Research on Quadratic Depletion Method for Reaction Rate Based on NECP-X

In depletion calculations, especially for gadolinium-bearing fuels, each burnup step often requires two flux calculations for predictor and corrector. However, in high-fidelity calculations, performing two physical calculations significantly reduces computational efficiency, leading to excessively high time costs in fuel cycle calculations. In this paper, quadratic depletion (QD) method is adopted in high-fidelity code NECP-X. The flux calculation in predictor is skipped, and a post-correction method is adopted to correct the number densities of seven gadolinium isotopes. In the correction step, quadratic interpolation is used for the reaction rates of gadolinium isotopes to improve the accuracy of depletion calculations of gadolinium-bearing fuels. Comparative depletion calculations are performed for both single-assembly and multi-assembly Gd-bearing fuel cases using traditional predictor-corrector method and quadratic depletion method. The results show that the quadratic depletion method cannot only improve the accuracy by at least a factor of 2, but also increase the efficiency by approximately 30%. Therefore, the proposed QD method can be well applied in Gd-bearing fuel depletion calculations.