New Effluent Limits at the Expanded Plant Capacity: 16-Civ-B5 Water Supply and Wastewater Treatment, May 2014, Q3

Question 3: New Effluent Limits at the Expanded Plant Capacity (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.

Flows, existing limits and the regulator's three conditions
Quantity	Symbol	Value
Existing rated capacity	$Q_{\text{rated}}$	10 000 m³/d
Expanded capacity	$Q_{\text{exp}}$	15 000 m³/d
Reference flow named by the regulator	$Q_{\text{ref}}$	12 000 m³/d
Current cBOD₅ limit	$C_{\text{BOD}}$	15 mg/L
Current total phosphorus limit	$C_{\text{TP}}$	1 mg/L
Condition 1 — cBOD₅ load at $Q_{\text{exp}}$	—	equal to the permissible load at $Q_{\text{ref}}$
Condition 2 — TP load at $Q_{\text{exp}}$	—	not more than 80 per cent of the permissible load at $Q_{\text{ref}}$
Condition 3 — total ammonia nitrogen load at $Q_{\text{exp}}$	$L_{\text{TAN}}$	not more than 60 kg/d

Find. The three new effluent concentration limits — cBOD₅, total phosphorus and total ammonia nitrogen, all in mg/L — that the expanded 15 000 m³/d plant must meet.

Figure 3.1 — The derivation runs load-first: convert each existing concentration limit to a load at the regulator's 12 000 m³/d reference flow, apply the stated condition to that load, then divide the permitted load by the expanded flow to recover the new concentration limit.

Approach. Every condition the regulator has written is a statement about mass per unit time, not concentration, so the whole question is one conversion applied three times: compute the permitted load, then divide it by the new flow. The only unit relationship needed is $1\ \text{mg/L} = 1\ \text{g/m}^3$, from which

$$\begin{aligned}L\ [\text{kg/d}] &\;=\; \frac{C\ [\text{mg/L}] \times Q\ [\text{m}^3/\text{d}]}{1000}\\[4pt] C\ [\text{mg/L}] &\;=\; \frac{1000 \times L\ [\text{kg/d}]}{Q\ [\text{m}^3/\text{d}]}\end{aligned}$$

Part (a) — establish the cBOD₅ load the regulator is willing to permit. The condition names the load that would be permissible at the reference flow of 12 000 m³/d under the existing 15 mg/L limit: $$L_{\text{BOD,ref}} \;=\; \frac{C_{\text{BOD}} \times Q_{\text{ref}}}{1000} \;=\; \frac{15 \times 12\,000}{1000} \;=\; 180\ \text{kg/d}$$ This is the number the river is judged able to assimilate, and it does not change when the plant gets bigger.
Convert that fixed load back to a concentration at the expanded flow. The same 180 kg/d must now be discharged in 15 000 m³ of effluent each day rather than 12 000 m³, so the permitted concentration falls in the same proportion: $$C_{\text{BOD,new}} \;=\; \frac{1000 \times L_{\text{BOD,ref}}}{Q_{\text{exp}}} \;=\; \frac{1000 \times 180}{15\,000} \;=\; \boxed{12.0\ \text{mg/L cBOD}_5}$$ The short cut worth remembering is that whenever the load is held constant the limit simply scales with the flow ratio, $C_{\text{new}} = C_{\text{old}} \times Q_{\text{ref}}/Q_{\text{exp}} = 15 \times 12\,000/15\,000 = 12.0$ mg/L. Had the 15 mg/L limit simply been carried across, the plant would have discharged $15 \times 15\,000/1000 = 225$ kg/d, which is 45 kg/d — a quarter — more than the river is permitted to receive.
Part (b) — establish the maximum permissible phosphorus load at the reference flow. Working from the existing 1 mg/L limit in exactly the same way, $$L_{\text{TP,ref}} \;=\; \frac{1.0 \times 12\,000}{1000} \;=\; 12.0\ \text{kg/d}$$
Apply the 80 per cent condition to obtain the permitted phosphorus load. The regulator allows only four-fifths of that load at the expanded capacity, which is the tightening that reflects phosphorus being the nutrient controlling eutrophication in the receiving water: $$L_{\text{TP,new}} \;=\; 0.80 \times 12.0 \;=\; 9.6\ \text{kg/d}$$
Convert the permitted phosphorus load to a concentration limit. Dividing by the expanded flow, $$C_{\text{TP,new}} \;=\; \frac{1000 \times 9.6}{15\,000} \;=\; \boxed{0.64\ \text{mg/L TP}}$$ Combining both effects at once gives the same answer, $0.80 \times 1.0 \times 12\,000/15\,000 = 0.64$ mg/L. Note how much harder this is than the cBOD₅ requirement: the concentration limit tightens by 36 per cent against 20 per cent, because the flow increase and the 80 per cent load reduction compound.
Part (c) — convert the ammonia load cap directly. The third condition is already expressed as a load, so no reference-flow step is needed; it is divided straight by the expanded flow: $$C_{\text{TAN,new}} \;=\; \frac{1000 \times L_{\text{TAN}}}{Q_{\text{exp}}} \;=\; \frac{1000 \times 60}{15\,000} \;=\; \boxed{4.0\ \text{mg/L as N}}$$ It is worth observing that the same 60 kg/d cap applied at the existing rated capacity of 10 000 m³/d would have corresponded to 6.0 mg/L, so the expansion tightens the ammonia limit by a third even though the regulator wrote only one number.
Check every answer by recomputing its load at the expanded flow. The three new limits must reproduce exactly the constraints they were derived from: $$\begin{aligned}\text{cBOD}_5{:}&\quad 12.0 \times \frac{15\,000}{1000} = 180\ \text{kg/d}\quad\checkmark\\[2pt] \text{TP}{:}&\quad 0.64 \times \frac{15\,000}{1000} = 9.6\ \text{kg/d}\quad\checkmark\\[2pt] \text{TAN}{:}&\quad 4.0 \times \frac{15\,000}{1000} = 60\ \text{kg/d}\quad\checkmark\end{aligned}$$ All three close, so the limits are internally consistent with the permit conditions.

Final Results — new effluent limits at the expanded capacity of 15 000 m³/d
Parameter	Permitted load	New concentration limit	Current limit	Tightening
cBOD₅	180 kg/d	12.0 mg/L	15 mg/L	20 per cent
Total phosphorus (TP)	9.6 kg/d	0.64 mg/L	1.0 mg/L	36 per cent
Total ammonia nitrogen (TAN)	60 kg/d	4.0 mg/L as N	not previously limited	new limit

Taken together the three limits define a materially different plant. Meeting 12.0 mg/L cBOD₅ at half again the flow is achievable within a well-run conventional activated-sludge process, but 0.64 mg/L total phosphorus is below what biological phosphorus removal alone will reliably deliver and calls for chemical precipitation with alum or ferric salts followed by tertiary filtration. The 4.0 mg/L ammonia limit requires year-round nitrification, which in a Canadian climate means designing the aerobic solids retention time for the coldest month rather than the annual average, and confirms that the expansion is a process upgrade and not merely a hydraulic one.

Check: the limits derived here are the permit conditions as written, evaluated at the design flow. Two checks belong in the real design. First, a load-based permit is normally accompanied by a maximum concentration for wet-weather flows; at a peak-day flow above 15 000 m³/d these concentration limits would deliver more than the permitted load unless the permit is written as a monthly average. Second, the receiving-water assimilative capacity behind the 180 kg/d figure is presumably set at a low-flow design condition such as the 7Q10; if the river's low flow has been revised downward since the original permit, the reference load itself would need re-examination before the expansion is approved.

Topic. Load-based effluent permitting — translating a receiving-water constraint expressed as mass per day into the concentration limit a treatment plant must meet at its design flow.

Key relations. $L = CQ/1000$ with $L$ in kg/d, $C$ in mg/L and $Q$ in m³/d, using $1\ \text{mg/L} = 1\ \text{g/m}^3$; the inverse $C = 1000L/Q$; and the constant-load scaling $C_{\text{new}} = C_{\text{old}}\,Q_{\text{ref}}/Q_{\text{new}}$.

Why this works. A river responds to mass, not to concentration. What determines the dissolved-oxygen sag downstream of an outfall, or whether an algal bloom develops in a nutrient-limited reach, is the number of kilograms of oxygen-demanding matter or phosphorus arriving each day; the volume of water they arrive in is irrelevant once mixing is complete. Writing the permit on load therefore closes the loophole that a concentration limit leaves open — a plant cannot comply by diluting, and a plant that grows cannot quietly grow its discharge with it. The arithmetic is a single mass balance applied at two different flows, and its consequence is that concentration limits automatically ratchet downward every time capacity increases, which is exactly the regulator's intent.

Common pitfall. The commonest error is anchoring the load on the wrong flow — using the existing 10 000 m³/d rated capacity, or the new 15 000 m³/d, instead of the 12 000 m³/d reference flow the regulator explicitly named. Using 10 000 would give 15.0 mg/L and 0.80 mg/L; both are wrong. A close second is applying the 80 per cent reduction to the concentration rather than to the load, which returns 0.80 mg/L instead of 0.64 mg/L and quietly permits a 25 per cent overload of phosphorus. Finally, watch the units: a phosphorus limit expressed as mg/L as P and an ammonia limit expressed as mg/L as N are not interchangeable with limits expressed as the compound.

Source. Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery, 5th ed., §3-4 (mass loading and flowrate analysis) and §4-2 (effluent discharge permits and load allocation); Davis & Cornwell, Introduction to Environmental Engineering, 5th ed., §9-2; CCME Canadian Environmental Quality Guidelines and the Canada-wide Strategy for the Management of Municipal Wastewater Effluent, which is the framework under which Canadian provincial load-based permits are issued.

Question 3 of 5: New Effluent Limits at the Expanded Plant Capacity

Question 3: New Effluent Limits at the Expanded Plant Capacity (25 marks)