Question 5 of 5: Stack Plume Dispersion (SO₂) and Oxides of Nitrogen

Problem 5: Stack Plume Dispersion (SO₂) and Oxides of Nitrogen (25 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.

(a) Ground-Level Centreline SO₂ Concentration at 3 km

Given. Stack physical height H_s = 150 m, diameter d = 1.5 m; SO₂ emission rate Q_m = 1.5 kg/s; stack exit velocity V_s = 10 m/s; stack gas temperature T_s = 315°C = 588.15 K; ambient temperature T_a = 25°C = 298.15 K; atmospheric pressure P = 95 kPa; wind speed at stack top u = 5 m/s; downwind distance x = 3 km; overcast summer afternoon.

Find. The ground-level, plume-centreline SO₂ concentration 3 km downwind.

Approach. (1) Compute the plume rise Δh from the supplied Holland equation and add it to the physical stack height for the effective height H. (2) Classify atmospheric stability (overcast conditions are Pasquill Class D, neutral, regardless of wind speed or time of day). (3) Read the D.O. Martin dispersion coefficients σ_y, σ_z for Class D at x = 3 km (≥1 km column) from the supplied table. (4) Evaluate the D.B. Turner ground-level (z = 0), centreline (y = 0) Gaussian plume equation.

1. Plume rise (Holland equation). $$\Delta h = \frac{V_s d}{u}\left[1.5 + (2.68\times10^{-2})(P)\left(\frac{T_s-T_a}{T_s}\right)d\right]$$ $$\Delta h = \frac{(10)(1.5)}{5}\left[1.5+(2.68\times10^{-2})(95)\left(\frac{588.15-298.15}{588.15}\right)(1.5)\right] = 3.0\left[1.5+1.883\right]$$ $$\Delta h = \boxed{10.1\ \text{m}}, \qquad H = H_s+\Delta h = 150+10.1 = 160.1\ \text{m}$$
2. Stability class. Per Pasquill–Turner classification, overcast conditions are assigned Class D (neutral) irrespective of wind speed or whether it is day or night — total cloud cover blocks both incoming solar heating and outgoing nocturnal radiative cooling, so no significant surface heating/cooling gradient develops.
3. Dispersion coefficients from the D.O. Martin table (Class D, x ≥ 1 km). With x = 3 km: $a=68$ (used for σ_y at any distance), and for σ_z at x ≥ 1 km: $c=44.5,\ d=0.516,\ f=-13$. $$\sigma_y = a\,x^{0.894} = 68\,(3.0)^{0.894} = \boxed{182\ \text{m}}$$ $$\sigma_z = c\,x^{d}+f = 44.5\,(3.0)^{0.516} - 13 = \boxed{65.4\ \text{m}}$$
4. Ground-level centreline concentration (Turner equation, y = 0, z = 0). With y = 0 and z = 0, both Gaussian factors reduce to the plume-centreline term evaluated at the effective height H: $$GLC(x,0,0,H) = \frac{Q_m}{\pi\,\sigma_y\,\sigma_z\,u}\,\exp\!\left[-\frac{1}{2}\left(\frac{H}{\sigma_z}\right)^{2}\right]$$ Substituting $Q_m = 1.5\ \text{kg/s} = 1500\ \text{g/s}$, $\sigma_y=182\ \text{m}$, $\sigma_z=65.4\ \text{m}$, $u=5\ \text{m/s}$, $H=160.1\ \text{m}$: $$\frac{H}{\sigma_z} = \frac{160.1}{65.4} = 2.447, \qquad \exp\!\left[-\tfrac12(2.447)^2\right] = \exp(-2.99) = 0.0501$$ $$GLC = \frac{1500}{\pi(182)(65.4)(5)}\times0.0501 = (8.03\times10^{-3})\times0.0501$$ $$GLC = \boxed{4.02\times10^{-4}\ \text{g/m}^3\ \ (\approx 402\ \mu\text{g/m}^3)}$$

(b) Oxides of Nitrogen: Sources, Species, and Control

(i) Major sources of oxides of nitrogen (NO_x) are overwhelmingly combustion-related: high-temperature fuel combustion in motor vehicle engines (mobile sources are typically the largest single NO_x contributor in urban airsheds), fossil-fuel-fired power plants and industrial boilers (the same high-sulfur coal plant of part (a) is simultaneously a major NO_x source), and other high-temperature industrial combustion processes (cement kilns, nitric-acid manufacture, and other process furnaces). The common mechanism across all three is thermal NO_x formation, in which combustion temperatures above roughly 1,300–1,600°C are hot enough to break atmospheric N₂'s triple bond and oxidize it, via the Zeldovich mechanism, regardless of the fuel's own nitrogen content.

(ii) The three oxides of nitrogen present in the ambient atmosphere in quantities significant to air pollution are nitric oxide (NO), nitrogen dioxide (NO₂), and nitrous oxide (N₂O). NO is the dominant species emitted directly from combustion and is rapidly oxidized in the atmosphere to NO₂, the reddish-brown gas that both irritates the respiratory system directly and drives the photochemical smog/ozone cycle referenced in Problem 1(b); N₂O is far more chemically stable (a long-lived greenhouse gas and stratospheric ozone-depleting species) rather than a smog precursor, but it is still tracked as a major NO_x-family pollutant because of its long-term atmospheric impact.

(iii) Two established techniques for controlling NO_x emissions are: combustion modification — e.g. low-NO_x burners, staged (air or fuel) combustion, and flue-gas recirculation, all of which work by lowering the peak flame temperature and/or the local oxygen availability in the hottest part of the flame, directly suppressing thermal NO_x formation before it occurs — and post-combustion flue-gas treatment, most commonly Selective Catalytic Reduction (SCR), in which ammonia or urea is injected into the flue gas upstream of a catalyst bed to reduce NO_x to harmless N₂ and H₂O (Selective Non-Catalytic Reduction, SNCR, achieves the same reduction without a catalyst, at a higher required temperature and somewhat lower efficiency).