Question 6 of 8: Section B — Two of Three Questions

Question B-1: Slurry-Phase Bioreactor Sizing (20 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. Initial TPHC $C_0=800$ mg/kg; target $C_t=100$ mg/kg; bench-scale first-order half-life $t_{1/2}=18$ d; contaminated soil volume $V_{soil}=500\ \text{m}^3$; field slurry flow rate $Q=5\ \text{m}^3/\text{d}$; soil:slurry dilution ratio $1:3$.

Find. (i) required residence time; (ii) field-reactor volume; (iii) total time to treat all 500 m³ of soil; (iv) scale-up considerations.

Approach. The bench test establishes a first-order biodegradation rate constant from the half-life; the field reactor is sized as a batch treatment cycle using that same rate constant, then the flow rate and total slurry volume set the overall campaign duration.

1. Rate constant from the half-life. $k=\dfrac{\ln 2}{t_{1/2}}=\dfrac{0.693}{18}=\boxed{0.0385\ \text{d}^{-1}}$.
2. Part (i) — residence time. First-order batch decay: $C_t=C_0 e^{-kt}\Rightarrow t=\dfrac{\ln(C_0/C_t)}{k}=\dfrac{\ln(800/100)}{0.0385}=\dfrac{\ln 8}{0.0385}$. Since $800/100=8=2^3$, this is exactly three half-lives: $t=3\times 18=\boxed{54.0\ \text{d}}$.
3. Part (ii) — field reactor volume. Sizing the continuously-fed field reactor to provide this residence time at the stated slurry flow rate: $V_{reactor}=Q\times\tau=5\ \text{m}^3/\text{d}\times 54.0\ \text{d}=\boxed{270\ \text{m}^3}$.
4. Part (iii) — total clean-up time. A soil:slurry dilution ratio of 1:3 means each unit volume of soil is mixed with 3 units of liquid to form the slurry, so 1 part soil becomes 4 parts total slurry mixture. Total mixture volume to be processed: $V_{mix}=V_{soil}\times(1+3)=500\times 4=2000\ \text{m}^3$. Processing this at the design flow rate: $t_{total}=V_{mix}/Q=2000/5=\boxed{400\ \text{d}}$ (≈ 1.1 years) — the total campaign length for the whole 500 m³ of contaminated soil, once the reactor is running continuously at steady state.

Part (iv) — scale-up issues. The bench reactor was “completely mixed,” an idealization that gets progressively harder to guarantee at 270 m³: incomplete mixing creates dead zones and short-circuiting that reduce the effective residence time below the design 54 d for part of the slurry, so the field reactor should be over-designed (or fitted with baffles/multiple mixers) rather than sized to the bench-derived $\tau$ exactly. Field soil is far more heterogeneous than the bench sample (grain size, clay content, contaminant distribution), so the bulk biodegradation rate may differ from the single bench value; running duplicate bench tests on soil from multiple locations before finalizing $k$ reduces this risk. Bioavailability can also decline with time (aging/sequestration of the diesel fraction into soil organic matter), which the bench test’s single decay curve may not capture over a full 54-day field cycle. Finally, nutrient and oxygen delivery, temperature control, and foaming/solids-handling issues that are trivial at bench scale become real operational and cost drivers at 270 m³, and should be piloted at an intermediate scale before full field commitment.