An anaerobic digester converts biodegradable feedstock into biogas (≈55–65% CH₄, rest mostly CO₂) through four microbial stages — hydrolysis, acidogenesis, acetogenesis, methanogenesis. The methanogens are the slowest and most temperature/pH-sensitive step, so they set the plant's real output.
Biogas rate (modified Gompertz):
B(t) = Bmax · exp{ -exp[ (Rm·e/Bmax)(λ-t) + 1 ] }
Methanogen activity factor f(T,pH):
f = fT(T) · fpH(pH), fT peaks ~37°C (meso) or ~55°C (thermo)
Electricity: P = Q_CH4 · LHV_CH4 · η_CHP
Q_CH4 = biogas flow × CH4 fraction, LHV_CH4 ≈ 9.97 kWh/m³, η_CHP ≈ 38%
- Loading rate — how much volatile-solids feedstock enters per m³ of digester per day. Push it too high relative to retention time and volatile fatty acids (VFAs) accumulate faster than methanogens can consume them, souring the tank.
- Temperature — mesophilic bacteria run best near 37°C, thermophilic near 55°C; drift more than a few degrees from the active regime's optimum and the activity factor collapses.
- Retention time (HRT) — how many days feedstock spends in the tank; too short and it exits before methanogens finish, too long wastes reactor volume.
- VFA/alkalinity ratio — the real-world stability gauge operators watch: above ~0.4 the digester is heading toward souring (falling pH, falling methane) even before gas output visibly drops.
Real-world relevance: this is the same lumped model — Gompertz kinetics plus a Monod-style temperature/pH activity factor — used to size farm and municipal biogas plants and combined-heat-and-power (CHP) generators that turn organic waste into dispatchable renewable electricity.