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23-Chem-B2 Environmental Engineering · May 2014

Question 5 of 7: Gaussian plume dispersion of a coal-fired power plant SO₂ stack

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

Notes on this paper

Paper format. EGBC 04-Chem-B2 Environmental Engineering, May 2014, 3 hours, closed-book with a candidate-prepared double-sided 8½×11-inch aid sheet. Seven problems, each worth 20 marks; candidates attempt any five, and only the first five answers in the workbook are marked. All seven problems are solved below as a complete study resource.

Reference texts: G. Tchobanoglous, F. L. Burton & H. D. Stensel (Metcalf & Eddy), Wastewater Engineering: Treatment and Reuse (4th ed., McGraw-Hill) — BOD kinetics, nutrient removal, activated-sludge design, sedimentation design; M. L. Davis & D. A. Cornwell, Introduction to Environmental Engineering (5th ed., McGraw-Hill) — drinking-water treatment, air pollution control, ion exchange, reverse osmosis, soil remediation, air quality modelling; C. D. Cooper & F. C. Alley, Air Pollution Control: A Design Approach — particulate/gas/vapour control, thermal/catalytic oxidation, odour control; S. P. Turner, Workbook of Atmospheric Dispersion Estimates (2nd ed., CRC Press) — the Gaussian plume model and Pasquill–Gifford stability classes. Canadian context follows the Canadian Environmental Protection Act (CEPA 1999), the Guidelines for Canadian Drinking Water Quality (Health Canada), the Canadian Council of Ministers of the Environment (CCME) Municipal Wastewater Effluent guidelines, and provincial air/water permitting practice (e.g. BC Environmental Management Act and Metro Vancouver air-quality bylaws).

Question 5: Gaussian plume dispersion of a coal-fired power plant SO₂ stack (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.

Given.

QuantitySymbolValue
Stack (effective) height$H$$150\ \text{m}$
SO₂ emission rate$Q$$30\ \text{g/min}=5\times10^5\ \mu\text{g/s}$
Average wind speed$u$$10\ \text{m/s}$
Stability—moderate solar radiation ⇒ Pasquill–Gifford Class B (moderately unstable)
Class-B coefficients (this paper's table)$a,b,c,d,e,f$$110,\ 1.1,\ -0.005,\ 110,\ 1.1,\ 0.04$
Target ground-level concentration$C$$5\ \mu\text{g/m}^3$

Find. The downwind distance $x$ on the plume centerline ($y=0$) at ground level ($z=0$) at which the predicted concentration falls to less than 5 µg/m³.

01.534.5600.430.861.31.72.12.63downwind distance x (km)ground-level C (µg/m³)C = 5 µg/m³ (target)peak ≈0.52stack H=150 m, Q=30 g/min, u=10 m/s, Class B
Fig. 5: Predicted ground-level centerline SO₂ concentration vs. downwind distance for the 150 m stack (Class B). The curve peaks at only ≈0.52 µg/m³ near x≈0.97 km — well below the 5 µg/m³ target line at every distance shown.

Approach. “Moderate solar radiation” is read directly from the Pasquill nomenclature as moderately unstable, Class B, giving $\sigma_y(x)$, $\sigma_z(x)$ from the Class-B row of the table. These feed the ground-level, on-axis Gaussian plume formula (the ground-reflection image term is already folded in), which is evaluated over a range of downwind distance $x$ (km) to find where it meets the 5 µg/m³ target.

  1. Ground-level centerline concentration formula. With a perfectly reflecting ground and no deposition, $$C(x,0,0;H)=\frac{Q}{\pi\,u\,\sigma_y\sigma_z}\exp\!\left(-\frac{H^2}{2\sigma_z^2}\right)$$
  2. Dispersion coefficients for Class B. With $x$ in kilometres and this paper's table row ($a=110,\,b=1.1,\,c=-0.005,\,d=110,\,e=1.1,\,f=0.04$), $$\sigma_y=110\,x^{\,1.1+0.005\ln x},\qquad \sigma_z=110\,x^{\,1.1-0.04\ln x}$$
  3. Evaluate $C(x)$ over a range of $x$ and locate the peak. Scanning $x$ shows $C$ rising from zero at the stack, reaching a peak of only $$C_{max}\approx0.52\ \mu\text{g/m}^3\ \text{near}\ x\approx0.97\ \text{km}$$ then falling slowly beyond that. The tall 150 m stack is what keeps the peak low: the plume only reaches the ground once $\sigma_z$ has grown to the order of $H/\sqrt2\approx106$ m, by which distance the product $\sigma_y\sigma_z$ in the denominator is already large, and the small emission rate ($Q=0.5$ g/s) combined with the strong 10 m/s wind dilutes the plume further.
  4. Compare the peak against the target. Because $C_{max}\approx0.52\ \mu\text{g/m}^3$ is already an order of magnitude below the 5 µg/m³ target — and this holds at every downwind distance, not just at the peak (confirmed by scanning $x$ from 0.05 km out to 20 km) — the predicted ground-level SO₂ concentration is below the 5 µg/m³ target at every distance from the stack, including $x=0$. $$\boxed{\text{No finite downwind distance is required: }C(x)<5\ \mu\text{g/m}^3\ \text{for all }x\ge0}$$ ==**Ground-level concentration stays below 5 µg/m³ everywhere (peak ≈ 0.52 µg/m³ at x ≈ 0.97 km); the target is met immediately from the stack**==
QuantityResult
Peak ground-level concentrationC_max ≈ 0.52 µg/m³ at x ≈ 0.97 km
Downwind distance where C first falls below 5 µg/m³x = 0 km (never exceeded)
Check — stability class robustness and the “5000 GW” power rating

“Moderate solar radiation” is read as Pasquill–Gifford Class B directly (A=extremely unstable, B=moderately unstable, C=slightly unstable); the classical wind-speed/insolation lookup table would actually default to Class D at $u=10$ m/s, but re-running the peak-concentration scan against every class A–E in this paper's table (Class A gives the highest peak, ≈0.62 µg/m³) confirms the “never exceeds 5 µg/m³” conclusion is robust to the stability-class choice, not an artifact of picking Class B. The plant's stated “5000 GW” power output (several hundred times the output of the largest real coal-fired plants, which are of the order of 5–7 GW) does not enter the plume formula at all — it is flavour text; only $Q=30$ g/min drives the calculation, and is taken at face value.

(ii) Engineering measures to reduce ground-level SO₂ concentration

Measure 1 — increase the effective stack height further (or add buoyant plume rise). Part (i) already shows that the 150 m stack height is the dominant reason ground-level concentration stays negligible — raising $H$ further pushes the exponential penalty term $\exp(-H^2/2\sigma_z^2)$ closer to zero at every practical downwind distance. Environmental impact: this is a purely local, near-field improvement; it does not reduce the total SO₂ mass emitted, it disperses the same load further and thinner, which historically contributed to long-range transboundary acid rain (a documented Canada–U.S. issue). Since the peak is already low here, this measure has diminishing marginal benefit for this specific plant.

Measure 2 — flue-gas desulfurization (wet limestone scrubbing). An absorption-based FGD system removes SO₂ from the flue gas before it reaches the stack, directly cutting the emission rate $Q$ (concentration scales linearly with $Q$) rather than redistributing it. Environmental impact: a genuine source-reduction measure (typically 90–98% SO₂ removal) with a saleable/landfillable gypsum by-product; it has real capital/operating cost and its own scrubber sludge/wastewater stream to manage, but unlike Measure 1 it reduces total emitted mass, which matters regardless of how tall the stack already is.

Measure 3 — fuel switching to lower-sulfur coal or natural gas. Reduces the SO₂ generated at the source, again lowering $Q$ directly. Environmental impact: a genuine source-reduction measure with co-benefits of reduced particulate and mercury emissions (switching away from coal), but it raises fuel cost and, for a switch to gas, shifts rather than eliminates the plant's greenhouse-gas profile.

Recommendation. Flue-gas desulfurization is the preferred option here: the stack is already tall enough that near-field ground-level concentration is not the binding constraint (part i), so a further stack-height increase (Measure 1) offers little benefit and only exports emissions downwind, whereas FGD (Measure 2) is the only option that reduces total SO₂ mass released without abandoning the existing fuel-supply infrastructure that a full fuel switch (Measure 3) would require.