Question 5 of 7: Gaussian plume dispersion of a power-plant SO₂ stack, and emission-reduction measures

Question 5: Gaussian plume dispersion of a power-plant SO₂ stack, and emission-reduction measures (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.

Given.

Find. The downwind distance $x$ on the plume centerline ($y=0$) at ground level ($z=0$) at which the predicted concentration falls to less than 4 µg/m³.

Approach. The Turner wind-speed/insolation lookup table selects the stability class before the dispersion coefficients can be evaluated: at 15 m/s (well above the ≈6 m/s mechanical-turbulence threshold) with moderate insolation, the table gives the neutral Class D, not a more-unstable class that daytime sun might otherwise suggest — the strong mechanical turbulence from the brisk wind dominates buoyant/thermal turbulence. Class-D coefficients feed the standard ground-level, on-axis Gaussian plume formula; because $\sigma_y,\sigma_z$ are power-law functions of $x$, the concentration-vs-distance relation is evaluated numerically.

1. Ground-level centerline concentration formula. With a perfectly reflecting ground, $$C(x,0,0;H)=\frac{Q}{\pi\,u\,\sigma_y\sigma_z}\exp\!\left(-\frac{H^2}{2\sigma_z^2}\right)$$
2. Dispersion coefficients for Class D. With $x$ in kilometres, $$\sigma_y=60\,x^{\,1.2+0.005\ln x},\qquad \sigma_z=70\,x^{\,0.9+0.07\ln x}$$
3. Locate the peak (worst-case) concentration. A numerical scan of $C(x)$ locates the maximum at $$x_{peak}\approx0.93\ \text{km},\qquad C_{max}\approx0.61\ \mu\text{g/m}^3$$
4. Compare the peak to the 4 µg/m³ target. The 100 m stack combined with a brisk 15 m/s wind disperses the plume so effectively that the ground-level concentration never approaches the target at all — the peak ($\approx0.61\ \mu\text{g/m}^3$) sits at only ≈15% of the 4 µg/m³ limit, everywhere downwind. There is no root $C(x)=4\ \mu\text{g/m}^3$ to solve for.
5. Robustness check across all stability classes. Repeating the peak search under Classes A–E (in case the insolation/stability call were disputed) gives peaks of 0.55, 0.52, 0.38, 0.61 and 0.35 µg/m³ respectively — every class stays comfortably under 4 µg/m³, so the conclusion is not sensitive to the exact stability-class assignment. $$C_{max}<4\ \mu\text{g/m}^3\ \text{for every stability class} \Rightarrow \text{target met at every downwind distance, including }x=0$$ ==**The ground-level SO₂ concentration never reaches the 4 μg/m³ target at any downwind distance (peak ≈0.61 μg/m³ at x≈0.93 km) — this is confirmed for every Pasquill–Gifford stability class, not just the Class-D lookup.**==

(ii) Engineering measures to reduce ground-level SO₂, compared by long-term performance and O&M needs

Measure 1 — Flue-gas desulfurization (FGD). A wet limestone/lime scrubber downstream of the boiler removes SO₂ before it reaches the stack, directly cutting the emission rate $Q$ in the dispersion formula. Long-term performance: the most robust and highest-certainty SO₂ reduction (routinely >90% removal), largely independent of weather/dispersion conditions, so it remains effective even if meteorology or stack conditions change. O&M needs: continuous limestone-slurry preparation and reagent supply chain, wastewater/gypsum by-product handling, and scrubber internals (mist eliminators, spray nozzles) require regular inspection and descaling — the highest ongoing O&M burden of the three measures.

Measure 2 — Increase effective stack height. Raising $H$ increases the $\exp(-H^2/2\sigma_z^2)$ dilution term, lowering ground-level concentration at any given $x$ (as this problem's own 100 m stack already demonstrates). Long-term performance: a permanent, passive improvement to ground-level dilution with no moving parts to maintain, but it achieves no reduction in the total SO₂ mass emitted — it only redistributes the same load over a larger downwind footprint, so its benefit is entirely local/ground-level, not a genuine emissions reduction. O&M needs: essentially none once constructed (periodic structural inspection only), the lowest O&M burden of the three, but a one-time capital cost for the structural modification/rebuild.

Measure 3 — Fuel switching to a lower-sulfur natural gas supply. Sourcing pipeline gas with lower sulfur content reduces $Q$ at the source without new equipment. Long-term performance: genuinely reduces the SO₂ mass emitted, but performance is contingent on continued availability of a lower-sulfur gas supply — a long-term regional supply-quality change (or a return to a higher-sulfur blend) could erode the benefit without the plant doing anything wrong. O&M needs: minimal on-site equipment O&M (no new hardware), but requires ongoing fuel-quality contracting/verification, a commercial rather than mechanical maintenance burden.

Preferred measure. Given the plant is already comfortably under the ground-level target (Part i), stack-height increase is the lowest-O&M, most durable option for preserving that margin, while FGD remains the measure of choice if a genuine SO₂ mass-emission reduction is separately required (e.g. for a source-performance permit limit) despite its materially higher ongoing O&M demand; fuel switching sits between the two, offering real mass reduction with low on-site O&M but carrying external supply-chain risk.