Sources and Dispersion of Atmospheric Pollutants: 23-Chem-B2 Environmental Engineering, December 2019, Q7

Problem 7: 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) Ground-level centerline NO₂ concentration at x = 1000 m

Given.

Quantity	Value
Stack height, H	50 m
Emission rate, Q	100 g/s
Wind speed, u (at 10 m)	4 m/s
Time / sky condition	1 h before sunrise, thinly overcast, >4/8 cloud cover
Downwind distance, x	1,000 m

Find. Ground-level centerline concentration C(x,0,0,H) at x=1,000 m, µg/m³.

Check — stability class and dispersion-coefficient source

Stability class. Per the exam's own wind-speed/insolation table, u=4 m/s falls in the "3–5 m/s" row; at night with >4/8 cloud cover that row gives Class D (the "<3/8 cloud" night column in the same row also gives D, so the choice is unambiguous regardless of exactly how "large cloud cover" is read).

Dispersion coefficients. Read from the exam's own Pasquill–Gifford σ_y/σ_z log-log charts (the standard Turner curves) on the Class D curve at x=1,000 m: σ_y≈68 m and σ_z≈33 m. Chart-reading tolerance is roughly ±2 m on σ_y and ±1 m on σ_z. As an analytic cross-check, the Briggs (1973) rural Class D fit to the same curves (x and σ in metres) is:

\sigma_y = 0.08x(1+0.0001x)^{-1/2}, \qquad \sigma_z = 0.06x(1+0.0015x)^{-1/2}

Also assumed: the 10 m wind speed is used directly at stack height (no power-law height correction, the standard simplification for this exam series), and the emission rate is used as given (the 10 t/hr, 3% heavy-oil figures are flavour text — Q is already stated directly in g/s).

Approach. Evaluate the ground-level centerline Gaussian plume equation (y=0, z=0) with the Class D dispersion coefficients at x=1,000 m.

Dispersion coefficients at x=1,000 m (exam charts, Class D). $\sigma_y \approx \boxed{68\ \text{m}}, \qquad \sigma_z \approx \boxed{33\ \text{m}}$
Ground-level centerline concentration. $C(x,0,0,H) = \frac{Q}{\pi\,u\,\sigma_y\,\sigma_z}\exp\!\left[-\frac{1}{2}\left(\frac{H}{\sigma_z}\right)^2\right]$ $C = \frac{100}{\pi\times4\times68\times33}\exp\!\left[-\frac{1}{2}\left(\frac{50}{33}\right)^2\right]\times10^6$ $C = \boxed{1{,}125\ \mu\text{g/m}^3}$
Within the chart-reading tolerance the result lies between about 1,050 and 1,200 µg/m³.
Cross-check with the Briggs rural Class D fit. $\sigma_y = 0.08(1000)(1.1)^{-1/2} = 76.28\ \text{m}, \qquad \sigma_z = 0.06(1000)(2.5)^{-1/2} = 37.95\ \text{m}$ $C = \frac{100}{\pi\times4\times76.28\times37.95}\exp\!\left[-\frac{1}{2}\left(\frac{50}{37.95}\right)^2\right]\times10^6 = 1{,}154\ \mu\text{g/m}^3$
This agrees with the chart-based value to within 3%.

Fig. 1 — Ground-level centerline NO₂ concentration vs. downwind distance (Class D, u=4 m/s, H=50 m), drawn with the continuous Briggs fit to the Class D curves: the profile peaks at 1,211 µg/m³ near x=0.82 km; at the asked x=1.0 km the concentration has just started to fall from the peak (1,154 µg/m³ on this fit; 1,125 µg/m³ using the chart-read σ values).

Quantity	Value
σ_y(1,000 m), Class D chart	≈68 m
σ_z(1,000 m), Class D chart	≈33 m
Ground-level centerline C at x=1,000 m	≈1,125 µg/m³ (Briggs cross-check 1,154)
(context) Peak concentration (Briggs fit)	1,211 µg/m³ at x≈820 m

Even at x=1 km, the predicted ground-level concentration (≈1,125 µg/m³) is very high relative to typical ambient NO₂ guidelines (on the order of a few hundred µg/m³ for a 1-hour average) — consistent with the large stated emission rate (100 g/s) and the stable Class D dispersion conditions, which disperse the plume relatively slowly compared to a daytime unstable atmosphere. This magnitude is exactly why part (ii) asks for engineering measures to reduce the ground-level impact.

(ii) Engineering measures to reduce ground-level NO₂ and carbon-footprint comparison

Measure	Effect on ground-level NO₂	Carbon-footprint comparison
Increase effective stack height	Raises H, increasing σ_z at the point the plume reaches ground level and directly lowering C (C∝exp[−½(H/σ_z)²]) — does not reduce total mass emitted, only relocates and dilutes the ground-level impact farther downwind.	Essentially carbon-neutral relative to baseline: no change in fuel burned or NO₂ mass emitted, so CO₂ footprint is unchanged; a taller stack has a small embodied-construction carbon cost but negligible operating-footprint impact.
Low-NOₓ combustion retrofit (staged combustion / flue-gas recirculation)	Reduces the NO₂ emission rate Q at the source (lower peak flame temperature suppresses thermal-NOₓ formation), directly lowering C at every downwind distance in proportion to Q.	Slightly increases the plant's own operating carbon footprint (marginal efficiency penalty from staged combustion can increase fuel burned per unit output by a small percentage), but this is a much smaller footprint cost than the emission-reduction benefit and is far lower-footprint than an add-on treatment system.
Selective catalytic reduction (SCR)	Achieves the largest NOₓ removal (typically 80–95%) via post-combustion ammonia/urea injection over a catalyst, giving the biggest reduction in Q and hence C.	Highest carbon-footprint cost of the three: manufacturing and transporting the ammonia/urea reagent has its own embodied carbon footprint, and the induced-draft fan pressure drop across the catalyst bed increases the plant's parasitic electrical load (and associated CO₂ if that electricity is not carbon-free).

The three measures form a clear trade-off: stack-height increase is carbon-neutral but does not cut total emissions (a dilution, not a reduction, strategy); combustion modification cuts emissions at the source for a small footprint penalty; and SCR achieves the deepest emission cut but carries the largest ancillary carbon cost, so the "best" choice from a whole-system carbon-footprint perspective depends on how much NOₓ reduction is actually required to meet the receptor-level standard.

Topic: Gaussian plume ground-level concentration; Pasquill–Turner stability class selection; engineering NOₓ controls and their carbon-footprint trade-offs.

Key relations: C(x,0,0,H)=Q/(πuσ_yσ_z)·exp[−½(H/σ_z)²]; Pasquill–Gifford σ_y,σ_z charts vs. downwind distance by stability class (Briggs 1973 rural formulas as the analytic fit).

Why this works: The Gaussian plume model assumes steady, uniform wind and continuous emission with Fickian (normally-distributed) dispersion in the crosswind and vertical directions; ground-level centerline concentration is maximized where the vertical plume spread σ_z has grown enough for the plume centreline's Gaussian tail to reach the ground, which is why C rises, peaks, then falls as x increases rather than being maximum right at the stack.

Common pitfall: Using the daytime insolation columns of the stability table for a before-sunrise condition (this is unambiguously the night columns); treating "increase stack height" as an emissions-reduction measure when it is actually a dilution/relocation measure with no net change in mass emitted or carbon footprint.

Source: Turner, Workbook of Atmospheric Dispersion Estimates, 2nd ed., Ch. 3–4 (stability classification, Gaussian plume equation, Briggs dispersion-coefficient formulas); Cooper & Alley, Air Pollution Control, 4th ed., Ch. 8 (NOₓ control technologies).

Question 7 of 7: Sources and Dispersion of Atmospheric Pollutants

Problem 7: Sources and Dispersion of Atmospheric Pollutants (20 marks)

(i) Ground-level centerline NO₂ concentration at x = 1000 m

(ii) Engineering measures to reduce ground-level NO₂ and carbon-footprint comparison