16-Civ-B5 Water Supply and Wastewater Treatment · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Examination, December 2014 — 98-Civ-B5 Water Supply and Wastewater Engineering. Three hours; closed book with one two-sided aid sheet and an approved calculator. Question 1 is compulsory and any three of Questions 2–5 are attempted; every question carries 25 marks. All five questions are solved below, because the set is intended as a study resource rather than an exam script.
Reference texts.
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.
| Quantity | Symbol | Value |
|---|---|---|
| WWTP rated capacity (effluent flow) | $Q_e$ | $10\,000\ \text{m}^3/\text{d}$ |
| River flow upstream of the outfall | $Q_r$ | $500\,000\ \text{m}^3/\text{d}$ |
| Background (upstream) total phosphorus | $C_{up}$ | $0.020\ \text{mg/L}$ |
| Current effluent TP limit | $C_{e,\text{now}}$ | $1.0\ \text{mg/L}$ |
| Current effluent cBOD5 and TSS limits | — | $15\ \text{mg/L}$ each |
| Permitted deterioration of the downstream concentration | — | $20$ percent of $C_{up}$ |
Find. The effluent total-phosphorus limit $C_e$ that holds the fully mixed downstream concentration at or below 120 percent of the upstream background, and the process changes at the WWTP needed to achieve it.
Approach. Draw a control volume around the mixing zone, write a steady-state mass balance on total phosphorus treating it as conservative over the short travel time to the point of complete mix, evaluate the balance forwards to show that the existing permit fails the water-quality objective, then invert the same balance to solve for the effluent concentration that just satisfies it.
This is the criterion every subsequent step must satisfy. Note how small it is: the permitted increment is only $0.004\ \text{mg/L}$, which is at the practical quantitation limit of routine low-level phosphorus analysis.
Both flows are already in $\text{m}^3/\text{d}$ and both concentrations in $\text{mg/L}$, so no unit conversion is needed here; the dilution available is
$$\frac{Q_r}{Q_e} = \frac{500\,000}{10\,000} = 50 : 1$$The plant at its rated capacity contributes exactly as much phosphorus mass as the whole river carries naturally ($10\ \text{kg/d}$ from each), which lifts the downstream concentration to 96 percent above background — nearly five times the permitted 20 percent increment. The existing permit therefore fails the objective by a wide margin, and this comparison is worth making explicitly before solving for the new limit.
Substituting the numbers,
$$C_e = \frac{(0.024)(510\,000) - (500\,000)(0.020)}{10\,000} = \frac{12\,240 - 10\,000}{10\,000}\ \text{mg/L}$$ $$\boxed{C_e = 0.224\ \text{mg/L as TP}}$$Checking the result forwards: $[(500\,000)(0.020) + (10\,000)(0.224)]/510\,000 = 0.024\ \text{mg/L}$, which is exactly $C_{allow}$, so the inversion is correct.
The permit must therefore tighten by 77.6 percent on concentration, equivalently a 4.46-fold reduction in phosphorus load. A load-based permit also has the useful property that it does not relax if the plant’s flow grows: at a future capacity of $15\,000\ \text{m}^3/\text{d}$ the same $C_{allow}$ would demand $C_e = 0.157\ \text{mg/L}$, so the concentration limit ratchets downward with every expansion while the load cap stays fixed.
Check: the answer is only as good as the design river flow. The required effluent concentration is very nearly proportional to the assimilative flow, so the value adopted for $Q_r$ governs the whole answer. The figure given, $500\,000\ \text{m}^3/\text{d}$, is an average flow; Canadian receiving-water assessments are normally made at a low-flow statistic such as the 7Q10 (the lowest seven-day average flow with a ten-year return period). If the 7Q10 were 20 percent of the mean, the same 20 percent-of-background objective would require $C_e = 0.064\ \text{mg/L}$ — a limit that no conventional secondary plant can meet and that would force membrane filtration or effluent reuse. The $0.224\ \text{mg/L}$ derived above is therefore the least stringent defensible limit; the design low flow must be confirmed with the provincial regulator before the number is used for anything.
Two further assumptions are declared: total phosphorus is taken as conservative over the mixing zone, which is conservative for the receiving water in the short term but ignores settling of particulate P and uptake by periphyton; and complete lateral mixing is assumed at the compliance point, which for a single-port outfall on a wide river may require several channel widths of travel and is normally addressed by a formal mixing-zone study.
| Quantity | Value |
|---|---|
| Allowable fully mixed downstream TP, $C_{allow}$ | $0.024\ \text{mg/L}$ |
| Downstream TP under the existing 1.0 mg/L permit | $0.0392\ \text{mg/L}$ (96 percent above background — fails) |
| Dilution available, $Q_r/Q_e$ | $50:1$ |
| Revised effluent TP limit, $C_e$ | $0.224\ \text{mg/L}$ |
| Equivalent TP load cap, $L$ | $2.24\ \text{kg/d}$ (from $10.0\ \text{kg/d}$) |
| Required tightening | $77.6$ percent on concentration; $4.46\times$ on load |
| Same objective at $Q_r = 0.2\,Q_{mean}$ (7Q10 check) | $0.064\ \text{mg/L}$ |
A conventional secondary plant with no deliberate phosphorus removal discharges $4$ to $8\ \text{mg/L}$ TP; biological uptake into waste sludge alone typically brings a well-run plant to $1.5$ to $2\ \text{mg/L}$, which is why the existing $1\ \text{mg/L}$ permit already implies some chemical dosing. Reaching $0.224\ \text{mg/L}$ — that is, below a quarter of a milligram per litre — sits at the boundary between chemical phosphorus removal and true tertiary treatment, and requires a combination of the following.
Chemical precipitation, intensified and staged. Alum, ferric chloride or ferric sulfate precipitates orthophosphate as $\mathrm{AlPO_4}$ or $\mathrm{FePO_4}$. Single-point dosing to the primary or the final effluent reaches roughly $0.5$ to $1\ \text{mg/L}$; to go below that the dose must be split — typically a first dose ahead of the primary clarifier and a second, trim dose ahead of a tertiary filter — because the removal follows a diminishing-returns curve and the metal-to-phosphorus molar ratio required rises steeply as the residual falls, from about 1.5 at $1\ \text{mg/L}$ to 3 or more below $0.3\ \text{mg/L}$. The consequences must be designed for: substantially more chemical sludge (a 30 to 50 percent increase in solids production is typical), a higher solids loading on the secondary clarifier, alkalinity destruction and a pH drop that may need lime or soda ash to offset, and a lower MLVSS/MLSS ratio in the mixed liquor.
Enhanced biological phosphorus removal (EBPR). Converting the front of the bioreactor to an anaerobic selector — a Phoredox or A/O configuration, or a five-stage Bardenpho if nitrogen removal is also wanted — lets phosphorus-accumulating organisms take up phosphorus in excess of metabolic need, which is then removed with the waste sludge. EBPR is the cheapest phosphorus on a running-cost basis and typically achieves $0.5$ to $1\ \text{mg/L}$ on its own, but it is sensitive to influent volatile fatty acids, to nitrate returned in the RAS, and to wet-weather dilution. In practice EBPR is used to carry the bulk of the load and chemical dosing to polish and to cover upsets.
Tertiary solids removal — the step that actually decides the answer. At $0.2\ \text{mg/L}$ most of the remaining phosphorus is particulate, bound in the residual suspended solids leaving the secondary clarifier, at roughly $0.02\ \text{mg}$ TP per mg TSS. An effluent carrying the permitted $15\ \text{mg/L}$ TSS therefore contributes about $0.3\ \text{mg/L}$ of TP by itself — more than the entire new limit. The TSS limit must consequently be tightened in step with the phosphorus limit, to roughly $5\ \text{mg/L}$ or better, which means adding a tertiary process: continuous-backwash or dual-media sand filtration, cloth-media disc filtration, ballasted flocculation, or membrane filtration in a membrane bioreactor retrofit. This coupling is the single most important practical point in the answer: a phosphorus limit below about $0.3\ \text{mg/L}$ is a solids-removal problem as much as a chemistry problem.
Supporting works and non-treatment options. Sludge handling must be re-rated for the additional chemical solids, and the sidestreams from thickening and dewatering must be managed because they release phosphorus back to the head of the plant. Chemical storage, containment and dosing control must be added. Monitoring must move to low-level total-phosphorus analysis with a detection limit well below the new limit, since the permit value is only an order of magnitude above typical laboratory noise. Finally, the non-treatment alternatives deserve a line in any real report: extending the outfall to a better-mixed reach, seasonal limits reflecting the growing season when eutrophication risk is real, effluent reuse or land application to remove the discharge entirely during low flow, and watershed-scale offsets against agricultural or stormwater phosphorus, which are frequently far cheaper per kilogram removed than the last increment of treatment.
