subdividing the core. These currents, together with the core keff, are then used as surface source in the fine-group heterogeneous calculation of the multi-pebble geometries. The developed method has been verified using reference Monte Carlo simulations of a simplified PBMR400 model. The pebbles in this model are individually positioned and have different randomly assigned burnup values. The APOLLO2 developed method matches the reference core keff within ±100 pcm, with relative differences on the production shape factors within ±4%, and maximum discrepancy of 3% at the hot spot. Moreover, the first criticality experiment of the HTR-10 reactor was used to perform a first validation of the developed model. The computed critical number of pebbles to be loaded in the core is very close to the experimental value of 16890, only 77 pebbles less. A method to calculate the equilibrium reactor state was also developed and applied to analyze the simplified PBMR-400 model loaded with different fuel types (UO2, Pu, Pu + MA). The potential of the APOLLO2 method to compute different fluxes for the different pebble types of a multi-pebble geometry was used to evaluate the bias committed by the average composition pebble approximation. Thanks to a "compensation of error", this bias is small when the core is loaded with UO2 fuel, with discrepancies on the power shape factors and main nuclide densities in discharged pebbles within ±1%, except for plutonium isotopes, with an underestimation of 3% for Pu at discard. The spectral differences between the pebbles being mostly linked to the resonance of Pu, this bias is important for the Pu loaded core, where differences up to ±10% on the power shape factors and on the main nuclide densities are observed. Based on the accumulated experience at CEA on prismatic HTGRs modeling, a coupled neutronicthermal hydraulic 3D core model of a PBR could be built, associating a multi-pebble geometry to each three-dimensional spectrum zone of the core.