Atmospheric Dispersion of SO2: 23-Chem-B2 Environmental Engineering, December 2016, Q6

Problem 6: 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.

Quantity	Value
Emission rate, Q	20 g/min = 0.333 g/s
Stack (effective release) height, H	60 m
Wind speed, u	2–3 m/s (mid-range 2.5 m/s used)
Insolation	Clear sky (strong solar insolation)
Target ground-level concentration	< 3 µg/m³

Find. The downwind distance x beyond which the predicted ground-level centerline concentration stays below 3 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 the descending limb crosses the 3 µg/m³ line.

Check: the exam gives a wind-speed range (2–3 m/s), not a single value, and “clear sky” rather than an explicit insolation category; the mid-range wind (2.5 m/s) with strong (clear-sky, daytime) insolation is taken from the standard Pasquill surface-wind/insolation chart as Class A–B, and Class B (“moderately unstable”) is used here — consistent with the table's own “moderated unstable dispersion parameters” framing (i.e. not the most extreme Class A).

Stability class. Wind 2–3 m/s with clear-sky (strong) insolation classifies as Pasquill Class B (“moderately unstable”). From the table: a=95, b=1.0, c=−0.006, d=140, e=1.3, f=0.05.
Dispersion coefficients. The exam's printed form places the log term in the exponent: $$\sigma_y=95\,x^{\,1.0+0.006\ln x},\qquad \sigma_z=140\,x^{\,1.3-0.05\ln x}$$ At x=1 km, ln x=0 so σy=95 m and σz=140 m; at x=0.5 km, σy≈47.6 m and σz≈55.5 m — consistent with published Pasquill–Gifford Class-B curves.
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=0.02–3.5 km (numerically, since σy,σz are transcendental in x) traces the usual elevated-source shape: C(x) rises steeply from 0 near the stack, peaks close in (the shorter 60 m stack here puts the peak much nearer the source than a taller stack would), then falls at larger x. See Fig. 6.
Locate the peak. The maximum occurs at $$x_{max}\approx 0.43\ \text{km}, \qquad C_{max}\approx 9.47\ \mu\text{g/m}^3$$ which is well above the 3 µg/m³ target, so — unlike a case where the peak never reaches the limit — there genuinely is a downwind crossing distance to find.
Locate the crossing on the descending limb. Solving $C(x)=3\ \mu\text{g/m}^3$ for x beyond the peak (numerically, by bisection) gives $$x \approx \boxed{0.99\ \text{km}\ (\approx 990\ \text{m})}$$ Beyond this distance the predicted ground-level concentration stays below the 3 µg/m³ threshold.

Fig. 6 — Predicted ground-level centerline SO2 concentration vs. downwind distance (Class B), against the 3 µg/m³ threshold.

Quantity	Value
Stability class	B (moderately unstable)
Peak location, x_max	≈0.43 km
Peak ground-level concentration, C_max	≈9.47 µg/m³
Distance beyond which C < 3 µg/m³	≈0.99 km (990 m)

(ii) Engineering measures, ranked least to most costly (20-year life-cycle)

Priority	Measure	20-year life-cycle cost basis	Long-term consideration
1 (least costly)	Operational/combustion optimization (excess-air tuning, load scheduling to avoid worst-case low-wind/stable-atmosphere hours)	No major capital outlay; recurring O&M/tuning cost only over the 20-year horizon.	Reduces peak ground-level impact opportunistically but does not reduce total SO2 mass emitted — a dispersion-timing fix, not a source reduction.
2	Increase effective stack height (taller stack or higher exit velocity/temperature for more plume rise)	Moderate capital (stack extension/rebuild), low incremental O&M; one-time capital amortized over 20 years.	Lowers near-field ground-level concentration (roughly ∝1/H²) but does not cut total SO2 mass — relocates and dilutes the same load farther downwind, increasing the plant's contribution to regional acid deposition.
3 (most costly)	Flue-gas desulfurization (wet limestone scrubbing) or fuel switching to lower-sulfur gas blend	High capital (scrubber/absorber train or fuel-supply contract change) plus ongoing reagent/disposal O&M over the full 20-year life.	Removes SO2 mass at the source (90–98% capture for FGD), cutting total loading everywhere, not just near the stack — the only option of the three that reduces the pollutant inventory rather than redistributing it.

Recommendation: operational tuning first (essentially free), stack-height increase as an interim measure if near-field concentration is the immediate concern, and flue-gas desulfurization as the long-term solution — because only source-mass reduction, not dilution, is consistent with the pollution-prevention hierarchy over a 20-year equipment life.

Topic: Gaussian plume dispersion modelling and staged SO2 emission-reduction strategy.

Key relations: $C(x,0,0,H)=\dfrac{Q}{\pi u\sigma_y\sigma_z}\exp\!\left[-\dfrac12\left(\dfrac{H}{\sigma_z}\right)^2\right]$; Pasquill–Gifford σy(x), σz(x) power-law/ln correlations by stability class.

Why this works: The ground-level factor $\exp[-\frac12(H/\sigma_z)^2]$ is essentially zero right at the stack (σz small, H/σz huge) and only rises once σz has grown enough for the plume to reach the ground in appreciable concentration; it then falls again at large x purely because σyσz keep growing in the denominator faster than the exponential term keeps rising — hence the single interior maximum every elevated-source plume has. A shorter, 60 m stack (vs. a 120 m stack) puts that peak much closer to the source and much higher in magnitude, which is exactly why the peak here (9.47 µg/m³) genuinely exceeds the 3 µg/m³ threshold.

Common pitfall: Assuming a stated wind-speed range or vague insolation description means the stability class can be skipped or guessed arbitrarily, when the exam's own table (and standard Pasquill-chart practice) expects a specific, justified class selection; also conflating “taller stack” with “less pollution” when it only redistributes the same mass over a larger area.

Source: Turner, Workbook of Atmospheric Dispersion Estimates, 2nd ed., Ch. 2–3 (Gaussian plume, Pasquill–Gifford stability classes); Cooper & Alley, Air Pollution Control, 4th ed., Ch. 3 (dispersion & control strategy comparison).

Question 6 of 7: Atmospheric Dispersion of SO2

Problem 6: Atmospheric Dispersion of SO2 (20 marks)

(i) Ground-level centerline concentration vs. downwind distance

(ii) Engineering measures, ranked least to most costly (20-year life-cycle)