Feedstock (volatile solids, VS) enters an anaerobic digester where microbes break it down into biogas — a mix of methane (CH₄) and CO₂. How much methane a given tonne of feedstock ultimately yields, and how fast, follows first-order Biochemical Methane Potential (BMP) kinetics: yield rises quickly at first then flattens as the readily-digestible fraction is used up. Temperature sets both the rate constant k and the ultimate yield B₀ — a thermophilic digester (55°C) digests faster than a mesophilic one (35°C) but needs tighter control. The biogas is burned in a combined heat and power (CHP) engine: its chemical energy, released by combustion, splits into electrical output (generator) and recoverable heat (engine/exhaust jacket), the rest lost. Overall biomass-to-electricity efficiency is the product of digestion yield, CH₄ energy content and CHP electrical efficiency.
Y(HRT) = B0 · (1 − e^(−k·HRT)) [Nm³ CH4 / kg VS]
Q_CH4 = feed(t VS/day)·1000·Y [Nm³ CH4/day]
P_biogas = Q_CH4 · LHV_CH4 / 86.4 [kW], LHV_CH4 = 35.8 MJ/Nm³
P_elec = P_biogas · η_elec
P_heat = P_biogas · η_thermal (η_elec + η_thermal ≈ 0.85, CHP)
η_overall = P_elec / (feed · E_VS), E_VS ≈ 17 MJ/kg VS
- Temperature (meso/thermo) — sets rate constant k and ultimate yield B₀ from the BMP curve; thermophilic reaches a given yield in fewer days but plateaus at a similar ceiling.
- Retention time (HRT) — how many days feedstock spends in the digester; short HRT leaves methane potential undigested, long HRT wastes tank volume once the curve has flattened.
- Feedstock loading — tonnes of volatile solids fed per day; scales biogas flow directly but must stay under the digester's organic loading limit to avoid souring.
- CHP electrical efficiency — how much of the biogas's combustion energy the engine-generator converts to electricity versus recoverable heat; typical reciprocating CHP units run 30–42% electrical.
Real-world relevance: this is the same chain a farm-scale or municipal biogas plant runs — BMP tests set the digester's design yield, retention time is the main lever operators have once it's built, and the electrical/heat split from the CHP engine is what determines whether the plant pays for itself.