Question 2 of 5: Anaerobic Digestion of Swine Manure

Question 2: 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. The design data supplied by the question are collected below; every additional figure needed to size a real digester (hydraulic retention time, volatile-solids destruction, biogas yield, methane fraction, influent temperature, insulation performance, and CHP waste-heat recovery) is not stated in the exam and is fixed here as a stated engineering assumption, each flagged in the callout below.

Find. Digester volume and dimensions; daily biogas production; digester heating requirement; whether recovered engine waste heat covers that requirement.

Approach. Convert the given dry-solids loading and slurry solids content into a slurry flow rate, size the digester volume from an assumed hydraulic retention time, estimate biogas production from an assumed volatile-solids destruction and yield, compute the sensible-heating and tank-conduction heat loads to hold 35 °C, and finally compare recoverable engine waste heat against that heating requirement.

1. Slurry flow rate. Dry solids: $\dot{m}_{TS} = 10{,}000 \text{ pigs} \times 1.0\ \text{kg/pig}\cdot\text{d} = 10{,}000\ \text{kg TS/d}$. At 5% solids content, the wet slurry mass flow is $\dot{m}_{wet} = \dot{m}_{TS}/0.05 = 200{,}000\ \text{kg/d}$, and at an assumed slurry density of 1,000 kg/m³, $$Q = \frac{200{,}000\ \text{kg/d}}{1{,}000\ \text{kg/m}^3} = \boxed{200\ \text{m}^3/\text{d}}$$
2. Digester volume and dimensions. With an assumed HRT of 20 days for mesophilic complete-mix digestion, $$V = Q \times \text{HRT} = 200\ \text{m}^3/\text{d} \times 20\ \text{d} = 4{,}000\ \text{m}^3$$ Splitting this into two identical digesters for operational redundancy gives $V_{each}=2{,}000\ \text{m}^3$. At an assumed working depth of 6 m, each digester's plan area is $A = V_{each}/h = 2{,}000/6 = 333.3\ \text{m}^2$, giving a circular tank diameter $$D = \sqrt{\frac{4A}{\pi}} = \sqrt{\frac{4(333.3)}{\pi}} = \boxed{20.6\ \text{m}}$$ so the design is two cylindrical digesters, each 20.6 m diameter × 6 m working depth (2,000 m³).
3. Daily biogas production. Assuming volatile solids are 80% of total solids for swine manure, $VS = 10{,}000 \times 0.80 = 8{,}000\ \text{kg VS/d}$. At an assumed 45% VS destruction in the mesophilic digester, $VS_{destroyed} = 8{,}000 \times 0.45 = 3{,}600\ \text{kg/d}$. With an assumed biogas yield of 0.75 m³/kg VS destroyed, $$V_{biogas} = 3{,}600 \times 0.75 = \boxed{2{,}700\ \text{m}^3/\text{d}}$$ At an assumed 60% methane content and a methane lower heating value of 35.8 MJ/m³, the biogas energy content is $2{,}700 \times (0.60 \times 35.8) = 58{,}000\ \text{MJ/d} \approx 671\ \text{kW}$ of continuous fuel-energy input to the engine-generator.
4. Digester heating requirement — sensible heat. Incoming slurry must be warmed from an assumed 10 °C influent temperature to the 35 °C digester temperature, a rise of 25 K. With slurry ≈ 95% moisture, its specific heat is taken close to water's, $c_p \approx 4.0\ \text{kJ/kg}\cdot\text{K}$: $$\dot{Q}_{sens} = \dot{m}_{wet}\, c_p\, \Delta T = 200{,}000 \times 4.0 \times 25 = 2.00\times10^{7}\ \text{kJ/d} = \boxed{231.5\ \text{kW}}$$
5. Digester heating requirement — tank conduction loss. Each tank's wall area is $\pi D h = \pi(20.6)(6)=388.3\ \text{m}^2$ and its two end caps (roof + floor) total $2 \times \tfrac{\pi}{4}D^2 = 666.7\ \text{m}^2$, giving $1{,}055.0\ \text{m}^2$ per tank and $2{,}110.0\ \text{m}^2$ for both. At an assumed insulated-tank $U = 0.5\ \text{W/m}^2\cdot\text{K}$ against a winter design ambient of −10 °C ($\Delta T = 45$ K), $$\dot{Q}_{loss} = U A \Delta T = 0.5 \times 2{,}110.0 \times 45 = \boxed{47.5\ \text{kW}}$$ giving a total digester heating requirement of $$\dot{Q}_{heat} = \dot{Q}_{sens}+\dot{Q}_{loss} = 231.5+47.5 = \boxed{279.0\ \text{kW}}$$
6. Waste-heat sufficiency check. With the biogas fuel-energy input of 671 kW (Step 3) and an assumed 40% of that recoverable as usable jacket-water/exhaust waste heat from the engine-generator, $$\dot{Q}_{waste} = 0.40 \times 671 = \boxed{268.5\ \text{kW}}$$ Comparing to the 279.0 kW requirement, the recovered waste heat covers $268.5/279.0 = 96\%$ of the digester heating load — marginally insufficient under the assumed winter design conditions. The shortfall is small (≈10.5 kW) and could realistically be closed by tightening tank insulation (lowering $U$) or by a modest auxiliary biogas-fired boiler sized for the winter deficit; it should not be read as a fundamental process failure.