Analysis of the neutron flux spectral differences and effects on the depletion in the fuel kernels of the PBMR fuel spheres

The Pebble Bed Modular Reactor (PBMR) is a high-temperature, helium-cooled graphite moderated pebble bed reactor with a multi-pass fuel management scheme and an online refuelling procedure. On average, a fuel sphere will pass through the reactor core six times before the discharge burnup is reached. The current calculations performed at PBMR for the core neutronic design and fuel management are based on the VSOP99 suite of codes. The 2-D core model is divided into 79 fuel regions, each one containing a mixture of six different fuel sphere types, called batches, with a nuclide composition associated with their burnup level. An inline spectrum calculation is performed for each fuel region to generate few-group microscopic cross sections for the diffusion and burnup calculations. The spectrum calculation is done by using a single set of nuclide atomic densities obtained from volume averaging the six batches. This averaging procedure is based on the assumption that the neutron spectra inside the different batches should be similar, due to the relatively long mean free path of the neutrons inside the pebble bed. The same sets of few-group (diffusion) or one-group (depletion) microscopic cross sections are thus used for all six batches. The aim of this paper is to evaluate the accuracy of this assumption. First, the variation of the neutron spectrum in the kernels with different burnup is analyzed, and consequently the importance of collapsing the cross sections with the proper spectrum in the kernels of each fuel sphere, instead of using the averaged fuel sphere spectrum (as done in VSOP99). Second, the effects of the spectrum used in generating the one-group cross sections employed for fuel depletion are studied by evaluating differences in the nuclide composition. The Monte Carlo code MCNP 5 is used for the spectrum evaluation and the FISPACT code is used for the depletion analyses. Results show that the approximate method used in VSOP99 to generate the cross sections is acceptable for the core neutronic design and fuel management analysis. The effects introduced are small with differences less than 1% for the 4-group macroscopic cross sections and less than 5% in nuclide densities, evaluated throughout the depletion range.