Anaerobic microbes break down biodegradable volatile solids (VS) in an oxygen-free tank, releasing biogas — a mix of methane (CH₄) and CO₂. The reactor is modelled as a continuously-stirred tank with first-order degradation kinetics whose rate depends on temperature, since each microbial community (mesophilic ~37°C, thermophilic ~55°C) has a narrow thermal optimum.
dS/dt = F − k(T)·S
k(T) = k_max · exp( −(T − T_opt)² / (2w²) )
Q_biogas = k(T)·S·Y (Y ≈ 0.35 m³/kg VS destroyed)
P_elec = Q_biogas·x_CH4·9.94 kWh/m³ · η_gen / 24
- Temperature shifts the reaction rate k(T) along a Gaussian bell around the microbial optimum — too cold or too hot and digestion stalls.
- Feed Rate sets the daily input F of fresh volatile solids into the substrate pool S.
- Reactor Volume scales tank capacity and the hydraulic retention time HRT = V·ρ/F.
- Mesophilic / Thermophilic switches the target community, moving T_opt and the maximum rate k_max (thermophilic digesters run faster but need more heating).
Rising bubbles carry biogas up through the substrate to a gas dome that feeds a combined-heat-and-power (CHP) unit, whose flame size tracks the instantaneous electrical power output — the same principle behind farm and landfill biogas plants supplying the grid today.