Question 3 of 7: Particle Characteristics, Chemistry of Solutions and Thermal Pollution

Question 3: Particle Characteristics, Chemistry of Solutions and Thermal Pollution (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) Colloidal versus Particulate (Settleable) Solids, and Their Treatment

Two key differences distinguish colloidal from particulate (settleable) solids in municipal wastewater:

1. Particle size and settling behaviour. Settleable particulates are large enough (typically > 1–100 µm, often visible grit, sand or fecal solids) that gravity dominates over Brownian motion, so they follow Stokes’ law and settle out of quiescent water in a practical retention time. Colloidal particles (roughly 0.001–1 µm) are small enough that Brownian motion keeps them in perpetual suspension; their settling velocity under gravity alone is negligible on any practical treatment timescale.
2. Surface charge and stability. Colloids remain suspended not only because of their size but because they typically carry a net (usually negative) surface charge, which creates electrostatic repulsion between particles and prevents them from aggregating into larger, settleable flocs (this is the basis of colloidal stability, described by DLVO theory). Settleable particulates are generally either uncharged/uncohesive (grit, sand) or already large enough that this surface-charge stabilization is not what keeps them suspended.

Because the two classes are removed by fundamentally different mechanisms, they need different unit processes:

For settleable particulates, screening/grit removal followed by primary sedimentation is sufficient: the particles are already dense and large enough to settle under gravity alone once coarse debris and grit (which would otherwise abrade or bury the process) are removed upstream.

For colloidal particles, gravity settling alone does nothing — they must first be destabilized. Coagulant addition (e.g., alum or ferric salts, or a cationic polymer) in a rapid-mix basin neutralizes or compresses the particles’ electrostatic double layer, removing the repulsive barrier; gentle mixing in a flocculation basin then allows the destabilized colloids to collide and grow into larger, settleable (or floatable) floc; that floc is finally removed by conventional gravity sedimentation or, where the floc is light and fluffy, by dissolved-air flotation (DAF), which attaches fine air bubbles to the floc and floats it to the surface for skimming.

(ii) Hardness of the Groundwater as CaCO3

Given. Groundwater near an abandoned copper mine with $Ca^{2+} = 100\ \text{mg/L}$, $Mg^{2+} = 600\ \text{mg/L}$, $Cu^{2+} = 200\ \text{mg/L}$; atomic weights $Ca=40$, $Mg=24$, $Cu=64$, $H=1$, $C=12$, $O=16$; both $Ca^{2+}$ and $Mg^{2+}$ (and, for reference, $Cu^{2+}$) are divalent.

Find. The total hardness of the water expressed as mg/L CaCO3, and its qualitative classification (soft / moderately hard / hard).

Approach. Hardness is, by definition (Standard Methods), the sum of the concentrations of the polyvalent cations that are conventionally recognized as hardness-forming — principally $Ca^{2+}$ and $Mg^{2+}$ — each converted to an equivalent mass of CaCO3 through the ratio of equivalent weights. Convert each ion’s concentration using $\text{mg/L as CaCO}_3 = C_{\text{ion}} \times (EW_{\text{CaCO}_3}/EW_{\text{ion}})$, where $EW = \text{(atomic or molecular weight)}/\text{valence}$, then sum and classify against the standard hardness scale.

1. Equivalent weight of CaCO3. Build its molecular weight from the given atomic weights ($Ca + C + 3O$), then halve for the divalent carbonate: $$\begin{aligned} MW_{\text{CaCO}_3} &= 40 + 12 + 3(16) = 100\ \text{g/mol} \\ EW_{\text{CaCO}_3} &= 100/2 = 50\ \text{g/eq} \end{aligned}$$
2. Equivalent weights of the ions. $$\begin{aligned} EW_{Ca} &= 40/2 = 20\ \text{g/eq} \\ EW_{Mg} &= 24/2 = 12\ \text{g/eq} \\ EW_{Cu} &= 64/2 = 32\ \text{g/eq} \end{aligned}$$
3. Convert $Ca^{2+}$ and $Mg^{2+}$ to CaCO3 equivalents. $$\begin{aligned} H_{Ca} &= 100\times\dfrac{50}{20} = 250\ \text{mg/L as CaCO}_3 \\ H_{Mg} &= 600\times\dfrac{50}{12} = 2500\ \text{mg/L as CaCO}_3 \end{aligned}$$
4. Sum for total hardness. $$\boxed{H = H_{Ca}+H_{Mg} = 250 + 2500 = 2750\ \text{mg/L as CaCO}_3.}$$ $Cu^{2+}$ is not included in the hardness sum — under the Standard Methods/Sawyer–McCarty definition, hardness is specifically the sum of the alkaline-earth (Group 2) cations $Ca^{2+}$ and $Mg^{2+}$, not every polyvalent cation present. For reference, if $Cu^{2+}$ were (incorrectly) included, it would add $200\times(50/32) = 312.5\ \text{mg/L as CaCO}_3$, for a total of 3062.5 mg/L — a common trap, since the question deliberately supplies Cu’s atomic weight alongside Ca and Mg’s.
5. Classify the water. On the standard hardness scale (soft < 75–100; moderately hard ≈ 75/100–150; hard > 150–300 mg/L as CaCO3), a total hardness of 2750 mg/L is far above the upper boundary of even the “hard” category — on the three categories offered, this water is classified as hard (in fact extremely so, an order of magnitude past the hard/very-hard boundary used by finer four-tier scales).

(iii) Meeting the Effluent Thermal Criterion

The plant must reduce its effluent temperature from a seasonal range of 12–25 °C to consistently below 10 °C, to protect a cold-water fishery whose ideal range (5–10 °C) leaves essentially no margin above the regulatory ceiling. Two engineering solutions, compared:

1. Cooling towers or a cooling pond ahead of discharge. Evaporative (wet) cooling towers, or a lined cooling pond/lagoon with sufficient surface area and detention time, actively remove heat from the effluent stream itself before it reaches the receiving water, so the temperature criterion is met at the point of discharge rather than relying on the receiving water to dilute the heat load away. This is the more robust solution where, as here, the criterion applies “year-round” with no stated allowance for a mixing zone: it works even during the worst-case summer condition (25 °C effluent, low-flow warm receiving water) when dilution-based approaches are weakest. The trade-offs are capital cost, ongoing energy/pumping cost, evaporative water loss (a consumptive use that may itself require a water-taking permit), and, for wet towers, the potential for drift and for Legionella growth requiring its own management program.
2. Diffuser (multi-port) outfall for rapid dilution/mixing. A submerged diffuser distributes the warm effluent through many small ports across the receiving water’s cross-section, achieving rapid initial dilution so the temperature criterion is met at the edge of a defined, regulator-approved mixing zone rather than at the pipe itself. This is typically far cheaper than cooling infrastructure and adds no energy demand, but it does not reduce the total heat load discharged — it only disperses it — so it protects fish in the bulk receiving water while still creating a smaller, warmer zone immediately around the outfall, and its performance depends on the receiving water having enough flow/volume to provide the required dilution ratio, especially during low-flow summer conditions when the fishery is most heat-stressed.

Given that the stated requirement is an absolute, year-round effluent criterion (not explicitly a mixing-zone standard) and that summer effluent (25 °C) is 15 °C above the target, active cooling is the more defensible primary solution for regulatory certainty, with a diffuser as a complementary measure to further protect the near-field zone.