Algorithms of solving the burnup equation with external feed

Burnup calculation is an essential task in nuclear reactor physics. Burnup equation is generally used to describe the generation, depletion and decay process in the nuclide system. In some nuclide systems, there may exist physical or chemical exchange with the surroundings, such as the spent fuel reprocessing facilities and some advanced reactors with continuous refueling and discharging like the liquid-metal-fuel reactor. This work studies the burnup calculations with considering external feed. Two external feed models, that is the relative feed and the absolute feed, are addressed. The burnup equations with external feed are solved by utilizing the variation of transmutation trajectory analysis (TTA) method and matrix exponential methods. The proposed models and methods have been implemented in the NUIT (NUclide Inventory Tool) code. Various test cases are calculated for validation, and the numerical results are satisfactory.