A crewed cabin's trace contaminant control system (TCCS) pulls cabin air through a physical/chemisorbent charcoal bed (captures higher-molecular-weight VOCs and ammonia) then a high-temperature catalytic oxidizer (destroys light gases like CO, H₂ and CH₄ by burning them to CO₂ and H₂O). The cabin is a well-mixed lumped volume:
dC/dt = G/V − (Q/V)·C·ε(t)
ε(t) = 1 − (1−η_ads)·(1−η_ox) (two beds in series)
The charcoal bed loads like a Langmuir trap and its adsorption efficiency falls as it saturates:
η_ads(t) = η_max·(1 − M/M_cap)
dM/dt = Q·C·η_max·(1 − M/M_cap)
The catalytic oxidizer's conversion follows Arrhenius kinetics — hotter runs faster, but more airflow means less time in the bed to react:
k(T) = A·exp(−Ea / (R·T)) [T in kelvin]
τ = V_ox / Q (residence time)
η_ox = 1 − exp(−k(T)·τ)
- Crew size — scales the VOC generation rate G (off-gassing + metabolic trace gases).
- Airflow Q — more flow dilutes the cabin faster but shortens oxidizer residence time τ, so conversion efficiency drops even as more air is processed.
- Oxidizer temperature — raises the Arrhenius rate constant k(T), pushing η_ox toward 1.
- Regenerate bed — desorbs the charcoal canister to vacuum, resetting loaded mass M to zero, exactly like the periodic thermal-vacuum regeneration cycle used on real ECLSS charcoal beds.
Real-world relevance: this is the same two-stage architecture (sorbent bed + catalytic oxidizer) NASA's TCCS uses on the ISS to keep formaldehyde, ammonia and other off-gassed trace contaminants below Spacecraft Maximum Allowable Concentration (SMAC) limits. This 2D view drives the identical mass-balance ODE as the 3D version — same Langmuir bed loading, same Arrhenius oxidation — but renders it as a schematic loop plus a live concentration-vs-time strip chart so breakthrough is easy to read at a glance.