A one-dimensional fuel burnup model of a PWR

A fuel burnup model of a Pressurized Water Reactor (PWR) was developed based on one-group diffusion theory and used simple thermal cross sections. A computer program which simulates the depletion of the core of a PWR was written based on this model. The basic idea was to develop a fuel depletion program which could be readily understood by nuclear engineering students. Thus, accuracy was sacrificed for the sake of simplicity.

The model was based upon a typical PWR with three concentric regions in the radial direction of differing fuel enrichment. Each of the regions was homogenized and the concentrations of the isotopes in each region were considered constant over a time interval. The isotopes considered were U-235, Pu-239, U-238, Xe-135, I-135, Sm-149, Pm-149 and the lumped burnable poison isotope.

The flux was approximated by the sum of two trigonometric functions. The magnitude and shape of the flux were determined by holding power constant, constraining system to be critical and varying the soluble boron concentration to find the fla~test possible positive flux. A flux magnitude computed in this manner was compared to a similar flux magnitude given in a Final Safety Analysis Report.

The concentrations of the isotopes were determined from the differential equations describing the rate of change of the concentrations. The behavior of the isotopes over core life was graphed and wherever possible compared to graphs from other sources. The concentrations calculated for U-235, U-238 and Pu-239 after 450 days were compared to the concentrations of the same isotopes calculated by a zero dimensional three-group model. The percentage difference between the concentrations determined by the two models varied from about 69% for Pu-239 to 1% for U-238.