Shrinking-Core Ilmenite Reduction — Lunar Oxygen ISRU (2D)

Reactor Conditions

Reduction temperature 950 °C

H₂ partial pressure 0.50 atm

Ilmenite content of feed 10.0 wt%

Grain size (d₅₀) 60 µm

Batch Progress

rate-limiting: —

X = 0.0%X_eq ≈ 0%

Elapsed (batch time)

0.0 h

O₂ yield rate

0 g/h

Cumulative O₂ (100 kg regolith charge)

0.0 g

How it works

Every grain reacts as a shrinking core: an unreacted ilmenite (FeTiO₃) center shrinks as a shell of solid product (Fe + TiO₂) builds up around it, exactly the geometry chemical engineers use to model gas-solid reactions like this one. For a grain of radius R at local conversion ξ (0→1), the core radius is r_c = R·(1 − ξ)^⅓ — visualized directly below as the dark core inside each grain's product shell.

H₂ must cross 3 resistances in series to reach the core:
  1) gas film around the grain        (τ_film)
  2) diffusion through the product shell (τ_diff, grows as the shell thickens)
  3) surface reaction at the core       (τ_rxn)
dξ/dt = 1 / [τ_film + 2τ_diff·((1−ξ)^-⅓−1) + (τ_rxn/3)·(1−ξ)^-⅔]
τ ∝ ρ_B·R / (k·C_H2)  (τ_diff scales as R², the other two as R)
X = ξ · X_eq(T, P)     — same reversible-equilibrium ceiling as the bulk reactor

Temperature — raises both the surface rate constant and the shell diffusivity via independent Arrhenius laws, so hotter batches convert faster and reach a higher equilibrium ceiling.
H₂ pressure — raises the bulk H₂ concentration driving every resistance, and pushes X_eq up via Le Chatelier.
Grain size — because shell-diffusion resistance scales with R² while surface reaction scales with R, halving grain size shrinks diffusion-limited batches roughly 4×, not just 2× — a genuinely different scaling law from a single lumped rate constant.
Rate-limiting step — the pill above compares τ_film, τ_diff and τ_rxn for a mid-size grain live; for most realistic conditions here, the thickening product shell (diffusion) dominates once the core has shrunk substantially, even when surface reaction dominates early on.

The population below spans a log-normal spread of grain radii around the slider's d₅₀ (σ≈0.3 in ln R); the bulk conversion and O₂ readouts are the mass-weighted average of each grain's own, independently-integrated ξ(t) — not a single lumped bulk number. O₂ mass is stoichiometric: each mole of FeTiO₃ (151.7 g/mol) converted and electrolyzed yields ½ mole O₂ (32 g/mol).

Unreacted ilmenite core Product shell (Fe + TiO₂) H₂ diffusing to core