Sources and Dispersion of Atmospheric Pollutants: 23-Chem-B2 Environmental Engineering, December 2018, Q6

Problem 6: Sources and Dispersion of Atmospheric Pollutants (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) Engineering approaches to reduce ground-level NO₂ concentration

Approach	Benefit	Disadvantage
Increase effective stack height (taller stack / plume-rise enhancement)	Raises the effective emission height H, which increases σ_z at the point where the plume reaches ground level and directly reduces the peak ground-level concentration (C ∝ exp[−½(H/σ_z)²]). Relatively low capital cost compared to add-on gas-cleaning equipment.	Does not reduce the total mass of NO₂ emitted — it only dilutes and relocates ground-level impact farther downwind (and potentially into a different jurisdiction/receptor), which regulators increasingly disallow as a stand-alone compliance strategy.
Low-NOₓ combustion technology (staged combustion, flue-gas recirculation, low-NOₓ burners)	Reduces NO₂ formation at the source (lower peak flame temperature and staged fuel/air mixing suppress thermal-NOₓ formation), cutting the total emission rate Q rather than just dispersing it.	Combustion modification can reduce boiler thermal efficiency slightly and requires burner/furnace retrofit capital cost; deep NOₓ reduction from combustion controls alone is typically limited to ~50–60%.
Selective catalytic reduction (SCR)	Post-combustion flue-gas treatment injecting ammonia/urea over a catalyst achieves high NOₓ removal efficiency (typically 80–95%), directly cutting the emission rate Q at the stack.	High capital and operating cost (catalyst replacement, ammonia reagent supply/handling) and risk of ammonia slip (unreacted NH₃ itself becoming a secondary emission) if not well controlled.

(ii) Downwind distance to the 4 µg/m³ ground-level threshold

Given.

Quantity	Value
Stack height, H	40 m
Emission rate, Q	20 g/min
Wind speed	11–15 m/s
Insolation	Clear sky
Threshold concentration	4 µg/m³

Find. Downwind distance x (km) at which the ground-level centerline concentration falls to below 4 µg/m³.

Check — stability-class selection

In the Pasquill–Turner surface-wind/insolation table, a surface wind above 6 m/s gives Class C under strong daytime insolation and Class D under moderate or slight insolation or at night. The question settles the choice itself: it asks for the moderated unstable dispersion parameters, and the only unstable class reachable at 11–15 m/s is C (clear-sky, strong insolation). Class D is neutral, not unstable, so it does not fit the wording.

Approach. Use the Class C coefficients (a=90, b=1.1, c=−0.004, d=100, e=1.1, f=0.04) in the printed power-law relations, with x in km and σ in m (the usual convention for this form: σ_y(1 km)=a, σ_z(1 km)=d). Evaluate the ground-level centerline concentration C(x,0,0,H) along the plume axis, find its peak, and locate where it drops back under 4 µg/m³. Since C ∝ 1/u, check the whole stated wind range (11–15 m/s), not just its midpoint. The lowest wind speed gives the highest concentration and is the conservative design case.

Convert the emission rate to SI. $Q_s = \frac{20\ \text{g/min}}{60} = 0.3333\ \text{g/s}$
Dispersion coefficients (Class C). $\sigma_y = 90\,x^{\,1.1+0.004\ln x}, \qquad \sigma_z = 100\,x^{\,1.1-0.04\ln x}$ For example, at x = 0.5 km: σ_y = 90(0.5)^1.0972 = 42.1 m and σ_z = 100(0.5)^1.1277 = 45.8 m.
Ground-level centerline concentration. With y=0 (centerline) and z=0 (ground level), the Gaussian plume equation reduces to: $C(x,0,0,H) = \frac{Q_s}{\pi\,u\,\sigma_y\,\sigma_z}\exp\!\left[-\frac{1}{2}\left(\frac{H}{\sigma_z}\right)^2\right]$ with H = 40 m.
Locate the peak. The peak position does not depend on u; scanning x gives the maximum at x ≈ 0.34 km (σ_y = 27.3 m, σ_z = 28.8 m): $C_{max} = 4.68\ (u=11),\quad 3.96\ (u=13),\quad 3.43\ (u=15)\ \ \mu\text{g/m}^3$ At the 13 m/s midpoint the plume only just stays under the limit (3.96 < 4 µg/m³). The limit is exceeded only when u < 13 × 3.96/4 ≈ 12.9 m/s.
Bisect for the crossings at the worst-case wind speed (u = 11 m/s). The concentration rises through 4 µg/m³ at x ≈ 0.27 km, peaks at 4.68 µg/m³, then falls back below the limit at $x = \boxed{0.44\ \text{km}\ (\approx 440\ \text{m})}$ Beyond this distance the predicted ground-level NO₂ concentration stays under 4 µg/m³ for every wind speed in the stated 11–15 m/s range.

Fig. 2 — Ground-level centerline NO₂ concentration vs. downwind distance (Class C, H = 40 m, Q = 20 g/min) for u = 11, 13 and 15 m/s. Only the 11 m/s curve rises above the 4 µg/m³ limit, peaking at 4.68 µg/m³ at x ≈ 0.34 km and falling back below it at x ≈ 0.44 km.

Quantity	Value
Stability class	C (unstable: clear sky, wind > 6 m/s)
Peak location	x ≈ 0.34 km (all wind speeds)
C_max at u = 11 / 13 / 15 m/s	4.68 / 3.96 / 3.43 µg/m³
Rising crossing (u = 11 m/s)	x ≈ 0.27 km
Distance beyond which C < 4 µg/m³ (answer)	x ≈ 0.44 km

Topic: Engineering controls for stack NOₓ emissions; Gaussian plume ground-level dispersion modelling.

Key relations: Gaussian plume ground-level centerline equation C=Q/(πuσ_yσ_z)·exp[−½(H/σ_z)²]; Pasquill–Turner stability classification (wind >6 m/s: Class C with strong insolation, D otherwise); power-law dispersion coefficients σ = a·x^{b−c·ln x}.

Why this works: The exponential term makes ground-level concentration essentially zero very close to the stack (the plume is still high above ground) and again far downstream (σ_y, σ_z have grown large enough to dilute the plume), producing a single interior maximum; whether a given threshold is ever exceeded depends on the interplay of stack height, stability class and emission rate, so the peak must always be computed first rather than assumed.

Common pitfall: Reading the printed relation as a·x^b − c·ln x (the log term is part of the exponent); assuming every high-wind case is neutral Class D without checking the insolation column; and assuming a stronger wind raises ground-level concentration, when u in the denominator means it dilutes the plume. With a wind-speed range, test the low end, since it is the worst case.

Source: Turner, Workbook of Atmospheric Dispersion Estimates, 2nd ed., Ch. 3–4; Cooper & Alley, Air Pollution Control, 4th ed., Ch. 10 (stack-gas NOₓ control technologies).

Question 6 of 7: Sources and Dispersion of Atmospheric Pollutants

Problem 6: Sources and Dispersion of Atmospheric Pollutants (20 marks)

(i) Engineering approaches to reduce ground-level NO₂ concentration

(ii) Downwind distance to the 4 µg/m³ ground-level threshold