Question 2 of 7: Problem 2 — Particle characteristics, chemistry of solutions and gases

Question 2: Problem 2 — Particle characteristics, chemistry of solutions and gases (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.

Part (i) — Particle removal principles and particle counting (9 marks)

Principle 1 — destabilisation and aggregation (coagulation and flocculation), for colloidal particles. The particles that dominate raw-water turbidity — clay platelets, silica, humic colloids, algal cells, in the 0.01 to 5 µm range — carry a net negative surface charge in natural water at pH 6 to 8. The resulting electrical double layer produces a repulsive energy barrier that prevents the particles from approaching one another, and because the settling velocity given by Stokes' law scales with the square of diameter, a 1 µm clay particle would take months to settle a metre. They are consequently stable indefinitely and cannot be removed by gravity as they stand. The engineering response is to destabilise them chemically, by dosing a hydrolysing metal coagulant such as alum or ferric chloride, or a polyaluminium chloride, at a controlled pH. Coagulation compresses the double layer, neutralises the surface charge, and produces aluminium or iron hydroxide precipitate that sweeps and enmeshes the colloids. Gentle, tapered flocculation at a controlled velocity gradient then promotes orthokinetic collisions so the destabilised particles grow into millimetre-scale flocs, whose settling velocity is now large enough for sedimentation or dissolved-air flotation to remove them. The controlling principle is surface chemistry: change the interparticle force balance, and transport does the rest.

Principle 2 — interception and attachment within a granular bed (depth filtration), for the residual fine particles. Particles that survive clarification, typically 1 to 30 µm of pinpoint floc, are removed in a rapid granular filter of sand, or dual-media anthracite over sand. The mechanism is not straining: the pore openings between 0.5 mm grains are perhaps 60 to 100 µm across, far larger than the particles being captured. Removal instead occurs by transport plus attachment throughout the depth of the bed. Transport brings a particle to the surface of a grain by interception where the streamline passes within one particle radius, by sedimentation onto the upper surface of the grain, and by Brownian diffusion for submicron particles; attachment then holds it there, but only if the particle has been chemically destabilised beforehand. This is why filter-aid polymer or a coagulant residual is essential, and why a filter cannot compensate for failed coagulation. The design implication is that a dual-media bed grades from coarse to fine in the direction of flow, so that solids penetrate and store through the depth of the bed rather than blinding the surface, giving long runs at low head loss until turbidity breakthrough or terminal head loss triggers backwash.

Why particle counters can improve on turbidity. Turbidity is a bulk optical surrogate: a nephelometer reports the intensity of light scattered at 90° by the whole suspension, and that signal is dominated by particles near the wavelength of the light, weighted by the square of diameter. It gives one aggregate number in NTU and can say nothing about how many particles there are or how large they are. An on-line particle counter, by contrast, sizes and counts individual particles as they pass a laser sensing zone, reporting counts per millilitre in discrete size bins. The decisive advantage is sensitivity in the size range that matters for public health. In the filtered-water range below 0.1 NTU, where the regulatory limit now sits, the turbidimeter is close to its noise floor and a developing filter breakthrough produces almost no measurable change — yet the counter will show an unambiguous rise in the 2 to 5 µm channel, the size class occupied by Cryptosporidium oocysts and Giardia cysts. Particle counting therefore detects the onset of breakthrough, end-of-run degradation and post-backwash turbidity spikes earlier and more specifically than turbidity, which is exactly the surveillance a multi-barrier drinking-water system needs for the pathogens that chlorine does not reliably inactivate.

Part (ii) — Hardness as CaCO₃ (6 marks)

Given. A lake-water analysis near a rock quarry reports three divalent metal cations in mg/L of the ion, which must be re-expressed on the calcium-carbonate equivalent basis before they can be added.

Find. The total hardness in mg/L as CaCO₃, and the classification of the water as soft, moderately hard or hard.

Approach. Convert each cation to its equivalent concentration by dividing by its equivalent weight, multiply by the equivalent weight of calcium carbonate, and sum; then compare the total against the standard hardness bands.

1. Build the calcium carbonate reference from the given atomic weights. $$M_{\text{CaCO}_3} = 40 + 12 + 3(16) = 100\ \text{g/mol} \qquad EW_{\text{CaCO}_3} = \frac{100}{2} = 50\ \text{g/eq}$$ The divisor is 2 because carbonate hardness is expressed per equivalent of charge, and both Ca²⁺ and CO₃²⁻ are divalent.
2. Write the general conversion. Hardness contributions must be added as equivalents, never as molar masses, because the ions have different atomic weights but the same charge: $$C_{\text{as CaCO}_3} = C_{\text{ion}} \times \frac{EW_{\text{CaCO}_3}}{EW_{\text{ion}}} = C_{\text{ion}} \times \frac{50}{A/2}$$
3. Convert calcium. Its equivalent weight is 40/2 = 20 g/eq: $$C_{\text{Ca}} = 160 \times \frac{50}{20} = 400\ \text{mg/L as CaCO}_3$$
4. Convert magnesium. Its equivalent weight is 24/2 = 12 g/eq: $$C_{\text{Mg}} = 50 \times \frac{50}{12} = 208\ \text{mg/L as CaCO}_3$$ Magnesium is the instructive case: it is reported at less than a third of the calcium concentration, yet because it is the lightest of the three it contributes more than half as much hardness. Ranking cations by their reported mg/L is therefore misleading.
5. Convert ferrous iron. Its equivalent weight is 56/2 = 28 g/eq: $$C_{\text{Fe}} = 40 \times \frac{50}{28} = 71.4\ \text{mg/L as CaCO}_3$$
6. Sum and box the hardness. Reporting both the conventional and the strict totals: $$TH_{\text{Ca+Mg}} = 400 + 208.3 = \boxed{608\ \text{mg/L as CaCO}_3}$$ $$TH_{\text{Ca+Mg+Fe}} = 400 + 208.3 + 71.4 = \boxed{680\ \text{mg/L as CaCO}_3}$$ In routine practice “total hardness” means calcium plus magnesium, because those two dominate every natural water; strictly, however, any polyvalent metallic cation contributes, so the 40 mg/L of ferrous iron adds a further 71 mg/L as CaCO₃ and both figures should be reported.
7. Classify the water. On the three-band scale the question offers — soft below 75, moderately hard 75 to 150, hard above 150 mg/L as CaCO₃ — a total of 608 mg/L is emphatically hard. On the four-band scale used in the GCDWQ and in Davis & Cornwell (soft < 60, moderately hard 60–120, hard 120–180, very hard > 180) it is very hard, by more than a factor of three.

Part (iii) — Toxic gases in anaerobic confined spaces, and control technologies (5 marks)

Toxic gas 1 — hydrogen sulphide (H₂S). Under the anaerobic conditions of a wet well, a force-main discharge or a submerged storage reservoir, sulphate-reducing bacteria in the slime layer reduce sulphate to sulphide, which partitions out of solution as hydrogen sulphide gas wherever the sewage is turbulent or falls freely. It is denser than air and therefore accumulates at the bottom of the space, exactly where a worker descends. Hydrogen sulphide is acutely toxic, with an eight-hour occupational exposure limit of 1 ppm and a ceiling of 5 ppm in British Columbia, and it is treacherous because it paralyses the olfactory nerve above roughly 100 ppm, so the characteristic rotten-egg odour disappears just as the atmosphere becomes lethal. Concentrations above 700 ppm cause immediate respiratory arrest. It is also the precursor of biogenic sulphuric acid corrosion, which destroys the crown of concrete sewers.

Toxic gas 2 — methane (CH₄). Methanogenic archaea generate methane in the same anaerobic environment. It is not toxic in the pharmacological sense but it is a simple asphyxiant that displaces oxygen, and above all it is flammable, with a lower explosive limit of 5 % by volume. Being lighter than air, it collects under the roof slab and at high points of the structure — the complementary hazard to hydrogen sulphide's low-level pooling, which is why a confined-space atmosphere must be tested at the top, middle and bottom of the space. Oxygen deficiency itself, produced by both microbial respiration and gas displacement, is the third hazard of the same origin; carbon dioxide and, where an upstream industrial discharge exists, carbon monoxide, are further candidates.

Technology 1 — forced-air ventilation. Continuous mechanical ventilation is the primary engineering control, and it addresses all of the hazards at once by dilution and removal. A blower with flexible ducting delivers clean air to the bottom of the space at a rate typically specified as 20 air changes per hour before entry and continuously throughout occupancy, with the intake located upwind of any discharge. Because ventilation is a control that can fail, it is paired with continuous multi-gas monitoring for oxygen, lower explosive limit, hydrogen sulphide and carbon monoxide, and with the full confined-space entry programme required by the provincial occupational health and safety regulation — hazard assessment, written entry procedure, lockout of pumps and inlets, attendant at the opening, harness and retrieval line, and rescue provisions. In a permanent pumping station the same principle appears as fixed dual-fan ventilation interlocked with the hatch and with the fixed gas detection system.

Technology 2 — source control of sulphide generation, plus foul-air treatment. Rather than diluting the gas after it forms, the release itself can be suppressed. Chemical dosing upstream is the standard tool: oxidants such as hydrogen peroxide or sodium hypochlorite, nitrate salts that allow denitrifying bacteria to outcompete the sulphate reducers, or iron salts that precipitate sulphide as insoluble ferrous sulphide; pH elevation with magnesium hydroxide shifts the sulphide equilibrium to the non-volatile bisulphide ion. Hydraulic measures — eliminating free-fall drops, reducing force-main retention time, and pigging the main — attack the biofilm that produces the sulphide. Where foul air must still be exhausted, it is treated before discharge in a biofilter, a biotrickling filter or an activated-carbon adsorber, or scrubbed chemically with caustic and hypochlorite, so that the odour and corrosion problem is not simply exported to the neighbours. This combination is preferable to ventilation alone because it reduces the hazard at source and simultaneously protects the concrete structure and the receiving community.