18-Env-A4 Water and Wastewater Engineering · May 2018
Question 5 of 5: Secondary Clarifier Loading and Return Sludge Concentration
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Notes on this paper
National Exams — May 2018 — 04-Env-A4 / Water and Wastewater Engineering. 3 hours duration; closed book with one double-sided aid sheet; approved Casio/Sharp calculator permitted. Question 1 is compulsory; the paper instructs candidates to attempt any three of the remaining four questions — all five are solved below for completeness.
Reference texts. Metcalf & Eddy, Wastewater Engineering: Treatment and Resource Recovery (5th ed.) — population equivalent, oxygen sag/Streeter–Phelps, activated-sludge process control (RAS/WAS, HRT/SRT), secondary clarifier design; Davis & Cornwell, Introduction to Environmental Engineering (6th ed.) — turbidity, alkalinity chemistry, digester fundamentals; MWH’s Water Treatment: Principles and Design (3rd ed.) — coagulation-flocculation mechanisms, ozonation, disinfection by-products, pH.
Find. The surface overflow rate at average and peak flow, the solids loading rate at average and peak flow, and the return-sludge solids concentration at average flow.
Approach. Compute the clarifier surface area from its volume and depth; take surface overflow rate as the forward (plant) flow over that area, since RAS returns to the aeration tank rather than crossing the weir; take solids loading rate as the MLSS concentration carried by the total flow entering the clarifier (influent plus RAS) over the same area; and close a solids mass balance across the clarifier (solids in with the combined flow equal solids out with the RAS, since the clarified effluent is assumed essentially solids-free) to back out the return-sludge concentration.
Check: RAS is stated as 50% of influent flow as a general operating ratio, so this solution scales RAS with the instantaneous influent flow at both average and peak conditions ($Q_r=0.5Q$ at each). If RAS pumps were instead held at a fixed average-flow rate during a peak event (a plausible alternative if RAS pump capacity is the limiting constraint), the peak solids loading rate would be lower than the value below; the surface overflow rate and the average-flow answers are unaffected either way.
(I) Surface overflow rate. Peak influent flow $Q_{peak}=Q\times PF=10{,}000\times2.5=25{,}000$ m³/d. $SOR=\dfrac{Q}{A}$: at average flow, $\dfrac{10{,}000}{600}=\boxed{16.7\text{ m}^3/\text{m}^2\cdot\text{d}}$; at peak flow, $\dfrac{25{,}000}{600}=\boxed{41.7\text{ m}^3/\text{m}^2\cdot\text{d}}$.
(II) Solids loading rate. RAS flow at average, $Q_{r,avg}=0.5(10{,}000)=5{,}000$ m³/d; at peak, $Q_{r,peak}=0.5(25{,}000)=12{,}500$ m³/d. $SLR=\dfrac{(Q+Q_r)\times MLSS}{A}$ (MLSS $=3{,}000$ mg/L $=3.0$ kg/m³): at average flow, $\dfrac{(10{,}000+5{,}000)(3.0)}{600}=\dfrac{45{,}000}{600}=\boxed{75.0\text{ kg/m}^2\cdot\text{d}}$; at peak flow, $\dfrac{(25{,}000+12{,}500)(3.0)}{600}=\dfrac{112{,}500}{600}=\boxed{187.5\text{ kg/m}^2\cdot\text{d}}$.
(III) Return sludge concentration at average flow. A steady-state solids mass balance across the clarifier, assuming negligible solids escape over the effluent weir, gives $(Q+Q_r)\,MLSS=Q_r\,X_r$, so $X_r=\dfrac{(Q+Q_r)\,MLSS}{Q_r}=\dfrac{(10{,}000+5{,}000)(3{,}000)}{5{,}000}=\dfrac{45{,}000{,}000}{5{,}000}=\boxed{9{,}000\text{ mg/L}}$.
