Quadratic Depletion Method for Gadolinium Isotopes in CASMO-5

The huge absorption cross sections of ¹⁵⁵Gd and ¹⁵⁷Gd cause strong spatial shielding effects in Gd-bearing pins. A high-order depletion method has been developed for CASMO-5 to address the issue of the small depletion steps typically required for Gd-bearing fuel assemblies. In this method, the microscopic absorption reaction rates of gadolinium isotopes are assumed to be quadratic functions of the number density of ¹⁵⁵Gd rather than the constant reaction rate assumption in the conventional predictor-corrector (PC) method. This quadratic function assumption models the variations of the spatial shielding effects over the depletion step and therefore improves the accuracy of depletion calculations with a negligible amount of calculation time increase. With this new method, a depletion step size four times larger than the step size used in a conventional PC method can be used for Gd-bearing assemblies without compromising accuracy.