Direct reduction replaces the blast furnace's carbon (coke) reductant with hydrogen gas:
Fe2O3(s) + 3 H2(g) → 2 Fe(s) + 3 H2O(g)
vs. the coke route:
2 Fe2O3(s) + 3 C(s) → 4 Fe(s) + 3 CO2(g)
Each pellet is modelled with the classic shrinking-core kinetics used for gas–solid reduction: an unreacted oxide core of radius rc shrinks inward inside a fixed pellet radius R as the reaction front advances. For a chemical-reaction-controlled regime:
1 − (1 − X) = r_c / R (core fraction f = r_c/R)
df/dt = −k(T) · s (interface recession rate)
k(T) = A · exp(−Ea / R_gas·T) (Arrhenius rate law)
X = 1 − f³ (metallization degree)
where s is the H₂-excess rate multiplier below. Raising temperature increases k(T) exponentially (Arrhenius); raising the H₂ excess ratio raises the hydrogen partial pressure at the pellet surface, which speeds the interfacial reaction with diminishing returns (saturation); raising descent speed shortens the residence time each pellet spends in the reduction zone, so it exits less metallized. The rate constants here are fitted for a demo timescale of seconds — real shaft-furnace residence times are several hours.
- Shell (rust-orange) — remaining Fe2O3/Fe3O4 oxide.
- Core (grey, metallic) — reduced metallic iron; shrinks as X → 1.
- CO₂ bars — the blast-furnace bar is the fixed literature baseline (~1.8 t CO2 per tonne of steel, BF-BOF route). The H2-DRI bar is mostly indirect — the electricity used to make hydrogen and run the electric-arc furnace — and rises with furnace temperature because more heating energy is drawn from the grid.