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23-Chem-B2 Environmental Engineering · Undated paper

Question 5 of 7: Gaussian Plume Dispersion of SO₂

Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)

Notes on this paper

National Exam 16-Chem-B2, Environmental Engineering — May 2019. 3 hours, Closed-Book Exam with a candidate-prepared 8½×11" double-sided aid sheet. Any five (5) of the seven questions constitute a complete paper (100 marks); all seven are solved below for completeness.

Reference texts: Metcalf & Eddy (Tchobanoglous, Burton, Stensel), Wastewater Engineering: Treatment and Reuse, 4th ed.; Davis & Cornwell, Introduction to Environmental Engineering, 5th ed.; Turner, Workbook of Atmospheric Dispersion Estimates, 2nd ed.; Cooper & Alley, Air Pollution Control: A Design Approach, 4th ed.

Problem 5: Gaussian Plume Dispersion of SO₂ (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 concentration at x = 3,000 m

Given.

QuantityValue
SO₂ emission rate, Q200 g/s
Stack height, H100 m
Wind speed, u7 m/s
Receptor offset, y, z0 m, 0 m (centerline, ground level)
Downwind distance, x3,000 m

Find. Ground-level centerline SO₂ concentration C(x,0,0,H) at x=3,000 m.

Check — stability class and dispersion coefficients
The coal burn-rate/sulfur-content figures are consistent with (but not needed for) the directly-given emission rate Q=200 g/s, so they are treated as context. Stability class: wind u=7 m/s falls in the ">6 m/s" row of the given Pasquill table, where the day columns are C/D/D for Strong/Moderate/Slight insolation; "one hour after sunrise" means a low sun angle and therefore Slight incoming solar radiation even under a clear sky, giving Class D (neutral). σy and σz are read from the exam's own Class D curves at x=3,000 m. Chart readings on log paper carry roughly ±5 m uncertainty in σz, which moves C by about ±20 µg/m³. The Briggs (1973) rural Class D formulas are used only as an independent cross-check. Other assumptions: flat terrain, steady wind, no plume rise (H taken as the effective stack height), full reflection at the ground, SO₂ treated as a non-reactive gas.

Approach. The steady-state Gaussian plume equation at ground level (z=0) on the plume centerline (y=0) reduces to a 1-D exponential in H/σz, once σy and σz are evaluated at the target downwind distance for the selected stability class.

  1. Dispersion coefficients at x=3,000 m, Class D (read from the exam's charts).
    $$ \sigma_y(3000\ \text{m}) \approx \boxed{175\ \text{m}} \qquad \sigma_z(3000\ \text{m}) \approx \boxed{71\ \text{m}} $$
  2. Ground-level centerline concentration.
    $$ C(x,0,0,H) = \frac{Q}{\pi u \sigma_y \sigma_z}\exp\left[-\frac{1}{2}\left(\frac{H}{\sigma_z}\right)^2\right] $$
    $$ C = \frac{200\times10^6\ \mu\text{g/s}}{\pi(7)(175)(71)}\exp\left[-\frac{1}{2}\left(\frac{100}{71}\right)^2\right] = 732.0\times0.371 $$
    $$ C \approx \boxed{271\ \mu\text{g/m}^3} $$
  3. Cross-check with the Briggs (1973) rural Class D formulas (x, σ in metres).
    $$ \sigma_y = 0.08x(1+0.0001x)^{-0.5} = 210.5\ \text{m}, \qquad \sigma_z = 0.06x(1+0.0015x)^{-0.5} = 76.75\ \text{m} $$

    These give C ≈ 241 µg/m³, about 11% below the chart-based value. That is within the usual spread between the Pasquill–Gifford charts and the Briggs fits, so the answer is taken as C ≈ 270 µg/m³ (a range of roughly 240–285 µg/m³ covers both methods and the chart-reading uncertainty).

x = 3,000 mC = 241 µg/m³02,0004,0006,0008,000075150225300Downwind distance, x (m)Ground-level centerline C (µg/m³)Class D Gaussian plume, H=100 m, u=7.0 m/s, Q=200 g/s
Cross-check curve: ground-level centerline SO₂ concentration vs. downwind distance computed with the Briggs rural Class D formulas (H=100 m, u=7 m/s, Q=200 g/s). It peaks at ≈261 µg/m³ near x≈2,190 m, so x=3,000 m sits just past the peak on the descending limb (241 µg/m³ on this curve; 271 µg/m³ with the exam-chart σ values).
QuantityValue
Stability classD (>6 m/s, slight insolation one hour after sunrise)
σy(3,000 m), exam chart≈175 m (Briggs: 210.5 m)
σz(3,000 m), exam chart≈71 m (Briggs: 76.75 m)
C(3,000 m, ground level, centerline)≈271 µg/m³ (Briggs cross-check: 241 µg/m³)

(ii) Engineering measures to reduce ground-level SO₂ and their carbon footprint

MeasureHow it reduces ground-level CCarbon-footprint comparison
Taller stackIncreases effective stack height H, which the plume equation shows drives the exp[−½(H/σz)²] term toward zero at any fixed downwind x, lowering ground-level concentration without changing the emission rate at all. Essentially carbon-neutral for the boiler itself (no process/fuel change), but the additional structural steel/concrete for the taller stack carries a one-time embodied-carbon cost and it does not reduce total SO₂ mass emitted — it only relocates the ground-level impact further from the source.
Wet limestone flue-gas desulfurization (FGD)Removes SO₂ from the flue gas chemically before it is emitted (Q itself is reduced, often by >90%), which lowers ground-level concentration at every downwind distance proportionally. Meaningfully reduces total SO₂ mass emitted, but the scrubber's induced-draft fans, limestone grinding/slurry pumping and reagent transport add a continuous parasitic electrical/process-carbon load to the plant, partly offsetting the environmental benefit.
Fuel switching (low-sulfur coal or natural gas)Directly lowers Q at the source by reducing the sulfur content of the fuel burned, again reducing ground-level concentration proportionally at every downwind distance. Switching to natural gas typically also lowers the plant's overall CO₂ carbon footprint (lower carbon intensity per unit energy than coal) in addition to eliminating most SO₂, making it generally the most carbon-favourable of the three options, though it may carry fuel-supply/cost constraints the other two measures do not.

The three measures fall into two categories: the taller stack is a dispersion-management measure (it does not reduce total emitted mass, only redistributes ground-level impact, so it addresses a local exceedance without addressing regional/cumulative loading), while FGD and fuel switching are source-reduction measures that lower Q itself and are therefore effective for cumulative and regional impact, not just the local receptor; fuel switching also happens to be the only one of the three that simultaneously improves the facility's CO₂ carbon footprint rather than trading one environmental cost (embodied carbon, parasitic load) for another.