Minimum critical masses of heterogeneous moderated plutonium and uranium metal systems and their practical application to operation limits - 14355

In criticality safety analysis it is important to recognize the significant differences in reactivity achieved when material transitions from the solid to solution regime. However, the intermediate area of mixed heterogeneous systems (i.e. collections of small pieces) has not been well characterized. To that end, a study has been completed to determine the effect of fissile material piece size/shape on minimum critical mass of a system. The study presented represents a calculation-based investigation of moderated arrays of fissionable material to expand on established plutonium and uranium solution curves of LA-10860 to add the heterogeneous regime between pure a solid and solution of fissionable material. The analysis performed consists of parametric studies utilizing the neutron transport code MCNP6 to calculate the critical mass of systems composed of moderated arrays of varying sizes of spheres, cubes, or elongated rods (height >> diameter). The boundary of the array is increased to find the critical mass for the particular piece geometry and fissile volume density. The different shapes were then compared at points with the same fissile volume density to demonstrate that the key relationship between varying piece shape is the surface area to volume ratio. The results show that as pieces get larger (i.e. more heterogeneous) the minimum critical mass starts to increase. This effect results from the moderation of neutrons becoming less and less effective due to increased self-shielding of larger individual pieces. For plutonium pieces at a surface area to volume ratio of < 13 the reactivity increase from additional neutron moderation can no longer overcome the reactivity decrease from the reduced core density (separation of material pieces). At this point the minimum critical mass is achieved when the plutonium is in a solid metal configuration. This effect is not noticed for uranium which responds much more quickly to moderation and thus almost any sized pieces will increase in reactivity when moderation is introduced. Summarizing the results of the calculation a surface area to volume ratio vs minimum critical mass curve is generated. The curve gives analysts a practical starting minimum critical mass in analysis of heterogeneous systems with known minimum material surface area to volume ratios. (authors)