Source-term modeling of radioactive krypton and xenon in activated carbon delay beds for molten salt reactor off-gas systems

Radioactive krypton (Kr) and xenon (Xe) continuously released from liquid-fueled molten salt reactors are transported to the cover-gas and off-gas treatment systems, where activated carbon delay beds play an important role in source-term control. This study develops a transient modeling framework for Kr/Xe transport, retention, decay, and activity evolution in activated carbon delay beds. The one-dimensional model couples axial convection, axial dispersion, linear driving force adsorption, Henry-equilibrium adsorption, and radioactive decay. The formulation is extended to multi-nuclide decay chains, allowing gaseous daughters to continue transport and adsorption while treating non-gaseous daughters as locally deposited products. Reactor-condition-dependent inlet source terms are provided through one-way coupling with MACT-based multi-node source-term calculations, including upstream holdup and pre-bed decay. The numerical implementation is verified against an analytical solution under the local-equilibrium limit and using the Method of Manufactured Solutions (MMS) for finite-rate Henry–LDF coupling, while the adsorption model is evaluated against dilute Kr fixed-bed breakthrough data. A reference case inspired by the Molten Salt Reactor Experiment (MSRE) is then analyzed to examine isotope-dependent penetration, parent-decay feeding, phase-resolved activity distribution, nuclide-wise activity contributions, and shutdown residual activity. The results show strong isotope-dependent attenuation: Kr-85m falls below 10 −3 of its inlet concentration at x/L ≈ 0.224, whereas Kr-85 penetrates the full bed and Xe-131m remains measurable at the outlet. Parent decay can noticeably enhance daughter concentrations; for the Kr-85m→Kr-85 chain, in-bed feeding increases the maximum normalized Kr-85 concentration to approximately 2.3. At 180 d, the adsorbed and deposited inventories account for approximately 99.6% of the bed-integrated activity, while the gas phase accounts for only 0.38%. Following shutdown, continued helium purge reduces the gas-phase inventory to 10.8% of its shutdown value at 0.83 d, whereas the total residual activity decreases more slowly, reaching 0.7% of its shutdown value at 30 d.