Physics-Constrained Constitutive Learning of Rate-Limiting Timescales for Efficient Hydrogen-Based Direct Reduction for Green Steel Making.

Hydrogen-based direct-reduction enables carbon-neutral primary ironmaking, yet widespread industrial adoption is constrained by sluggish late-stage kinetics, which lower production efficiency and increase energy and hydrogen consumption. Here, we develop a conversion-resolved constitutive framework that infers effective reaction and transport timescales directly from measured reduction trajectories and maps their constitutive dependence on operating conditions, pellet architecture, and composition. The scientifically constrained additive model (SCAM) framework is then used to convert these trajectory-inferred timescales into interpretable constitutive maps, symbolic laws, and regime boundaries across variations in processing conditions and pellet microstructure/composition. We find that internal diffusion accounts for most of the incremental reduction time at intermediate to high conversion percentages, and the reaction-to-diffusion control boundary shifts systematically with conversion progression and evolving porous microstructure. Temperature and hydrogen partial pressure mainly accelerate early-stage conversion rates, whereas the late-stage conversion rates are governed by the pellet-to-pore length scale, average porosity, and tortuosity. Pellet composition primarily affects the late-stage diffusion-controlled regime through its influence on pore-morphology descriptors, while a residual effect persists in the reaction-controlled regime. The resulting regime maps and symbolic laws yield experimentally anchored pellet-scale constitutive relations to identify reduction-stage-specific rate-limitations and guide industrial pellet design, thereby providing actionable guidelines for more efficient green steelmaking.