A 60-Cow Biogas Plant That Stalls in Winter
A 60-cow crossbred dairy produces 12 kg of dung per cow per day at 16% total solids, of which 80% is volatile solids. The farm plans a fixed-dome biogas plant for 12 m³/day of cooking gas plus a 2 kW generator set consuming about 0.75 m³ of biogas per kWh. Biogas yield is 0.25 m³ per kg of volatile solids at 35°C, falling to about 40% of that at 18°C in an unheated digester. Slurry is diluted to 9% total solids for feeding; required retention is 30 days at 35°C and 60 days at 18°C. Winter slurry temperature is 15°C and the farmer proposes burning biogas in a water heater at 60% efficiency (biogas LHV 21 MJ/m³) to hold the digester at 35°C. Water has a specific heat of 4.18 kJ/kg·K.
1. Size the digester and daily gas production, and check the plant against the farm's demand.
Read the worked answer
Dung = 60 × 12 = 720 kg/day; TS = 0.16 × 720 = 115 kg/day; VS = 0.80 × 115 = 92 kg/day.
Gas at 35°C = 0.25 × 92 = 23 m³/day. This is close to published yields of about 0.04 m³ per kg of fresh dung (720 × 0.04 = 29), so the figure is in the right band.
Slurry at 9% TS: total mass = 115/0.09 = 1,280 kg/day, i.e. about 1.28 m³/day of feed.
Digester volume = 1.28 × 30 = 38.4 m³, design for 40 m³; dome gas storage of 25–30% of daily output, about 6–7 m³.
Demand = 12 m³ cooking + 2 kW × 5 h = 10 kWh × 0.75 = 7.5 m³ for the generator, total 19.5 m³/day against 23 m³ produced - only a 15% margin, which is thin once any digester upset occurs. The generator is a large share of demand for a small farm, and a fixed dome cannot deliver 7.5 m³ in a burst from 6–7 m³ of storage.
2. Assess the winter heating proposal quantitatively. Is burning biogas to heat the digester viable?
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At 18°C the yield falls to 0.40 × 23 ≈ 9 m³/day, less than half the 19.5 m³ demand - the plant effectively fails in winter.
Heating energy: 1,280 kg/day × 4.18 kJ/kg·K × (35 − 15) K = 107 MJ/day just to warm the feed. At 60% heater efficiency that needs 178 MJ, i.e. 178/21 ≈ 8.5 m³ of biogas per day - about 37% of the summer output and approaching all of the winter output. Add wall and roof losses from a 40 m³ uninsulated dome sunk in cold ground (easily another 30–60 MJ/day) and the heater consumes more gas than the plant makes in winter.
So the proposal is thermodynamically self-defeating: the digester is being asked to fund its own warming.
Viable alternatives, in order of cost-effectiveness: insulate the dome with a straw or earth cover and a windbreak; pre-warm feed with a solar water heater or heat exchanged from compost; accept operation at 25–28°C with roughly 50–60% yield and cut winter demand; and add a co-substrate such as poultry litter or food waste to lift gas yield per unit volume.
3. The farmer wants to run the 2 kW generator daily. Evaluate this use of the gas and recommend priorities.
Read the worked answer
2 kW × 5 h = 10 kWh, consuming 7.5 m³ of biogas. Energy in = 7.5 × 21 = 157 MJ = 43.8 kWh, so overall conversion efficiency = 10/43.8 ≈ 23%. That is plausible for a small spark-ignition biogas set, but it means three-quarters of a scarce fuel is discarded as heat.
Cooking gas is the highest-value use: it displaces LPG or firewood at near-100% utilisation, whereas the generator displaces grid electricity at 23% utilisation. On a plant with a 15% production margin, the generator is also the first load that should be cut.
Recommendation: priority order is (1) cooking 12 m³, (2) digester temperature stability and feed pre-warming within the insulated dome, (3) generator only when gas is in surplus, typically late summer when yield is high and cooking demand is unchanged. If continuous electricity is genuinely needed, size the plant for the co-substrate and digester volume that supports it - do not simply add the load to a plant already at its limit.