Biogas Engineering & Anaerobic Co-Digestion, Buswell-Mueller (1952) & Boyle Stoichiometry
Buswell Anaerobic Biomethane Potential (BMP) Formula
Calculate Empirical Substrate Molar Mass (g/mol), Stoichiometric Dry Biogas Methane Share (%), Theoretical Biomethane Potential BMP (Nm³ CH4/kg VS), and Practical Yield (Nm³/t VS).
Co-digesting grease-trap lipids (C57H104O6) instead of starch/glucose (C6H12O6) nearly TRIPLES Buswell methane yield from 0.373 to 1.013 Nm³/kg VS while enriching biogas from 50% to 70.2% CH4!
**Arthur M. Buswell & H.F. Mueller (`1952`) and William C. Boyle (`1976`)** balanced anaerobic methanogenesis of any organic volatile-solids formula **`C_c H_h O_o N_n`** (`Molar Mass M = 12.011*c + 1.008*h + 15.999*o + 14.007*n` g/mol) with water into **`CH_4 + CO_2 + NH_3`**: every mole of substrate yields **`n_{CH4} = (c / 2) + (h / 8) - (o / 4) - (3 * n / 8)`** moles of methane alongside `n_{CO2} = c - n_{CH4}` moles of carbon dioxide! Because `n_{CH4} + n_{CO2} = c` exactly, **Dry Biogas Methane Concentration equals `(n_{CH4} / c) * 100%`**, **Theoretical Biomethane Potential (`STP` `22.414` L/mol) equals `BMP_{th} = (n_{CH4} * 22.414) / M`** (`Nm³ CH_4 / kg VS`), and applying **Anaerobic Biodegradability Fraction `f_D` (`%`, deducting recalcitrant lignin + `~5%–8%` biomass synthesis)** gives **Practical Digester Yield `Y_{CH4} = BMP_{th} * 1,000 * (f_D / 100)`** (`Nm³ CH_4 / t VS`)!
Verify on Carbohydrate/Starch Feedstock (`C_6 H_{12} O_6`) in a Mesophilic Digester—Carbon `c` = 6 (B2), Hydrogen `h` = 12 (B3), Oxygen `o` = 6 (B4), Nitrogen `n` = 0 (B5), and Volatile-Solids_Biodegradability `f_D` = 82.0% (B6): Formula Molar Mass equals `180.16` g/mol (E2), Stoichiometric Biogas Methane Share equals **`50.0%` `CH_4`** (`50%` `CO_2`! E3), Theoretical `BMP_{th}` equals **`0.373` Nm³/kg VS** (E4), and Practical Methane Yield equals **`306.1` Nm³ `CH_4`/t VS** (E5)!
| Buswell-Boyle Anaerobic Stoichiometry KPI (STP 22.414 L/mol) | Formula | Verified Output |
|---|---|---|
| Empirical Molar Mass M (g/mol) | 12.011*c + 1.008*h + 15.999*o + 14.007*n | 180.16 g/mol glucose (885.45 triolein) |
| Dry Biogas CH4 Concentration (%) | (((c/2) + (h/8) - (o/4) - (3*n/8)) / c) * 100 | 50.0% CH4 starch (70.2% CH4 lipid fat!) |
| Theoretical BMPth (Nm³ CH4/kg VS) | (Moles_CH4 * 22.414) / Molar_Mass_g_mol | 0.373 Nm³/kg VS (1.013 Nm³/kg lipid!) |
| Practical Yield (Nm³ CH4/t VS) | Theoretical_BMP * 1000 * (Biodeg_fD_Pct / 100) | 306.1 Nm³/t VS (870.8 Nm³/t FOG boost!) |
Buswell-Mueller (1952) & Boyle C_c H_h O_o N_n Biomethane Stoichiometry Formula
Validate `Carbon c` in `[1, 200]`, `Hydrogen h` in `[1, 400]`, `Oxygen o` in `[0, 150]`, `Nitrogen n` in `[0, 50]` (`with positive n_{CH4} in (0.05 * c, c)`), and `Biodegradability f_D` in `[10, 98]`%!
=LET(cc_a, B2, hh_a, B3, oo_a, B4, nn_a, B5, fd_p, B6, mm_g, 12.011 * cc_a + 1.008 * hh_a + 15.999 * oo_a + 14.007 * nn_a, nc_m, (cc_a / 2) + (hh_a / 8) - (oo_a / 4) - (3 * nn_a / 8), bm_p, (nc_m * 22.414) / mm_g, IF(OR(cc_a < 1, cc_a > 200, hh_a < 1, hh_a > 400, oo_a < 0, oo_a > 150, nn_a < 0, nn_a > 50, nc_m <= 0.05 * cc_a, nc_m >= cc_a, fd_p < 10, fd_p > 98), "Invalid Buswell Input", ROUND(bm_p * 1000 * (fd_p / 100), 1)))Food-Waste Grease/Lipid Triolein Co-Digestion (`C_57 H_104 O_6`, `f_D = 86%`) CHP Surge Check
Dose `C_{57} H_{104} O_6` triglyceride fat (`B2 = 57`, `B3 = 104`, `B4 = 6`, `B5 = 0`, `B6 = 86%`): Highly reduced hydrocarbon chains push Biogas Quality E3 to **`70.2%` `CH_4`** and Theoretical `BMP_{th}` E4 to **`1.013` Nm³/kg VS**, nearly **tripling Practical Yield E5 to `870.8` Nm³ `CH_4`/t VS** (warning operators to ramp FOG slowly so long-chain fatty acids never foam or inhibit acetoclastic methanogens)!
=IF(ISTEXT(E5), E5, LET(mm_g, 12.011 * B2 + 1.008 * B3 + 15.999 * B4 + 14.007 * B5, nc_m, (B2 / 2) + (B3 / 8) - (B4 / 4) - (3 * B5 / 8), ROUND((nc_m * 22.414) / mm_g, 3)))Try the example
Use the original values or change them to test your understanding.