Question 1 of 7: Behaviour of Gaseous Pollutants and Control of Particulate Emissions

Question 1: Behaviour of Gaseous Pollutants and Control of Particulate Emissions (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) SOx: Formation Kinetics, Combustion Parameters and Atmospheric Behaviour

(a) Kinetics of formation. Sulfur oxides form when sulfur bound in the fuel (organic S and pyritic S in coal, or dissolved sulfur compounds in fuel oil) is released and oxidized during combustion. The dominant, very fast reaction is direct oxidation of elemental/organic sulfur to sulfur dioxide, $\text{S} + \text{O}_2 \rightarrow \text{SO}_2$, which goes essentially to completion within the flame residence time because fuel sulfur oxidizes faster than the fuel carbon matrix burns out. A small fraction (typically 1–5%) of the SO₂ is further oxidized in the flame and in the hot post-combustion gas to sulfur trioxide, $\text{SO}_2 + \tfrac{1}{2}\text{O}_2 \rightarrow \text{SO}_3$, a slower reaction that is promoted by excess oxygen, high temperature residence, and catalytic metal-oxide surfaces (e.g., vanadium or iron oxide ash particles).

(b) Two important combustion parameters. (1) Fuel sulfur content — SOx formation is essentially stoichiometric in fuel sulfur, so switching to a lower-sulfur fuel is the single most effective lever on SOx output. (2) Excess air (O₂ availability) — because SO₂→SO₃ conversion is oxygen-limited, operating with high excess air increases the SO₃/SO₂ split (worsening acid-dewpoint corrosion and blue-haze plume opacity) even though total sulfur oxidized stays essentially unchanged.

(c) Atmospheric behaviour and environmental concern. SO₂ is a moderately reactive, water-soluble gas that is itself a respiratory irritant, but its principal environmental concern is secondary: in the atmosphere SO₂ is oxidized (via OH-radical gas-phase chemistry and aqueous-phase reactions in cloud/fog droplets) to sulfate ($\text{SO}_4^{2-}$) aerosol and dilute sulfuric acid. This secondary sulfate is a major contributor to fine particulate matter (PM2.5) and to acid deposition (acid rain/snow), which acidifies lakes and soils and damages forests and building materials far downwind of the source — making SOx a regional, not just a local, air-quality problem.

(ii) NOx Formation from Coal Combustion and Its Control

Coal-fired NOx forms by three mechanisms operating together. Thermal NOx dominates in the hottest zones of the flame (>1300 °C): atmospheric N₂ and O₂ dissociate and recombine through the Zeldovich chain ($\text{O} + \text{N}_2 \rightarrow \text{NO} + \text{N}$, $\text{N} + \text{O}_2 \rightarrow \text{NO} + \text{O}$), and its rate is exponentially sensitive to peak flame temperature. Fuel NOx comes from the organically bound nitrogen already present in coal (typically 1–2% by weight), which oxidizes at much lower temperature than the thermal pathway and can dominate total NOx in coal flames. Prompt NOx is a minor, fast-forming contribution from hydrocarbon radicals (CH, CH₂) reacting with N₂ in the fuel-rich flame front.

A widely used pre-combustion/in-furnace technology is low-NOx burner design with staged combustion: fuel and air are introduced in stages (a fuel-rich primary zone followed by a fuel-lean burnout zone), which lowers peak flame temperature and local O₂ availability at the moment nitrogen would otherwise oxidize, cutting thermal and fuel NOx by roughly 30–50% with no consumable reagent. A widely used post-combustion technology is selective catalytic reduction (SCR): ammonia or urea is injected into the flue gas ahead of a catalyst bed (typically vanadium/titanium oxide), where NOx is reduced to N₂ and water, $4\text{NO} + 4\text{NH}_3 + \text{O}_2 \rightarrow 4\text{N}_2 + 6\text{H}_2\text{O}$, achieving 80–90%+ NOx removal at the cost of catalyst, reagent, and ammonia-slip management.

(iii) Terminal Settling Velocity and the Limits of Gravity Settling

Given. A single particle in air at 20 °C:

Find. The Stokes terminal (gravitational) settling velocity $v_t$, and whether laminar (Stokes) settling is a valid assumption.

Approach. Substitute directly into the supplied Stokes'-law expression, then check the particle Reynolds number to confirm the laminar (Stokes) regime the formula assumes actually applies.

1. Convert to consistent SI units. $d_p = 25\times10^{-6}\ \text{m}$, $\rho_p = 3000\ \text{kg/m}^3$, $g = 9.81\ \text{m/s}^2$.
2. Substitute into the terminal-velocity equation. $$v_t = \frac{g\rho_p d_p^2}{18\mu_g} = \frac{(9.81)(3000)(25\times10^{-6})^2}{18(1.81\times10^{-5})}.$$
3. Evaluate. $$v_t = \boxed{0.0565\ \text{m/s} \approx 56.5\ \text{mm/s}}.$$
4. Check the Stokes-flow assumption. The particle Reynolds number is $$Re_p = \frac{\rho_g v_t d_p}{\mu_g} = \frac{(1.20)(0.0565)(25\times10^{-6})}{1.81\times10^{-5}} \approx 0.094,$$ which is well below the $Re_p \approx 1$ ceiling for Stokes' law, confirming laminar creeping flow around the particle and validating the formula as used (no Cunningham slip correction is needed either, since $d_p = 25\ \mu\text{m}$ is far above the sub-micron range where slip becomes significant).

Gravitational settling chambers rely on nothing but this settling velocity to separate particles from a moving gas stream: a particle survives to the collector floor only if its residence time in the chamber exceeds $H/v_t$, where $H$ is the settling height. Because $v_t \propto d_p^2$, halving the particle diameter cuts $v_t$ by a factor of four — a 5 µm particle of the same density settles at only about $56.5\times(5/25)^2 \approx 2.3$ mm/s, roughly 25× slower than the 25 µm particle solved above. Achieving useful capture of anything in the PM10/PM2.5 range at that settling speed would require an impractically long, low, wide chamber for any realistic gas throughput. This is exactly why gravity settlers are used only as coarse pre-cleaners: they cheaply strip out the large, abrasive, fast-settling grit (which would otherwise erode fan blades and overload a downstream cyclone, ESP or baghouse) while leaving the fine fraction — which dominates the health-relevant PM2.5/PM10 mass and requires a higher-force-density mechanism (centrifugal, electrostatic or inertial-impaction) — to the primary control device.