Mathematical formulation of mass transport kinetics for residual water within damaged spent fuel cladding during vacuum drying

The quantitative reduction and verification of residual water are fundamental prerequisites for ensuring the long-term structural integrity of spent nuclear fuel (SNF) dry storage systems. This study presents a novel, high-fidelity analytical heat-and-mass-transfer model designed to transcend empirical observations and provide a deterministic predictive framework for vacuum drying kinetics within damaged fuel cladding. By coupling the Hertz-Knudsen-Schrage phase transition kinetics with Knudsen-number-dependent pneumatic conductance, the framework successfully decouples the global mass depletion into three distinct temporal regimes: flashing-induced hydrodynamic liquid expulsion, quasi-steady interfacial evaporation, and capillary-limited asymptotic decay. The analytical formulation demonstrates a geometric choke effect in micro-scale defects ( D p ≤ 0.3 mm ). This effect forces an early transition from viscous to free-molecular flow. Furthermore, the model captures a counter-intuitive anomalous drying delay at elevated initial temperatures (80 °C) through a Richardson-number-based buoyancy stagnation modifier. Long-term state-space evaluations incorporating the Kelvin equation reveal that complete dehydration is thermodynamically restricted, converging to an asymptotic retention plateau of approximately 0.15 g due to microscopic capillary forces ( r cap = 1.5 μ ). The integrated numerical framework demonstrates exceptional accuracy, maintaining a depressurization RMSE below 5 kPa and global mass prediction errors strictly within a ± 10 % band, thereby offering a robust theoretical foundation for optimizing industrial SNF drying protocols.