Question 1 of 5: Definitions — Water and Wastewater Terminology

Question 1: Definitions — Water and Wastewater Terminology (25 marks: 5 each)

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. Nitrification in wastewater treatment (5 marks)

Nitrification is the two-step biological oxidation of ammonia nitrogen to nitrate, carried out by autotrophic (chemolithotrophic) bacteria that use $CO_2$/bicarbonate as their carbon source and the oxidation reaction itself as their energy source. In the first step, ammonia-oxidizing bacteria (classically Nitrosomonas) convert ammonium to nitrite, $NH_4^++1.5O_2\rightarrow NO_2^-+H_2O+2H^+$; in the second, nitrite-oxidizing bacteria (Nitrobacter) convert nitrite to nitrate, $NO_2^-+0.5O_2\rightarrow NO_3^-$. The overall reaction consumes about $4.6\ \text{g}\ O_2$ per gram of ammonia-N oxidized and destroys roughly $7.14\ \text{g}$ of alkalinity (as $CaCO_3$) per gram of N, so nitrifying systems must be checked for both oxygen supply and alkalinity/pH buffering. Nitrifiers grow far more slowly than heterotrophs, so nitrification only occurs at a sufficiently long solids retention time (SRT) — typically 8–15 days at 10 °C for municipal activated sludge — and the required SRT rises sharply as temperature falls, which is the usual design-limiting condition for northern Canadian plants.

ii. A “Blank Sample” and “Seed” in the standard BOD5 test (5 marks)

The BOD test measures the oxygen consumed by micro-organisms as they degrade organic matter in a sample incubated in the dark at 20 °C for 5 days. A blank is a BOD bottle containing only dilution water (and seed, if the dilution water is seeded) with no sample added; it is run alongside every batch to confirm the dilution water itself is not exerting a measurable oxygen demand (its DO depletion should be $\le 0.2\ \text{mg/L}$) and is used to correct for any small demand the dilution water does exert. A seed is an inoculum of active, acclimated micro-organisms — typically settled domestic sewage or a commercial seed culture — added to the dilution water when the sample itself (e.g. a disinfected effluent or an industrial waste) does not contain enough viable organisms to exert its BOD within the test period; the seed's own oxygen demand must then be subtracted from the seeded-dilution-water blank so that only the sample's own demand is reported.

iii. Oxygen sag curve in stream pollution (5 marks)

The oxygen sag curve describes how dissolved oxygen (DO) in a receiving stream falls and then recovers downstream of an organic (BOD) discharge, the net result of two competing first-order processes: deoxygenation from BOD exertion by the discharged organics (rate constant $k_d$) and reaeration of the stream from the atmosphere (rate constant $k_r$). The Streeter–Phelps equation gives the DO deficit $D$ (saturation DO minus actual DO) at travel time $t$ downstream as $$D=\frac{k_dL_0}{k_r-k_d}\left(e^{-k_dt}-e^{-k_rt}\right)+D_0e^{-k_rt},$$ where $L_0$ is the ultimate BOD of the mixed stream at the discharge point and $D_0$ is the initial deficit. Immediately downstream, deoxygenation dominates and DO falls; as the discharged BOD is consumed, reaeration takes over and DO recovers toward saturation. The lowest point on the curve is the critical deficit $D_c$ at the critical time $t_c=\dfrac{1}{k_r-k_d}\ln\!\left[\dfrac{k_r}{k_d}\left(1-\dfrac{D_0(k_r-k_d)}{k_dL_0}\right)\right]$, found by setting $dD/dt=0$; this point is where fish kills and the worst water-quality impacts occur and is the design basis for stream assimilative-capacity and effluent-limit calculations.

iv. Temporary and Permanent Hardness in water (5 marks)

Total hardness is the sum of the multivalent-cation content of water, dominated in practice by $Ca^{2+}$ and $Mg^{2+}$, reported as an equivalent concentration of $CaCO_3$. Temporary (carbonate) hardness is the portion of total hardness associated with bicarbonate ($HCO_3^-$) and carbonate ($CO_3^{2-}$) anions — numerically the lesser of total hardness and total (carbonate) alkalinity — and is called “temporary” because it can be removed simply by boiling the water, which drives off $CO_2$ and precipitates $CaCO_3$: $Ca(HCO_3)_2\rightarrow CaCO_3\downarrow+CO_2\uparrow+H_2O$. Permanent (non-carbonate) hardness is the remainder of total hardness, associated with anions such as sulfate, chloride and nitrate ($CaSO_4$, $MgCl_2$, etc.); it is not removed by boiling and requires chemical softening (lime–soda ash) or ion exchange. The distinction matters for softening-process design, because lime alone removes carbonate hardness while non-carbonate hardness needs soda ash (or an equivalent source of $CO_3^{2-}$) in addition.

v. Headloss and Backwashing in Filtration (5 marks)

Headloss in a granular (rapid sand or dual-media) filter is the pressure drop across the media bed as water is forced through the pore spaces between grains; it starts at a low, clean-bed value (typically well under 1 m) and rises progressively as filtered particles accumulate in the pores and reduce their effective cross-section, following (for laminar flow) the Kozeny–Carman/Rose form $h_L\propto \dfrac{v\,L}{d^2}\cdot\dfrac{(1-\varepsilon)^2}{\varepsilon^3}$. A filter run is terminated either when headloss reaches the available driving head (clogging) or when effluent turbidity begins to break through, whichever governs first. Backwashing restores the filter by reversing the flow — pumping water (often with an air scour) upward through the bed at a rate sufficient to fluidize and expand the media (typically 20–50% bed expansion), scouring accumulated floc off the grains and carrying it out through a trough to waste; the bed is then allowed to resettle (coarser/denser grains first) before the next filter run resumes.