Primary Clarifier Design: 18-Env-A4 Water and Wastewater Engineering, May 2017, Q5

Question 5: Primary Clarifier Design (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.

Primary clarifier influent and design parameters
Quantity	Symbol	Value
Average day flow	$Q$	10,000 m³/d
Influent TSS	$TSS_{in}$	250 mg/L
Influent VSS	$VSS_{in}$	200 mg/L
Influent BOD₅	$BOD_{in}$	200 mg/L
TSS removal efficiency	$R_{TSS}$	60%
Sludge solids concentration	$P_s$	4%
Sludge specific gravity	$SG$	1.03
Surface overflow rate	$SOR$	60 m³/m²·d
Peak flow factor	$PF$	2.25
Side water depth	$H$	3.0 m

Find. The effluent TSS/VSS/BOD₅ loads, the daily primary-sludge volume, the required clarifier surface area, and the HRT at average flow.

Approach. Apply the given 60% TSS removal to TSS directly; assume VSS is removed at the same fractional efficiency as TSS (settling does not discriminate strongly by volatility) and estimate BOD₅ removal from the standard primary-clarifier TSS-vs-BOD₅ removal correlation, then work the mass-balance, sludge-volume, overflow-rate and HRT calculations in sequence.

Check: BOD₅ removal is not directly given. Metcalf & Eddy’s typical primary-clarifier performance curves put BOD₅ removal roughly 25 percentage points below TSS removal over the normal design range (50–70% TSS / 25–40% BOD₅); at 60% TSS removal this gives an assumed 35% BOD₅ removal, used below. VSS removal is assumed equal to the stated TSS removal (60%), since a primary clarifier removes solids by settling velocity, not by volatile/fixed composition.

Effluent concentrations. $TSS_{eff}=TSS_{in}(1-R_{TSS})=250(0.40)=\boxed{100\text{ mg/L}}$. $VSS_{eff}=200(0.40)=\boxed{80\text{ mg/L}}$. $BOD_{eff}=200(1-0.35)=\boxed{130\text{ mg/L}}$.
Convert to loads. $Load\,(\text{kg/d}) = C\,(\text{mg/L}) \times Q\,(\text{m}^3\text{/d}) / 1000$. Influent: $TSS=2{,}500$, $VSS=2{,}000$, $BOD_5=2{,}000$ kg/d. Effluent: $TSS_{eff}=100(10{,}000)/1000=\boxed{1{,}000\text{ kg/d}}$, $VSS_{eff}=80(10{,}000)/1000=\boxed{800\text{ kg/d}}$, $BOD_{eff}=130(10{,}000)/1000=\boxed{1{,}300\text{ kg/d}}$.
(II) Primary sludge volume. Mass of TSS removed, $M_{removed}=2{,}500-1{,}000=1{,}500$ kg/d (checks against $2{,}500\times0.60=1{,}500$). Sludge density $=SG\times1000=1{,}030$ kg/m³. $V_{sludge}=\dfrac{M_{removed}}{\rho_{sludge}\times P_s}=\dfrac{1{,}500}{1{,}030\times0.04}=\boxed{36.4\text{ m}^3\text{/d}}$.
(III) Clarifier surface area. Peak flow $Q_{peak}=Q\times PF=10{,}000\times2.25=22{,}500$ m³/d. $A=\dfrac{Q_{peak}}{SOR}=\dfrac{22{,}500}{60}=\boxed{375\text{ m}^2}$.
(IV) HRT at average flow. Clarifier volume $=A\times H=375\times3.0=1{,}125$ m³. $HRT=\dfrac{V}{Q}=\dfrac{1{,}125}{10{,}000}=0.1125\text{ d}=\boxed{2.7\text{ h}}$.

Question 5 — final results
Quantity	Value
Effluent TSS / VSS / BOD₅ load	1,000 / 800 / 1,300 kg/d
Primary sludge volume	36.4 m³/d
Clarifier surface area	375 m²
HRT at average day flow	0.1125 d (2.7 h)

Topic: Primary clarifier mass-balance sizing: removal efficiency, sludge production, overflow rate, HRT.

Key relations: $Load=C\times Q$; $V_{sludge}=\dfrac{M_{removed}}{SG\times1000\times P_s}$; $A=Q_{peak}/SOR$; $HRT=V/Q$.

Why this works. A primary clarifier is sized on two independent criteria that must both be checked — surface overflow rate (a settling-velocity criterion, governed at the worst-case peak flow) and detention time (a floc-formation/quiescence criterion, reported at the routine average flow) — while the sludge mass balance simply tracks where the removed TSS physically goes.

Common pitfall. Sizing surface area at average flow instead of peak flow (undersizes the clarifier for its worst-case hydraulic load); assuming BOD₅ removal equals TSS removal (they track together but BOD₅ removal is consistently lower, since it also includes dissolved/colloidal BOD that settling cannot capture); using influent rather than removed TSS mass for the sludge-volume calculation.

Source: Metcalf & Eddy §5 (primary treatment, TSS/BOD removal correlations, clarifier design).

Question 5 of 5: Primary Clarifier Design

Question 5: Primary Clarifier Design (25 marks)