Question 1 of 19: Widget-Industry Effluent — River Dilution Assessment

Question 1: Widget-Industry Effluent — River Dilution Assessment (6 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.

Given. Effluent flow and concentration of X, the river's minimum flow and its existing background concentration of X, and the regulatory limit on X in the river at minimum flow, with complete mixing assumed at the outfall.

Find. The fully-mixed downstream concentration of X, and a defensible treatment recommendation to the client based on how it compares with the regulatory limit.

Approach. Apply a steady-state, complete-mixing mass balance across the outfall to find the downstream concentration, then compare it against the Provincial limit.

1. Mass balance at complete mixing. With no reaction (X is non-reactive) and steady flow, the mixed concentration just downstream of the outfall is the flow-weighted average of the two inputs: $$C_{mix} = \dfrac{Q_e C_e + Q_r C_{bg}}{Q_e + Q_r}$$ Substituting: $C_{mix} = \dfrac{(0.1)(3000) + (10)(20)}{0.1 + 10} = \dfrac{300 + 200}{10.1}$ $$\boxed{C_{mix} \approx 49.5\ \text{mg/L}}$$
2. Compare against the regulatory limit. The predicted in-river concentration (49.5 mg/L) sits well below the Provincial Regulatory Agency's 80 mg/L maximum, leaving a margin of $80 - 49.5 = 30.5\ \text{mg/L}$ — about 38% of the limit still unused even after the upstream competitor's own contribution is already included in the background term.

The recommendation to the client follows directly from the numbers, not just from "similar industries" experience: discharging the process water untreated is predicted to meet the Provincial limit with a real margin, so no treatment is required on a pure compliance basis. That said, a responsible recommendation goes one step further than the arithmetic. The 49.5 mg/L result assumes the stated minimum river flow, complete mixing immediately at the outfall, and a static background — none of which is guaranteed year-round, and a future or currently-undisclosed second competitor could erode the same margin the widget industry is relying on. The practical recommendation is therefore: (1) confirm compliance is not treated as a one-time calculation — require an ongoing effluent and in-river monitoring program at minimum-flow periods to verify the 49.5 mg/L prediction against real data before committing to "no treatment"; (2) install minimal preliminary treatment (screening/oil-grease removal) regardless, both as good industrial practice and as a buffer against any future tightening of the limit or reduction in available assimilative capacity as other dischargers arrive on the same reach; and (3) document the mixing-zone assumption (complete mixing at the point of compliance) with the regulator, since a near-field, incompletely-mixed zone could locally exceed 80 mg/L even though the far-field average does not.