Question 3 of 7: Particle Characteristics, Water Hardness and Thermal Pollution

Question 3: Particle Characteristics, Water Hardness 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) Suspended versus Settleable Particulates and Their Treatment

Two key differences between suspended (non-settleable/colloidal) and settleable (particulate) solids in municipal wastewater:

1. Settling behaviour and particle size. Settleable particulates are relatively large and dense enough to settle out of suspension under gravity alone within a practical detention time (roughly >100 μm – grit, fecal solids, larger organic debris). Suspended (non-settleable/colloidal) particles are fine (roughly 1–100 μm or smaller) and are kept in suspension by Brownian motion and electrostatic surface charge, so they will not settle in a reasonable time by gravity alone.
2. Removal mechanism required. Because settleable solids already have enough mass to overcome the water’s drag under gravity, a purely physical/mechanical process (quiescent sedimentation) removes them directly. Suspended colloidal solids are stabilized by surface charge that keeps particles apart, so a physical process alone cannot remove them efficiently — a chemical step (coagulant addition to neutralize the charge) must first destabilize the particles before a physical step (flocculation and sedimentation, or filtration) can remove them.

For settleable particulates, a primary clarifier provides sufficient quiescent detention time for the particles’ own settling velocity to carry them to the tank floor, from where they are mechanically scraped to a hopper. For suspended colloidal particulates, the coagulant (e.g., alum or a ferric salt) first neutralizes the negative surface charge that keeps the fine particles apart; gentle mixing during flocculation then allows the now-destabilized particles to collide and grow into larger floc, which is finally removed by sedimentation or granular-media filtration — a process gravity settling alone cannot achieve on the original colloidal particles.

(ii) Hardness of the Quarry-Area Groundwater

Given. Divalent-cation concentrations from the groundwater analysis, with atomic weights $Ca=40$, $Mg=24$, $Cu=64$, $H=1$, $C=12$, $O=16$ as stated on the exam:

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

Approach. Hardness, by the Standard Methods/Sawyer–McCarty definition, is the sum of the alkaline-earth cations $Ca^{2+}$ and $Mg^{2+}$ only, each converted to an equivalent mass of CaCO₃ via the ratio of equivalent weights; $Cu^{2+}$ is a transition-metal cation supplied alongside Ca and Mg as a deliberate decoy and is not a hardness-forming ion under this definition.

1. Equivalent weight of CaCO₃. Build its molecular weight from the given atomic weights ($Ca+C+3O$), then halve for the divalent carbonate: $$MW_{CaCO_3} = 40+12+3(16) = 100\ \text{g/mol}, \qquad EW_{CaCO_3} = 100/2 = 50\ \text{g/eq}.$$
2. Equivalent weights of the cations. Equivalent weight $=$ atomic weight $\div$ valence, all three ions being divalent: $$EW_{Ca} = 40/2 = 20\ \text{g/eq}, \qquad EW_{Mg} = 24/2 = 12\ \text{g/eq}, \qquad EW_{Cu} = 64/2 = 32\ \text{g/eq}.$$
3. Convert $Ca^{2+}$ and $Mg^{2+}$ to CaCO₃ equivalents. $$H_{Ca} = 80\times\dfrac{50}{20} = 200.0\ \text{mg/L as CaCO}_3, \qquad H_{Mg} = 60\times\dfrac{50}{12} = 250.0\ \text{mg/L as CaCO}_3.$$
4. Sum for total hardness. $$\boxed{H = H_{Ca}+H_{Mg} = 200.0+250.0 = 450.0\ \text{mg/L as CaCO}_3.}$$ $Cu^{2+}$ is not included in this sum: under the Standard Methods/Sawyer–McCarty definition, hardness is specifically the Group 2 alkaline-earth pair $Ca^{2+}+Mg^{2+}$, not every polyvalent cation a water analysis happens to report. For reference only, $Cu^{2+}$ would contribute $30\times(50/32) = 46.9\ \text{mg/L as CaCO}_3$ if (incorrectly) included, giving 496.9 mg/L — a common trap, since the question deliberately supplies copper’s atomic weight alongside calcium’s and magnesium’s.
5. Classify the water. Against the standard hardness scale (0–75 soft, 75–150 moderately hard, 150–300 hard, >300 very hard), $H=450.0$ mg/L places this water in the very hard category.

(iii) Protecting the Cold-Water Fishery from Thermal Pollution

Two potential engineering solutions to keep the mixing-zone temperature below the regulated 10 °C limit, given the cooling water is discharged year-round at 30 °C into a fishery with an ideal range of only 5–10 °C:

1. Add mechanical or natural-draft cooling-tower capacity, or route the discharge through a cooling pond, ahead of release. Actively removing heat from the water before it reaches the river/lake meets the temperature target at the point of discharge itself; sizing the additional cooling capacity to bring the discharge to within a few degrees of the receiving water’s ambient temperature is the most direct year-round solution and does not depend on the receiving water having spare assimilative (dilution) capacity, which is important here because the requirement is year-round, including low-flow periods.
2. Install a submerged multi-port diffuser outfall to achieve rapid initial dilution within a small, regulator-approved mixing zone. Distributing the 30 °C discharge through many small ports across the river/lake’s cross-section achieves fast initial mixing with the ambient water, confining the temperature rise to a small mixing zone upstream of the main fishery habitat rather than creating a long, continuous warm plume through it — a lower-capital option than added cooling capacity, though (unlike option 1) it depends on year-round ambient flow/volume being sufficient to dilute a 30 °C discharge down to <10 °C at the edge of the mixing zone, which should be checked against the lowest-flow season.