16-Civ-B5 Water Supply and Wastewater Treatment · May 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. 98-Civ-B5 Water Supply and Wastewater Engineering, National Examination, May 2014. Three hours; closed book with one aid sheet written on both sides; approved calculator permitted. Question 1 is compulsory and the candidate then attempts any three of Questions 2–5. Every question carries 25 marks, so the paper is marked out of 100. All five questions are solved below — the set is a study resource, not a three-hour sitting.
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. Five terms to define, five marks each. So that the definitions are anchored in real numbers rather than left abstract, each one is illustrated below against the same reference plant — the activated-sludge works that Question 4 of this paper describes.
| Quantity | Symbol | Value |
|---|---|---|
| Average plant flow | $Q$ | 15 000 m³/d |
| Aeration-tank volume | $V$ | 5 000 m³ |
| Mixed-liquor suspended solids | $X$ | 3 000 mg/L |
| Total secondary-clarifier surface area | $A$ | 1 000 m² |
| Influent soluble BOD5 to aeration (assumed) | $S_0$ | 200 mg/L |
Find. For each term: a defining statement, the governing relation, a representative value, and why a designer or operator cares.
Check: the illustrative influent BOD5 of 200 mg/L and the MLVSS/MLSS ratio of 0.80 are assumed typical municipal values — they are not stated in the paper. They are used only to size the illustrative numbers; every definition and relation stands independently of them.
Definition. Softening is the unit process that removes hardness — principally the divalent cations $\mathrm{Ca}^{2+}$ and $\mathrm{Mg}^{2+}$ — from a water, converting them to an insoluble solid that is settled and filtered out, or exchanging them for sodium. Hardness is always reported as an equivalent concentration of calcium carbonate, $\text{mg/L as CaCO}_3$, so that calcium and magnesium can be added together.
The dominant municipal route is lime–soda ash softening. Carbonate (temporary) hardness is precipitated with hydrated lime, which raises the pH and converts bicarbonate to carbonate:
$$\mathrm{Ca(HCO_3)_2} + \mathrm{Ca(OH)_2} \;\longrightarrow\; 2\,\mathrm{CaCO_3}\!\downarrow\; +\; 2\,\mathrm{H_2O}$$Magnesium needs a higher pH still, around 10.8 to 11.0, at which it drops out as the hydroxide, and the calcium introduced with that extra lime must itself be removed by soda ash:
$$\begin{aligned}\mathrm{MgSO_4} + \mathrm{Ca(OH)_2} &\;\longrightarrow\; \mathrm{Mg(OH)_2}\!\downarrow\; +\; \mathrm{CaSO_4}\\ \mathrm{CaSO_4} + \mathrm{Na_2CO_3} &\;\longrightarrow\; \mathrm{CaCO_3}\!\downarrow\; +\; \mathrm{Na_2SO_4}\end{aligned}$$On an equivalent basis the lime demand for carbonate hardness works out at $37.05/50.04 = 0.740$ mg of $\mathrm{Ca(OH)_2}$ per mg of hardness as $\mathrm{CaCO_3}$, which is the number a designer uses to size a lime silo. Ion exchange over a sodium-form resin, and nanofiltration or reverse osmosis, are the alternatives at smaller scale or where the residuals from lime softening are unattractive.
Significance. Hardness carries no health-based limit in the Guidelines for Canadian Drinking Water Quality, but it drives operating cost and customer complaints: scale in water heaters and boilers, soap and detergent consumption, and scale in the distribution mains. Practical treated-water targets are 80 to 120 $\text{mg/L as CaCO}_3$; softening below roughly 50 $\text{mg/L as CaCO}_3$ is neither achievable at reasonable cost nor desirable, because a very soft water is aggressive and will attack cement linings and lead-bearing plumbing. Softening also generates a large residuals stream — roughly two kilograms of dry solids for each kilogram of hardness precipitated — which usually dominates the plant's solids-handling design.
Definition. The food-to-microorganism ratio is the mass of biodegradable organic matter applied to an activated-sludge reactor each day divided by the mass of active biomass held in that reactor:
$$\mathrm{F/M} \;=\; \frac{Q\,S_0}{V\,X_v} \quad \text{in} \quad \frac{\text{kg BOD}_5\ \text{applied per day}}{\text{kg MLVSS in the reactor}} \;=\; \text{d}^{-1}$$where $Q$ is the influent flow, $S_0$ the influent BOD5, $V$ the aeration-tank volume and $X_v$ the mixed-liquor volatile suspended solids. For the reference plant, taking MLVSS as 0.80 of the 3 000 mg/L MLSS gives $X_v = 2\,400$ mg/L, so the food applied is $15\,000 \times 0.200 = 3\,000$ kg BOD5/d against an inventory of $5\,000 \times 2.4 = 12\,000$ kg MLVSS:
$$\mathrm{F/M} \;=\; \frac{3\,000}{12\,000} \;=\; \boxed{0.25\ \text{d}^{-1}}$$Significance. F/M is the primary loading control on a conventional activated-sludge plant, and it is the inverse cousin of the sludge age: a low F/M means a large, well-oxidised, long-retained sludge and a high F/M means a young, fast-growing one. Conventional plants are designed at 0.2 to 0.4 d$^{-1}$; extended aeration runs at 0.05 to 0.15 d$^{-1}$ and high-rate systems above 0.5 d$^{-1}$. The value governs settleability as much as treatment efficiency. Run too low and filamentous organisms, which compete well when substrate is scarce, take over and the sludge bulks; run too high and the biomass never flocculates, leaving a dispersed, turbid effluent and an oxygen demand the blowers cannot meet. Operators therefore adjust wasting to hold F/M inside a narrow band rather than chasing effluent BOD directly.
Definition. The surface overflow rate, sometimes called the surface loading rate or the overflow velocity, is the volumetric flow applied to a sedimentation basin divided by its plan surface area:
$$\mathrm{SOR} \;=\; \frac{Q}{A} \qquad \left[\text{m}^3/\text{m}^2\!\cdot\!\text{d}\right]$$Dimensionally that is a velocity, and this is the whole point of the parameter. In the ideal-basin analysis a particle entering at the surface must reach the floor before the water carrying it reaches the outlet weir; the settling velocity that exactly satisfies this is the critical velocity $v_c$, and the algebra returns $v_c = Q/A$ with the basin depth cancelling out. For the reference plant, $\mathrm{SOR} = 15\,000/1\,000 = 15$ m³/m²·d, which is a critical velocity of $15 \times 1000/86\,400 = 0.174$ mm/s. Every particle settling faster than 0.174 mm/s is removed completely; slower particles are removed in the proportion $v_s/v_c$.
Significance. Because depth cancels, the SOR — not the volume and not the detention time — is the parameter that sizes a clarifier for solids capture. A deeper tank buys storage and buffers sludge blankets, but it does not capture a finer particle; only more plan area does. Typical design values are 30 to 50 m³/m²·d for primary clarifiers, 16 to 28 m³/m²·d at average flow for activated-sludge secondary clarifiers, and 20 to 40 m³/m²·d for water-treatment sedimentation basins. It is also the parameter that governs wet-weather performance: SOR rises in direct proportion to flow, so a plant sized at average flow must still be checked at the peak hourly rate before solids wash over the weirs.
Definition. Residual chlorine is the oxidising chlorine still present in the water after the chlorine demand of the water has been satisfied. It is measured as three quantities that add up: the free residual (hypochlorous acid $\mathrm{HOCl}$, hypochlorite ion $\mathrm{OCl^-}$ and dissolved $\mathrm{Cl_2}$), the combined residual (chloramines, chiefly $\mathrm{NH_2Cl}$), and the total residual, which is their sum. All three are reported as mg/L as $\mathrm{Cl_2}$.
Free chlorine speciates with pH about the dissociation $\mathrm{HOCl} \rightleftharpoons \mathrm{H^+} + \mathrm{OCl^-}$, whose $\mathrm{p}K_a$ is 7.54 at 25 °C. That places 91.6 per cent of the free residual as the far more germicidal $\mathrm{HOCl}$ at pH 6.5, 50 per cent at pH 7.54, and only 9.9 per cent at pH 8.5 — which is why a lime-softened, high-pH water disinfects poorly unless it is recarbonated first.
Significance. The residual does two separate jobs. Inside the plant it is half of the $CT$ product, $CT = C \times t_{10}$, which is how inactivation credit is claimed: a contact tank holding $C = 1.0$ mg/L free chlorine with a $t_{10}$ of 100 minutes delivers $CT = 100$ mg·min/L, to be compared against the Health Canada $CT$ tables for the design temperature and pH. In the distribution system the residual is a sentinel and a safeguard, suppressing regrowth and biofilm and signalling contamination the moment it disappears; Canadian provincial regulators typically require a detectable free residual, commonly at least 0.2 mg/L, at the far ends of the system. The counterweight is disinfection by-product formation — trihalomethanes and haloacetic acids grow with residual, contact time and natural organic matter — so residual is a quantity to be held inside a window, not maximised.
Definition. The Sludge Volume Index is the volume in millilitres occupied by one gram of mixed-liquor suspended solids after the mixed liquor has been allowed to settle quiescently for 30 minutes in a one-litre cylinder:
$$\mathrm{SVI} \;=\; \frac{SV_{30}\,[\text{mL/L}] \times 1000}{X\,[\text{mg/L}]} \qquad [\text{mL/g}]$$For the reference plant, a settled volume of 300 mL/L at an MLSS of 3 000 mg/L gives $\mathrm{SVI} = 300 \times 1000/3000 = 100$ mL/g. The reciprocal of the SVI is the concentration the sludge can thicken itself to, here $10^6/100 = 10\,000$ mg/L, which is the practical ceiling on the return-sludge concentration.
Significance. SVI is the single cheapest and most informative operating test in a biological plant, because activated sludge fails at the clarifier long before it fails in the reactor. An SVI below about 100 mL/g is a dense, compact, well-flocculated sludge; 100 to 150 mL/g is acceptable; above roughly 150 mL/g the sludge is bulking, the blanket climbs toward the weirs, and solids begin to leave with the effluent. Because a rising SVI usually signals filamentous growth from low F/M, nutrient deficiency, low dissolved oxygen or septic influent, the trend gives the operator days of warning before the effluent suspended solids move. It also feeds design directly: the state-point analysis that sets the clarifier solids loading rate is built on the settling flux curve that SVI characterises.
