Question 3 of 5: Anaerobic Digestion of Swine Manure

Question 3: Anaerobic Digestion of Swine Manure (25 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given.

Find. Digester volume and dimensions; daily biogas production (volume and methane fraction); at least two common process upsets with mitigation.

Approach. Convert the dry-solids loading and slurry solids content into a slurry flow rate and size the digester volume from an assumed hydraulic retention time, then apply the Buswell stoichiometric equation to the given organic-fraction chemical formula to get the theoretical daily biogas volume and composition, and finally discuss common digester process upsets and their mitigation.

1. Slurry flow rate. Dry solids: $\dot m_{TS} = 10{,}000\ \text{pigs}\times1.0\ \text{kg/pig}\cdot\text{d} = 10{,}000\ \text{kg TS/d}$. At 5% solids content, $\dot m_{wet} = 10{,}000/0.05 = 200{,}000\ \text{kg/d}$, and at an assumed slurry density of 1,000 kg/m³, $$Q = \frac{200{,}000}{1{,}000} = \boxed{200\ \text{m}^3/\text{d}}$$
2. Digester volume and dimensions. With an assumed HRT of 20 days, $$V = Q\times\text{HRT} = 200\times20 = 4{,}000\ \text{m}^3$$ Split into two identical digesters, $V_{each}=2{,}000\ \text{m}^3$; at an assumed working depth of 6 m, plan area $A=2{,}000/6=333.3\ \text{m}^2$, giving $$D=\sqrt{\frac{4A}{\pi}} = \boxed{20.6\ \text{m}}$$ so the design is two cylindrical digesters, each 20.6 m diameter × 6 m working depth (2,000 m³ each).
3. Buswell equation for the given organic formula. For a substrate $C_nH_aO_bN_c$, the anaerobic (Buswell/Boyle) stoichiometric equation is $$C_nH_aO_bN_c + \left(n-\tfrac{a}{4}-\tfrac{b}{2}+\tfrac{3c}{4}\right)H_2O \rightarrow \left(\tfrac{n}{2}+\tfrac{a}{8}-\tfrac{b}{4}-\tfrac{3c}{8}\right)CH_4 + \left(\tfrac{n}{2}-\tfrac{a}{8}+\tfrac{b}{4}+\tfrac{3c}{8}\right)CO_2 + c\,NH_3$$ With $n=50,\ a=100,\ b=35,\ c=1$ (from C₅₀H₁₀₀O₃₅N), $$\text{mol CH}_4 = 25+12.5-8.75-0.375=\boxed{28.375},\qquad \text{mol CO}_2 = 25-12.5+8.75+0.375=\boxed{21.625}$$ per mole of substrate consumed (plus 1 mol NH₃) — a methane fraction of $28.375/50=56.8\%$ by volume, consistent with typical biogas composition.
4. Daily biogas volume. The substrate's molar mass is $M=50(12)+100(1)+35(16)+1(14)=1{,}274\ \text{g/mol}$. Treating all 10,000 kg/d of dry solids as this compound, $$n_{substrate} = \frac{10{,}000{,}000\ \text{g/d}}{1{,}274\ \text{g/mol}} = 7{,}849\ \text{mol/d}$$ Since every mole of substrate yields $(28.375+21.625)=50$ mol of total biogas (one mole of gas per carbon atom), $$n_{biogas} = 50\times7{,}849 = 392{,}465\ \text{mol/d}$$ At 22.4 L/mol (STP), $$V_{biogas} = 392{,}465\times22.4\ \text{L/mol} = \boxed{8{,}791\ \text{m}^3/\text{d}}\quad(\text{56.8\% CH}_4 \approx 4{,}989\ \text{m}^3/\text{d CH}_4)$$ This is the theoretical maximum (100% conversion); real digesters typically destroy only 40–70% of the volatile solids fed, so field biogas would be correspondingly lower.
5. Common process upsets and mitigation. Organic/hydraulic overload (souring): feeding faster than the methanogen population can consume the resulting volatile fatty acids (VFAs) lets VFAs accumulate, dropping pH below the stable ~6.5–7.5 range and inhibiting methanogenesis further — a self-reinforcing "sour" digester. Mitigation: introduce feed-rate changes gradually, monitor the VFA-to-alkalinity ratio routinely, and add buffering capacity (lime or sodium bicarbonate) if the ratio trends upward. Ammonia toxicity: high-nitrogen substrates (such as this swine manure) can push free (un-ionized) ammonia to levels that inhibit methanogens, especially if pH or temperature rises. Mitigation: dilute or co-digest with a lower-nitrogen substrate to keep total ammonia-N in a safe range, and hold temperature and pH stable to limit the free-ammonia fraction. A third common upset, temperature shock from an abrupt cold feed slug or heating-system failure, is mitigated by an insulated, actively heated tank with gradual (not abrupt) feed introduction.