Bioenergy, Anaerobic Digestion & Wastewater Resource Recovery
Anaerobic Digester VS Destruction, Biogas & CHP kWe Formula
Calculate Mesophilic Anaerobic Digester Destroyed Volatile Solids (kg/d), Raw Biogas Production (Nm³/d), Pure Biomethane Yield (Nm³/d), and Continuous Cogeneration CHP Power (kWe).
Multiply biogas yield by DESTROYED volatile solids—not influent total solids—and separate CH4 from CO2!
Mesophilic (35°C–38°C) anaerobic digesters convert thickened primary and waste-activated sludge into renewable biogas (~60%–65% CH4, ~35%–40% CO2). Two unit errors inflate biogas CHP feasibility models: first, applying Specific Biogas Yield (~0.85–1.00 Nm³/kg VS_destroyed) to Influent VS instead of Destroyed VS (VS_in * VS_Destruction_Efficiency); second, multiplying raw biogas volume directly by pure methane’s Lower Heating Value (~10.0 kWh/Nm³ CH4) without multiplying by Methane Volume Fraction (~0.65)! Dividing daily fuel energy (CH4_Nm3_d * 10.0 kWh/Nm³) by 24 hours and multiplying by Jenbacher/gas-engine electrical efficiency (~40%) gives continuous kWe.
Verify on a Municipal Mesophilic Digester—Influent_Volatile_Solids = 8,000 kg/d (B2), VS_Destruction_Efficiency = 0.55 (55.0%, B3 -> Destroyed VS = 4,400.00 kg/d in E2), Specific_Biogas_Yield = 0.90 Nm³/kg VSd (B4 -> Raw Biogas = 3,960.00 Nm³/d in E3), Methane_Vol_Fraction = 0.65 (65.0%, B5 -> Pure CH4 = 2,574.00 Nm³/d in E4), and CHP_Electrical_Efficiency = 0.40 at 10.0 kWh/Nm³ CH4 LHV (B6): Continuous Cogeneration Electrical Output equals (2,574 * 10.0 / 24) * 0.40 = 429.00 kWe (E5)!
| Anaerobic Digester & CHP KPI (8,000 kg VS/d, 55% Destr, 0.90 Nm³/kg, 65% CH4) | Formula | Verified Output |
|---|---|---|
| Destroyed Volatile Solids (kg/d) | Influent_VS_kg_d * VS_Destruction_Eff | 4,400.00 kg/d (6,000 @ Co-Digest) |
| Raw Biogas Production (Nm³/d) | Destroyed_VS_kg_d * Biogas_Yield_Nm3_kg | 3,960.00 Nm³/d (5,400 @ Co-Digest) |
| Pure Biomethane Flow (Nm³/d) | Raw_Biogas_Nm3_d * Methane_Fraction | 2,574.00 Nm³/d (3,510 @ Co-Digest) |
| Continuous CHP Power (kWe) | (Biomethane_Nm3_d * 10.0 / 24) * CHP_Eff | 429.00 kWe (585.00 @ Co-Digest) |
Biogas Mass-Balance & Continuous CHP Electrical Power Formula
Validate Influent_VS > 0, VS_Destruction in (0.10, 0.90], Biogas_Yield in (0.30, 1.50], Methane_Frac in (0.40, 0.80], and CHP_Eff in (0.20, 0.55]!
=LET(vs_i, B2, ds_e, B3, bg_y, B4, ch_f, B5, el_e, B6, IF(OR(vs_i <= 0, ds_e <= 0.1, ds_e > 0.9, bg_y <= 0.3, bg_y > 1.5, ch_f <= 0.4, ch_f > 0.8, el_e <= 0.2, el_e > 0.55), "Invalid Digester Input", LET(vs_d, vs_i * ds_e, ch_m, vs_d * bg_y * ch_f, ROUND((ch_m * 10 / 24) * el_e, 2))))High-Strength Food-Waste Co-Digestion Lift Check (10,000 kg VS/d @ 60% Destruction)
Add high-strength food/FOG co-digestion waste lifting Influent_VS B2 to 10,000 kg/d and VS_Destruction B3 to 0.60: Destroyed VS E2 rises to 6,000.00 kg/d, Biomethane E4 reaches 3,510.00 Nm³/d, and Continuous CHP Power E5 jumps by +156 kWe to 585.00 kWe!
=IF(ISTEXT(E5), E5, ROUND(B2 * B3 * B4 * B5, 2))Try the example
Use the original values or change them to test your understanding.