Dynamically simulating the fuel cycle in a fusion reactor is crucial to developing a better understanding of the safe and reliable operation of this complex system. In this work, we propose a tritium processing system for ITER'S plasma exhaust. The dynamic simulation of this proposed system is then performed with the TRUFFLES (TRitiUm Fusion Fuel cycLE dynamic Simulation) model. The fuel management, storage, and fueling operations are developed and coupled with previous cryopump and fuel cleanup unit subsystems to fully realize the complete torus exhaust flow cycle. Results show that tritium inventories will vary widely depending upon reactor operation, individual subsystem and unit operation designs. A diverse collection of batch-controlled subsystems with changes in their processing parameters are simulated in this work. In particular, the effects from the fuel management subsystem's fuel reserve and tank switching times are quantified using sensitivity studies.