Models
Interactive models for exploring metallurgy, energy and decarbonization. Change the assumptions, compare scenarios and follow the reasoning.
I use all the models presented here in my teaching or research and have programmed them with the assistance of AI tools. If you find any errors or have suggestions for improvement, please email me at likejiang@ustb.edu.cn. All suggestions will be recognized in the acknowledgements.
Model directory
Choose a model to open its interactive workspace.
- Ironmaking Cost Parity Lab ↗Compare carbon- and hydrogen-based ironmaking costs within a shared thermodynamic benchmark.
- Ellingham Diagram ↗Explore how temperature changes standard-state formation energies across reaction families.
- Baur–Glässner Diagram ↗Explore iron-oxide phase equilibria as temperature and CO/CO₂ or H₂/H₂O composition change.
- Rd–C Diagram ↗Explore competing carbon constraints in a simplified blast-furnace teaching model.
- Pellet Reduction Kinetics Lab ↗Compare isothermal hydrogen-reduction curves from the Unreacted Shrinking Core Model and Grain Model.
Combustion heating
Electric heating
Ironmaking Cost Parity Lab
What combination of coal price, electricity price and carbon charge makes hydrogen ironmaking cost-competitive? Compare two routes within a shared material and enthalpy benchmark.
- Inputs
- Coal-equivalent, electricity and carbon prices; a common iron product state; energy assumptions and electricity emissions.
- Outputs
- Resource demand, heat and electricity requirements, model CO₂ emissions, input costs and conditional price-parity maps.
- Scope
- One tonne of pure iron from pure hematite. A thermodynamic benchmark before equipment, operating costs and a full engineering model.
Calculations run in your browser. Equations, references and downloadable results are included.
Standard Gibbs energy
on its stated molar basis
Ellingham Diagram
Explore temperature-dependent formation energies for oxides, carbides, nitrides, fluorides and chlorides. Select a reaction family or display all its curves; compare oxide formation with carbon, CO and hydrogen oxidation.
- Inputs
- Reaction family, temperature, displayed reactions and an optional oxide–reductant pair.
- Outputs
- Gibbs-energy curves, phase labels, selected-temperature values and downloadable chart data.
- Scope
- A teaching model built from referenced chart endpoints. Standard-state tendencies are distinct from gas-composition effects and process feasibility.
Compare actual CO/CO₂ or H₂/H₂O conditions in the Baur–Glässner model.
and oxide equilibrium
and oxide equilibrium
Baur–Glässner Diagram
See how temperature and reducing-gas composition determine the equilibrium tendency of iron-oxide reduction. Switch between CO and hydrogen atmospheres and inspect individual conditions.
- Inputs
- Temperature, CO/(CO + CO₂) or H₂/(H₂ + H₂O), and pressure for the optional carbon-equilibrium line.
- Outputs
- Phase boundaries, stable-phase estimates, gas thresholds and downloadable chart data.
- Scope
- Ideal gas mixtures and pure, nominal solid phases using the supplied course Gibbs functions. This is an internally consistent teaching approximation.
The model explains the low-temperature FeO limit and the difference between its data and real wüstite.
and the direct-reduction fraction
and hot-blast sensitivity
Rd–C Diagram for Blast Furnace
Explore how direct reduction, effective CO utilization and a heat-demand scenario change the carbon constraints in a simplified blast-furnace diagram. Follow a worked example and compare the original course curves.
- Inputs
- Direct-reduction fraction, FeO-stage CO utilization, heat-demand scenario and hot-blast temperature.
- Outputs
- Carbon constraint curves, conditional intersections and a lowest envelope value within the stated teaching equations.
- Scope
- One tonne of nominal hot metal using the supplied course equations. Coefficient assumptions and incomplete balance closure are explained; results do not predict a plant coke rate.
Includes an introduction, reading guide, equations and downloadable results.
Each model includes its assumptions, equations and references to help you interpret the results.
Pellet Reduction Kinetics Lab
Explore hydrogen reduction of hematite pellets with the Unreacted Shrinking Core Model and Grain Model. Compare reduction curves, experimental observations and idealized reaction structures.
- Inputs
- Temperature, reference case and model selection.
- Outputs
- Reduction degree, iron distribution among phases, characteristic times and downloadable results.
- Scope
- Pure hydrogen, isothermal, atmospheric pressure; source-code reference parameters with explicit model assumptions.
Calculations run in your browser. Experimental comparisons and schematic animations are identified separately.