System-level modeling of a lead–bismuth-cooled reactor coupled with a supercritical carbon dioxide (S-CO₂) recompression Brayton cycle requires consistent treatment of working-fluid thermophysical properties, inter-loop heat transfer, hydraulic behavior, and turbomachinery dynamics. In this study, RELAP5 is extended to establish an integrated system model that includes the reactor core, the lead–bismuth eutectic (LBE) primary loop, a printed circuit heat exchanger (PCHE), the S-CO₂ recompression Brayton cycle, and the turbomachinery shaft dynamics. For LBE, a modified soft-sphere Helmholtz equation of state is adopted for thermodynamic closure, such that pressure, internal energy, entropy, and the associated response derivatives are derived consistently from a single thermodynamic potential. For CO₂, the specific Gibbs free energy is reconstructed using two-dimensional quintic Hermite interpolation, providing a common thermodynamic basis for evaluating state properties and the derivatives used in pressure–internal-energy inversion near the critical region. Turbines and compressors are represented using two-dimensional performance maps coupled with the shaft dynamic equations. Their pressure-rise or pressure-drop characteristics are incorporated into the RELAP5 hydraulic network as equivalent hydraulic source terms, allowing the operating points of the turbomachinery to evolve in response to changes in system pressure distribution and flow rate rather than being prescribed by fixed-flow boundary conditions. The extended code is assessed using an LBE natural-circulation benchmark and a transcritical CO₂ blowdown case. The predicted steady-state natural-circulation mass flow rate differs from the reference value by −3.67%, while the calculated pressure and temperature evolutions during CO₂ blowdown are consistent with the experimental and simulation trends. At 75 s, the cumulative mass residual is 0.0111% of the initial CO₂ inventory. On this basis, a 15 MW integrated lead–bismuth-cooled reactor–S-CO₂ recompression cycle model is established, with all key steady-state parameters deviating from their design values by less than 1%. Two controlled transients were analyzed, involving a 20% reduction in external load torque and an approximately 20% reduction in primary coolant flow. The resulting power, flow, pressure and temperature responses were examined under the specified control configurations. The developed RELAP5 extensions and coupled system model provide a basis for subsequent studies of system operation, control strategies, and accident transients.

lead-bismuth-cooled reactor,supercritical carbon dioxide Brayton cycle,RELAP5,system modeling,dynamic coupling