Question 4 of 7: Water Quality Characterization, BOD and DAF

Problem 4: Water Quality Characterization, BOD and DAF (20 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.

(i) Alkalinity, dissolved oxygen and metals measurement

Alkalinity is quantified by acid-titration to the methyl-orange/pH≈4.5 endpoint, converting the volume of standard sulfuric acid consumed to mg/L as CaCO3 — an indirect measure of the water's carbonate/bicarbonate buffering capacity rather than a directly-sensed species. Dissolved oxygen is measured directly with a membrane (Clark-cell) or optical luminescence DO probe, or indirectly by the Winkler iodometric titration (manganous sulfate fixation, iodine liberation, thiosulfate titration) used as the reference/calibration method for field probes. Metals concentration is measured directly by atomic absorption spectroscopy (AAS) or ICP-MS/ICP-OES after acid digestion of the sample, or indirectly screened in the field via ion-selective electrodes or colorimetric test kits for a specific metal, with the instrumental method used to confirm compliance-grade results.

(ii) BOD test

The BOD-bottle DO drop measures the diluted mixture's oxygen depletion; scaling by the reciprocal of the dilution fraction recovers the demand of the undiluted tertiary effluent. The 20-day plateau (no further DO drop) is taken as the point where essentially all of the carbonaceous demand has been exerted, i.e. DO depleted at day 20 ≈ ultimate CBOD (L0).

Given.

Find. The 5-day CBOD (CBOD5) and the ultimate CBOD (L0) of the tertiary effluent, undiluted.

Approach. Apply the standard BOD dilution formula, scaling the bottle's DO depletion by the reciprocal of the sample fraction P = V_sample/V_total (no seed correction given, so none is applied).

1. Dilution (sample) fraction. $$P = \frac{V_{sample}}{V_{total}} = \frac{350}{500} = 0.70$$
2. 5-day CBOD of the undiluted effluent. $$CBOD_5 = \frac{DO_i - DO_5}{P} = \frac{5.0 - 0.3}{0.70} = \boxed{6.71\ \text{mg/L}}$$
3. Ultimate CBOD (L0), from the stabilized 20-day DO. Since the DO has stopped falling by day 20, essentially the full carbonaceous demand has been exerted, so DO_i−DO₂₀ scaled the same way is the ultimate CBOD of the undiluted sample. $$L_0 \approx \frac{DO_i - DO_{20}}{P} = \frac{5.0 - 0.05}{0.70} = \boxed{7.07\ \text{mg/L}}$$
4. Consistency check (not asked, verification only). Back-calculating the first-order rate constant from CBOD5/L0 via $CBOD_5=L_0(1-e^{-k\cdot5})$ gives k≈0.60 d^-1 — well above the typical municipal-effluent range (0.1–0.3 d^-1), because CBOD5/L0≈0.95 here: this tertiary effluent's small remaining carbonaceous demand is essentially fully exerted within the first 5 days, consistent with a highly polished, readily-oxidized residual organic fraction rather than typical raw or primary wastewater kinetics.

(iii) Dissolved air flotation (DAF)

Feed enters the DAF cell's contact zone, where a pressurized recycle stream supersaturated with air is injected; as the recycle depressurizes to atmospheric, it precipitates a cloud of fine microbubbles (∼10–100 µm) that attach to suspended solids/oil droplets and lower their effective density below that of water, causing them to rise (float) rather than settle:

Following the exam's diagram: the feed is first dosed with flocculants in the chemical mix tank so fine solids/oil droplets agglomerate into bubble-attachable flocs; part of the clarified effluent is pumped by the recycle pump to the air drum (saturator), where compressed air dissolves into it under pressure, and this air-saturated water is released through the air sparger at the flotation-tank inlet. Distribution baffle rods spread the flow evenly across the tank. The bubble–particle agglomerates rise and accumulate as a froth layer skimmed off the surface (froth/float draw-off), heavier residual solids are drawn off as sludge from the bottom hopper, and the clarified water passes under the underflow baffle and over the outlet weir as effluent. The key design equation is the air-to-solids ratio, $$\frac{A}{S}=\frac{1.3\,s_a(fP-1)R}{Q_i\,X}$$ where s_a is air solubility, f is the saturation efficiency, P the saturator pressure, R the recycle flow, Q_i the influent flow and X the influent solids concentration — sized (typically 0.02–0.06 kg air/kg solids) from bench/pilot testing so enough microbubbles attach to float the target solids or oil droplets within the cell's hydraulic retention time. Sludge thickening applications concentrate biological floc (which settles poorly because of its low density and gas entrainment) into a denser float layer; oily-wastewater applications rely on the same buoyancy-reversal mechanism to separate free/emulsified oil droplets that a gravity clarifier would otherwise pass through.