18-Env-A5 Air Quality and Pollution Control Engineering · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — December 2015 — 04-Env-A5 / Air Quality and Pollution Control Engineering. 3 hours duration; closed book with a candidate-prepared 8½×11 in double-sided aid sheet; Casio or Sharp approved calculator only. Any five (5) questions constitute a complete paper (the first five answers as they appear are marked); all seven are solved below for completeness. Each question is worth 20 marks with section marks shown in brackets.
Reference texts. Cooper & Alley, Air Pollution Control: A Design Approach (4th ed.); Wark, Warner & Davis, Air Pollution: Its Origin and Control (3rd ed.); Davis & Cornwell, Introduction to Environmental Engineering (6th ed.); Canadian Environmental Protection Act, 1999 (CEPA) and the Canadian Ambient Air Quality Standards (CAAQS) administered by the CCME and Environment and Climate Change Canada.
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.
The main difference between the three plume types is the density of the released gas relative to ambient air, which governs whether the plume independently rises, sinks/spreads, or simply follows the wind field. A buoyant plume is less dense than ambient air (typically because it is hot) and rises. A dense-gas plume is denser than ambient air (a heavy molecular weight, or cold temperature, or both) and slumps toward the ground and spreads laterally rather than rising. A passive/neutral plume has a density close to ambient air and simply advects with the mean wind field, with no independent vertical motion of its own.
Buoyant plume dominates when: (1) the stack gas exits with a large temperature differential above ambient (e.g. power-plant flue gas at 150 °C into 15 °C ambient air); (2) the atmosphere is unstable (strong daytime solar heating, Pasquill class A/B), so ambient convective turbulence reinforces the plume's own thermal rise; (3) wind speed is low, letting the buoyant/thermal momentum dominate before the plume bends over into the mean wind.
Dense-gas plume dominates when: (1) the released gas itself has a molecular weight well above air's (~29 g/mol), e.g. chlorine or propane; (2) the release is a refrigerated/cryogenic liquid (e.g. LNG) generating a cold vapour cloud that entrains and cools surrounding air, increasing its effective density further; (3) the atmosphere is calm and stable (Pasquill class E/F, light wind, a near-surface inversion), letting the cloud slump and pool rather than being mixed upward and diluted.
Passive/neutral plume dominates when: (1) the released gas density is close to ambient (e.g. natural gas, or any plume far enough downwind that its initial density difference has already equilibrated with the surrounding air); (2) wind speed is moderate to high, so mechanical (wind-shear) turbulence overwhelms any residual buoyancy or density difference; (3) the atmosphere is neutrally stable (Pasquill class D — overcast, or strong wind), so the plume simply travels with the mean wind field.
The Pasquill classes (A, extremely unstable, through F, moderately stable) categorize the atmosphere's vertical mixing intensity from solar insolation and wind speed by day, or cloud cover and wind speed by night. In the Gaussian model, the stability class is the key input that selects the empirical dispersion-coefficient curves σy(x) and σz(x) (the Pasquill–Gifford curves): unstable classes give rapidly growing σ's (fast dilution overall, but an erratic, looping plume that can bring brief high concentrations to the ground nearby), while stable classes give slowly growing σ's (a narrow, coherent plume that stays elevated and travels far before diluting). In an Eddy diffusivity model, the same physical stability information is expressed instead as an eddy diffusion coefficient K in the governing diffusion equation — larger, more energetic turbulent eddies under unstable conditions give a larger K (faster spreading), while suppressed vertical motion under stable conditions gives a smaller K. Either way, the Pasquill class is the single meteorological classification that lets the same governing equation be parameterized correctly for the actual conditions at the time of release.
The two most important parameters are wind speed, $u$, and effective stack height, $H$. Wind speed appears in the denominator of the Gaussian equation and is directly, inversely proportional to the predicted concentration — from a simple mass balance, a given emission rate $Q$ is diluted into a volume of air proportional to $u$, so halving the wind speed roughly doubles the ground-level concentration. Effective height appears inside the exponential term $\exp\!\left(-H^2/2\sigma_z^2\right)$, which is extremely sensitive to $H$ because it is a squared term inside an exponential: a modest change in effective stack height (physical stack height plus plume rise) produces a large, non-linear change in the concentration reaching the ground. $H$ also governs where downwind the maximum occurs, because the location of peak ground-level concentration is found by maximizing this same exponential term against the growing $\sigma_z(x)$ curve. $\sigma_y$ and $\sigma_z$ themselves matter too, but they are derived quantities (set by stability class and downwind distance), not independent parameters an engineer chooses directly the way stack height and local wind conditions are.
