Deterministic neutronics analysis codes and methods established at Idaho National Laboratory were applied in computing the core multiplication factor of the high temperature reactor-Proteus pebble bed reactor critical facility. These same calculations were performed previously using earlier versions of the codes with less developed methods. The results of that earlier study (reported in INL/EXT-09-16620) indicated that the cross sections generated using COMBINE-7.0 did not yield satisfactory estimates of k eff , concluding that the modeling of control rods was not satisfactory. Over the past year, improvements to the homogenization capability in COMBINE have enabled the explicit modeling of tri-isotropic particles, pebbles, and heterogeneous core zones, including control rod regions, using a new multiscale version of COMBINE in which the one-dimensional discrete ordinate transport code ANISN has been integrated. The new COMBINE is shown to yield benchmark quality results for pebble unit cell models, the first step in preparing few-group diffusion parameters for core simulations. Presented in this report are results of this modeling effort where the full critical core is modeled, but with cross sections generated using the capabilities and physics of the improved COMBINE code. The new PEBBED-COMBINE model enables the exact modeling of the pebbles and control rod region along with better approximation to structures in the reflector. Initial results for the core multiplication factor indicate significant improvement in the Idaho National Laboratory's tools for modeling the neutronic properties of a pebble bed reactor. Errors on the order of 1.6 to 2.5% in k eff are obtained; a significant improvement over the 5 to 6% error generated by previous versions of the code. This is acceptable for a code system and model in the early stages of development, although too high for a production code. Analysis of a simpler core model indicates an over-prediction of the flux in the low end of the thermal spectrum. Reasons for this discrepancy are under investigation. Since new homogenization techniques and assumptions were used in this analysis, further confirmation and validation are required. Further refinement and review of the complex Proteus core model are likely to reduce the errors even further. vii viii