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23-Chem-B2 Environmental Engineering · May 2016

Question 5 of 7: Atmospheric Dispersion of SO2

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exam 04-Chem-B2, Environmental Engineering — May 2016. 3 hours, Closed-Book Exam with a candidate-prepared 8½×11" double-sided aid sheet. Any five (5) of the seven questions constitute a complete paper (100 marks); all seven are solved below for completeness.

Reference texts: Metcalf & Eddy (Tchobanoglous, Burton, Stensel), Wastewater Engineering: Treatment and Reuse, 4th ed.; Davis & Cornwell, Introduction to Environmental Engineering, 5th ed.; Turner, Workbook of Atmospheric Dispersion Estimates, 2nd ed.; Cooper & Alley, Air Pollution Control: A Design Approach, 4th ed.

Problem 5: Atmospheric Dispersion of SO2 (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) Ground-level centerline concentration vs. downwind distance

Given.

QuantityValue
Emission rate, Q20 g/min = 0.333 g/s
Stack (effective release) height, H120 m
Wind speed, u5 m/s
InsolationModerate solar radiation
Target ground-level concentration< 2 µg/m³

Find. The downwind distance x beyond which the predicted ground-level centerline concentration stays below 2 µg/m³.

Approach. Classify the Pasquill–Gifford stability class from wind speed + insolation, read a/b/c/d/e/f from the supplied table, build σy(x) and σz(x), then evaluate the ground-level (z=0) centerline (y=0) Gaussian-plume concentration $C(x,0,0,H)=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left[-\dfrac{1}{2}\left(\dfrac{H}{\sigma_z}\right)^2\right]$ over the downwind distance and locate where it crosses the 2 µg/m³ line.

  1. Stability class. Wind 5 m/s with moderate insolation classifies as Pasquill Class C (“moderately unstable”) — exactly the case the exam table calls out (“moderated unstable dispersion parameters”). From the table: a=120, b=1.0, c=−0.006, d=70, e=1.0, f=0.05.
  2. Dispersion coefficients. With x in km and σ in m, the ln term sits in the exponent: $\sigma_y=120\,x^{\,1.0+0.006\ln x}$ and $\sigma_z=70\,x^{\,1.0-0.05\ln x}$. At x=1 km (ln 1 = 0): σy = 120 m, σz = 70 m; at x=1.21 km: σy ≈ 145 m, σz ≈ 84.4 m — consistent with published Pasquill–Gifford Class-C curves (σy≈120–150 m, σz≈65–80 m at 1 km), confirming the parameter mapping.
  3. Ground-level centerline concentration. Evaluating $C(x)=\dfrac{Q}{\pi u\sigma_y(x)\sigma_z(x)}\exp\!\left[-\dfrac12\left(\dfrac{H}{\sigma_z(x)}\right)^2\right]$ across x=0.1–10 km (numerically, since σy,σz are transcendental in x) traces the usual elevated-source shape: C(x) rises from 0 near the stack, peaks, then falls slowly at large x. See Fig. 5.
  4. Locate the peak. The maximum occurs at $$x_{max}\approx 1.21\ \text{km}, \qquad C_{max}\approx\boxed{0.63\ \mu\text{g/m}^3}$$
  5. Compare to the 2 µg/m³ threshold. Because even the theoretical maximum ground-level concentration (0.63 µg/m³, at x≈1.21 km) is already below 2 µg/m³, the predicted concentration is below the 2 µg/m³ threshold at every downwind distance x>0 — there is no finite crossing distance because the plume never reaches the limit in the first place. (This conclusion is insensitive to the exact stability class chosen: repeating the calculation for Classes A through E gives Cmax between 0.62 and 1.33 µg/m³, all below 2 µg/m³.)
02468100.00.51.01.52.0Downwind distance x (km)Ground-level centerline C (μg/m³)threshold = 2 μg/m³C_max ≈ 0.63 μg/m³ @ x≈1.21 km
Fig. 5 — Predicted ground-level centerline SO2 concentration vs. downwind distance (Class C), against the 2 µg/m³ threshold.
QuantityValue
Stability classC (moderately unstable)
Peak location, xmax≈1.21 km
Peak ground-level concentration, Cmax≈0.63 µg/m³
Distance at which C < 2 µg/m³All x > 0 (limit never reached)
Check: the stack's physical height (120 m) is used directly as the effective release height H, since no exit velocity/temperature is given for a plume-rise correction — a real plume-rise addition (Briggs) would only push the peak farther out and the concentration lower still, reinforcing the conclusion.

(ii) Engineering measures to reduce ground-level SO2

Three measures, ranked from purely dispersive to source-reducing:

  1. Increase effective stack height (taller stack, or higher exit velocity/temperature for more plume rise). Lowers ground-level concentration near the source (Cmax∝1/H² approximately) but does not reduce the total SO2 mass emitted — it relocates the impact farther downwind and increases the source's contribution to regional/long-range transport and acid deposition. “Dilution” solutions like this are the weakest long-term choice.
  2. Flue-gas desulfurization (wet limestone scrubbing). Removes SO2 mass from the stack gas before release (90–98% capture), directly cutting total loading everywhere, not just at ground level near the stack. Produces a gypsum/scrubber-sludge by-product needing disposal or beneficial reuse, and has the highest capital and O&M cost of the three.
  3. Fuel switching / pre-combustion desulfurization (lower-sulfur natural gas blend, or sulfur removal upstream). Reduces SO2 at the source with lower capital cost than FGD, but is constrained by fuel supply/cost and does not achieve as deep a reduction as scrubbing for a high-sulfur feed.

Recommendation: flue-gas desulfurization (or fuel switching where fuel supply allows) is preferred over stack-height dilution, because it reduces the total mass of SO2 released rather than merely relocating where it lands — consistent with the pollution-prevention hierarchy (reduce at source before disperse/dilute) and avoiding the regional acid-deposition liability a taller stack creates.