Two coupled reactions run in a spacecraft's oxygen-recovery loop. Water electrolysis makes breathing O₂ (and byproduct H₂) from Faraday's law; the Sabatier reactor then reacts that H₂ with the crew's exhaled CO₂ to recover water, closing part of the loop:
Electrolysis: 2H₂O → 2H₂ + O₂ ṅ(H₂) = I / (2F)
Sabatier: CO₂ + 4H₂ → CH₄ + 2H₂O (ideal ratio H₂:CO₂ = 4:1)
Conversion η(T) ≈ exp(-(T-350°C)² / (2·70²)) × (1 - degradation)
Whichever reagent is scarcer limits conversion. Too little H₂ (current too low) leaves CO₂ unscrubbed; too much H₂ leaves it unreacted — both vent overboard as wasted mass. Reactor temperature away from ≈350 °C, or an aged catalyst, drops the conversion efficiency η even at the perfect 4:1 ratio.
Note on the 50% ceiling: the O₂ made by electrolysis leaves the loop permanently as breathing gas, so even at a perfect 4:1 ratio and η=1 the Sabatier reactor can only return water for the fraction of electrolysis water that was split to make the H₂ it actually consumes — at most half of what electrolysis used. This diagram's "loop well-optimized" verdict is calibrated to that real 50% ceiling (the original 3D version compared closure against an 85% threshold that this mass balance can never reach — fixed here after checking the numbers with a standalone script).
- Crew size — sets the fixed CO₂ production load (≈1.04 kg/person/day).
- Electrolysis current — sets H₂ (and O₂) supply via Faraday's law.
- Reactor temperature / catalyst degradation — set the Sabatier conversion efficiency η.
- Goal — maximize water loop closure and minimize vented mass by matching current to 4× the crew's CO₂ molar rate at the reactor's best operating temperature.
This is the real chemistry behind ISS's OGA + Sabatier assembly and every closed-loop deep-space ECLSS design study. Drag inside the flow diagram to pan, scroll to zoom.