Kinetic Modeling of Solid-State CaSO4 Carbothermic Reduction via Discrete Particle Size Distribution Dynamics

Abstract This study introduces a comprehensive, multiscale kinetic modeling framework bridging global macroscopic reactor performance with discrete, particle-level evolution. By integrating a discrete particle size distribution (PSD) via a modified Sasaki discretization, the model enables high-fidelity estimation of regional conversion, porosity, and morphological topology, often obscured by conventional lumped kinetics. Validated against a complex solid-state carbothermic reduction of CaSO4, the framework demonstrates robust predictive accuracy for global conversion (r2 > 0.95), specific surface area (r2 > 0.91), and PSD (r2 > 0.90). Decoupling CaSO4 conversion from carbon consumption prevents overparameterization while accurately resolving dominant mass fraction morphology. Incorporating roughness-induced nucleation and stress-induced core fragmentation, the model reveals that high-rugosity particles bypass internal fluid transport bottlenecks, achieving high conversion without energy-intensive mechanical compaction. Ultimately, capturing this dynamic structural reorganization establishes a rigorous mechanistic link between microscale morphology and macroscopic reactor performance.