Macroscopic depletion models for nodal reactor analysis

Nodal reactor analysis packages consist of three major models: an assembly spectrum/depletion model, a global diffusion theory model, and a global depletion model. Numerous assembly spectrum codes have been developed, and they are capable of providing isotopic depletion rates and assembly-averaged cross sections for individual assemblies. One of the principal approximations in such assembly codes is that the intra-assembly flux distributions (and isotopic depletion rates) can be characterized by an infinite medium of identical assemblies or by a repetitive array of several fuel types. Global reactor behavior is then modeled by solving the nodal diffusion equations using homogenized cross sections, which have been derived from the assembly spectrum/depletion model. Individual nodes are then depleted using the global flux distributions obtained from the nodal diffusion solution. The macroscopic depletion model makes implicit assumptions that are not required in the microscopic depletion model, and this paper presents results of a benchmark pressurized water reactor (PWR) depletion problem, which quantify the magnitude of the errors introduced by the macroscopic depletion approximations