A space habitat can't dump food scraps and inedible biomass overboard forever — an anaerobic digester lets methanogenic bacteria break that organic waste down into methane-rich biogas (usable as fuel or feedstock for a Sabatier-style reactor) plus a stabilized digestate. The whole process is first-order microbial kinetics, exactly as it runs on Earth:
Degradable-VS destroyed fraction: B(T,HRT) = B_max · (1 - e^(-k(T)·HRT))
Arrhenius rate constant: k(T) = k₁ · exp[ -(E_a/R) · (1/T_K - 1/T_K,ref) ]
CH4 yield (Buswell-scale): V_CH4 = Y_CH4 · VS_destroyed (0.35 L CH4 / g VS)
Energy content: E = V_CH4[m³] · 9.94 kWh/m³
- Feed rate — kilograms of crew organic waste (food scraps, inedible biomass, paper) fed per day; sets the volatile-solids (VS) load the microbes have to work through.
- Temperature — plugs into the Arrhenius rate law (E_a ≈ 65 kJ/mol, a typical activation energy for anaerobic digestion) relative to a 35°C mesophilic reference. Rate roughly doubles every 10°C up to the thermophilic band (≈55°C), then drops off sharply as the culture destabilizes above ≈58°C.
- Retention time (HRT) — how many days waste spends in the tank before it's replaced; longer HRT lets the first-order decay 1−e^(−kt) get closer to the maximum degradable fraction, with diminishing returns.
- C:N ratio — carbon-to-nitrogen ratio of the feedstock. Methanogens run best near 25:1; too low (nitrogen-rich, e.g. mostly food waste) risks ammonia toxicity, too high (carbon-rich, e.g. mostly paper) starves them of nitrogen — modelled here as a Gaussian penalty centred on 25:1.
Real-world relevance: this is the same microbial kinetics that runs municipal and agricultural anaerobic digesters on Earth, proposed for closing the waste loop on long-duration missions — recovered methane can fuel a stove or fuel cell, or feed a Sabatier reactor's carbon stream, instead of the organic fraction being dead mass a crew has to carry home.