Pellet Reduction
Kinetics Lab
One pellet. Two model descriptions.
Explore how hydrogen reduction evolves over time.
A transparent model comparison. Curves use the supplied source-code parameter sets; they have not been refitted here. Experimental points provide a comparison, not a claim of general predictive validity. Explore the assumptions and parameter provenance below.
Reduction over time
Reduction degree is the fraction of removable oxygen removed, on a hematite-to-iron basis.
- 50% reduction
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- 90% reduction
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- 50% reduction
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- 90% reduction
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From oxide to iron
for both models
Three shrinking interfaces
Ideal concentric reaction fronts
Idealized cross-section of a spherical pellet, reconstructed from the three interface conversions. Radii follow rᵢ/rₚ = (1 − Xᵢ)⅓; the pellet radius remains constant. Colored areas are geometric cross-sections, not phase-fraction areas.
Many grains, one pellet
Schematic grain representation
Schematic only. Identical grain glyphs depict the bulk iron allocation. Their placement and dimensions are illustrative; this model does not calculate a radial phase or gas-concentration field.
Phase shares are normalized to iron atoms, not oxide mass or solid volume. FeO is the nominal wüstite phase used by this model.
Two idealizations,
shared physical limits.
The USCM separates the pellet into idealized product layers. The grain model represents reaction in constituent grains through additive reaction-time expressions. Both use three sequential reduction steps.
A closer match to a reduction curve does not by itself establish the correct internal mechanism. Heat transfer, cracking, swelling and independent evolution of the pore network can matter in real pellets and are outside this first comparison. The transport calculation does include phase-specific porosities derived from the source model.
Numerical diagnostics will be shown after a calculation.
Behind the curves
Model scope and assumptions
- A spherical hematite pellet at a prescribed, uniform temperature and pressure.
- Pure H₂ in the bulk feed; the equilibrium and transport treatment includes H₂/H₂O.
- Three sequential steps: hematite → magnetite → nominal wüstite → iron.
- Equilibrium-corrected interfacial kinetics under reducing conditions, with quasi-steady transport assumptions. This implementation permits reduction only.
- Fixed external pellet size and source-preset structural parameters, with derived phase-specific porosities; no explicit heat balance, cracking, swelling or independently evolving pore network.
- The selected 973–1173 K cases are above the approximate 843 K lower stability limit of wüstite. No low-temperature two-step formulation is offered here.
Source-script conditions. This demonstration retains the supplied model geometry, flow, porosity and density values; these settings have not been independently verified against the Methods of Zakeri et al. (2025). The displayed cases cover approximately 700–900 °C (973–1173 K), while the published experiments cover 700–1000 °C. The value 0.26 is the source transport porosity. Bulk and grain densities are separate source inputs and are not derived from that porosity.
Results describe these stated idealizations and parameter sets. They are not a plant design calculation or a guarantee of reduction performance for a different pellet.
Conversion, interfaces and phase accounting
For each sequential reaction, Xᵢ is the fraction of the pellet iron inventory that has completed that step.
fFeO = X₂ − X₃ · fFe = X₃
Physically ordered conversions satisfy 0 ≤ X₃ ≤ X₂ ≤ X₁ ≤ 1, with phase fractions summing to one. Time-to-reduction values are interpolated from the computed trajectory; “not reached” means the target was not reached within the simulated time window.
USCM couples interfacial reaction, product-layer diffusion and external gas-film transport. The grain-model implementation uses source-specific characteristic times and an additive-time formulation. Their separate kinetic parameters must not be interpreted as interchangeable intrinsic constants.
Source parameters and experimental comparison
Parameter provenance will appear after the source data loads.
The first public version retains the reference parameter sets from the supplied scripts. It does not run an optimizer or infer new parameters from a visitor’s choices.
Numerical method and reproducibility
The calculation runs in an isolated browser worker. This keeps the controls responsive; cancelling a run terminates that worker. Source-preset parameters, calculated samples and diagnostics are included in the JSON model record.
Numerical verification. Across 24 cross-implementation cases, the maximum absolute difference in reduction degree was below 2.5 × 10−7. This checks numerical agreement between implementations; it does not establish experimental validation. Download the scientific verification report.
Download scientific notes · Download the web-edition source ZIP
CSV exports use seconds for time, kelvin for temperature and fractions from 0 to 1 for conversion and iron allocation. The displayed diagrams and plots derive from the same computed time series.
References and data sources
- Loading the source bibliography…
Experimental values are transcribed source data supplied with the research scripts. Consult the original publication for experimental methods and the meaning of the reported measurements.