Solving Advection Problems with Isotopic Evolution with SCALE/ORIGEN

Depletion modeling of advanced reactors with liquid fuel, such as molten salt reactors (MSRs), is complicated by the flowing fuel. Activation and decay of nuclides in the liquid fuel depend on the fluid position, which changes continuously with time. Furthermore, addition and removal of chemical species through processes such as off-gassing, plating, and fueling introduce spatially dependent factors. The general mathematical model for a nuclide n in this type of system is an advection-reaction-decay partial differential equation (PDE), dn/dt = -λn(x, t) - v dn/dx + f, where λ is a decay term, v is the speed attached to the advection term, and f is a reaction term. In actuality, the decay term contains decay physics and reaction physics, but the proportionality to n defines the type of PDE. This paper presents a methodology for solving an advection-reaction-decay system in which solutions are sought along streamlines throughout the flowing fuel system. The solution can provide insight into important operating metrics such as delayed neutron precursor drift and spatially dependent isotope inventory. Although this solution mechanism could prove too computationally intensive for production tools to simulate long-term MSR operations, it can provide benchmark quality solutions for code verification and analysis insights for safeguards and source term applications.