Question 4 of 10: Recycled Bioreactor — Hydraulic and Solids Retention Time

Question 4: Recycled Bioreactor — Hydraulic and Solids Retention Time (5 points)

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. Reactor volume $V = 200\ \text{m}^3$; influent flow $Q = 400\ \text{m}^3/\text{d}$; wasted-biomass concentration $X = 15\ \text{g/L}$; biomass wasting rate $P_x = 300\ \text{kg/d}$.

Find. The hydraulic retention time (HRT) and solids retention time (SRT), and what they imply about reactor performance.

Approach. Compute HRT from the reactor volume and flow, and SRT from the mass of biomass held in the reactor divided by the daily wasting rate; then compare the two to judge whether the "recycled" design is achieving meaningful biomass retention.

1. Hydraulic retention time. $$\text{HRT} = \frac{V}{Q} = \frac{200\ \text{m}^3}{400\ \text{m}^3/\text{d}} = 0.5\ \text{d} = \boxed{12\ \text{hours}}$$
2. Solids retention time. Using $\theta_c = VX/P_x$ with $X$ as the reactor biomass concentration, $$\theta_c = \frac{(200\ \text{m}^3)(15\ \text{kg/m}^3)}{300\ \text{kg/d}} = \frac{3000\ \text{kg}}{300\ \text{kg/d}} = \boxed{10\ \text{days}}$$

The ratio $\theta_c/\text{HRT} \approx 10\ \text{d} / 0.5\ \text{d} = 20$ is the signature of a genuinely "recycled" design: the system decouples solids age from hydraulic flow-through, holding biomass roughly twenty times longer than the water that carries it. An SRT of 10 days is well above the 4–10-day range typically needed for stable nitrification at moderate temperatures, and the 15 g/L MLVSS is characteristic of a high-rate, high-recycle system (conventional activated sludge normally runs 1.5–4 g/L; only high-recycle/MBR-type systems reach 15 g/L) — consistent with the biomass concentration and the "recycled" description reinforcing each other. Expected performance is therefore favourable: good BOD removal and nitrification capacity, low risk of biomass washout, and reasonable settleability provided the recycle/return system keeps up with the high MLVSS. If performance were found deficient in practice, the improvement measures follow directly from these two numbers: increasing SRT (reducing $P_x$) favours slow-growing nitrifiers if ammonia removal is the shortfall; conversely, if solids are approaching the settleability limit for the clarifier/thickening step, the wasting rate should be increased (shortening SRT) rather than the HRT, since HRT is already short and further HRT reduction would only aggravate contact-time limitations, not biomass concentration issues.