Effects of random pebble distribution on the multiplication factor in HTR pebble bed reactors

In pebble bed reactors the pebbles have a random distribution within the core. The usual approach in modeling the bed is homogenizing the entire bed. To quantify the errors arising in such a model, this article investigates the effect on keff of three phenomena in random pebble distributions: non-uniform packing density, neutron streaming in between the pebbles, and variations in Dancoff factor. For a 100 cm high cylinder with reflective top and bottom boundary conditions 25 pebble beds were generated. Of each bed three core models were made: a homogeneous model, a zones model including density fluctuations, and an exact model with all pebbles modeled individually. The same was done for a model of the PROTEUS facility. keff calculations were performed with three codes: Monte Carlo, diffusion, and finite element transport. By comparing keff of the homogenized and zones model the effect of including density fluctuations in the pebble bed was found to increase keff by 71 pcm for the infinite cylinder and 649 pcm for PROTEUS. The large value for PROTEUS is due to the low packing fraction near the top of the pebble bed, causing a significant lower packing fraction for the bulk of the pebble bed in the homogenized model. The effect of neutron streaming was calculated by comparing the zones model with the exact model, and was found to decrease keff by 606 pcm for the infinite cylinder, and by 1240 pcm for PROTEUS. This was compared with the effect of using a streaming correction factor on the diffusion coefficient in the zones model, which resulted in Δstreaming values of 340 and 1085 pcm. From this we conclude neutron streaming is an important effect in pebble bed reactors, and is not accurately described by the correction factor on the diffusion coefficient. Changing the Dancoff factor in the outer part of the pebble bed to compensate for the lower probability of neutrons to enter other fuel pebbles caused no significant changes in keff, showing that variations in Dancoff factor in pebble bed reactors can be ignored.