The Sabatier reaction combines carbon dioxide with hydrogen over a nickel (or ruthenium) catalyst to make synthetic methane and water: CO₂ + 4H₂ → CH₄ + 2H₂O. It is exothermic and strongly favours methane at moderate temperatures, but higher temperature accelerates the surface kinetics while simultaneously shifting the equilibrium back toward the reactants — so real methanation reactors run a "volcano" curve with a sweet spot rather than getting better forever.
CO2 + 4 H2 -> CH4 + 2 H2O ΔH ≈ -165 kJ/mol
rate(T) = kinetic(T) · equilibrium_shift(T) · catalyst_activity
- Gray spheres = CO₂, pale spheres = H₂ feed gas drifting into the reactor.
- Orange pellets = the fixed catalyst bed in the reactor's middle third, where conversion actually happens.
- Green spheres = CH₄ (synthetic natural gas), blue spheres = H₂O byproduct, both drifting out the far end toward pipeline injection.
- H₂:CO₂ feed ratio — the stoichiometric ideal is 4:1; starving the feed of H₂ (below 4) leaves CO₂ unconverted, while a large excess wastes hydrogen without helping conversion much.
- Temperature — too cold and the catalyst is sluggish; too hot and the equilibrium turns back toward CO₂ + H₂, which is why the reaction rate peaks in the middle of the slider rather than at either end.
- Flow rate — faster flow means less time in contact with the catalyst bed (lower residence time), which lowers conversion per pass even at ideal temperature.
- Catalyst activity — models a fresh (100%) vs. aged/poisoned (lower) catalyst bed; a degraded catalyst converts less gas per unit time regardless of temperature.
Real-world relevance: this is the core chemistry of "power-to-gas" — using surplus renewable electricity to make hydrogen, then combining it with captured CO₂ to produce a drop-in substitute for fossil natural gas that can be injected straight into the existing pipeline network.