Air Pollutant Dispersion & Emission Control Design

How pollutants spread in the atmosphere and how we control them. Learn the atmospheric boundary layer, lapse rates and stability classes, wind profiles, the Gaussian plume model and dispersion coefficients, effective stack height and plume rise, maximum ground-level concentration, stack design, air-quality indices, and control devices (cyclones, bag filters, ESPs, scrubbers, SCR) with efficiency calculations — with Python for a Gaussian plume.

Once pollutants leave a stack or exhaust pipe, the atmosphere transports and dilutes them. How much reaches people depends on wind speed, turbulence (atmospheric stability), stack height and terrain. The Gaussian plume model estimates these ground-level concentrations and is the basis of regulatory models.

Engineering controls reduce emissions at source; dispersion modelling checks that what remains meets ambient air-quality standards.

An analogy

A plume is like ink in a moving stream: the current (wind) carries it downstream while eddies (turbulence) spread it sideways and vertically. A taller stack is like releasing the ink higher above the riverbed — it has spread out more before it touches bottom.

Atmospheric stability

Air cools with height (dry adiabatic lapse rate ≈ 9.8 °C/km). If the real atmosphere cools faster, rising air keeps rising — unstable (sunny afternoons, good dispersion). If it cools slower or warms with height (inversion), air resists vertical motion — stable (clear nights, poor dispersion, smog). Pasquill–Gifford classes A (very unstable) to F (stable) summarise this.

Plume behaviour and stack height

Plume shapes: looping (unstable), coning (neutral), fanning (stable), fumigation and lofting (inversions). Effective height adds plume rise from momentum and buoyancy (Briggs formulas). Maximum ground concentration scales roughly with 1/H², so doubling the effective height cuts it by about 4× — the 'tall stack' approach (which disperses rather than removes pollution).

Control devices

Match device to pollutant:

Regulatory models and air-quality management

AERMOD (steady-state Gaussian with boundary-layer meteorology and terrain) and CALPUFF (puff model for long range) are regulatory standards; CFD and chemical transport models (CMAQ, WRF-Chem) handle urban and regional air quality including secondary pollutants (PM2.5, ozone). Air-quality indices (AQI) communicate health risk; emission inventories and source apportionment guide policy.

Formulas

Worked example: Devices in series

Given: Cyclone 80% then bag filter 99.5%

Find: Overall efficiency.

Answer: 99.9%

Worked example: ESP collection area

Given: Q = 200 m³/s, w = 0.1 m/s, target 99%

Find: Plate area.

Answer: 9210 m²

Worked example: Wind at stack height

Given: u₁₀ = 4 m/s, p = 0.15, h = 60 m

Find: u(60).

Answer: 5.2 m/s

Gaussian plume ground-level concentrations

import math
# Gaussian plume: ground-level centreline concentration downwind of a stack
Q = 100.0                  # g/s SO2
u = 5.0                    # m/s wind at stack height
H = 60.0                   # effective stack height, m
# Briggs rural, stability class D: sy = 0.08x(1+0.0001x)^-0.5, sz = 0.06x(1+0.0015x)^-0.5
def conc(x):
    sy = 0.08 * x / math.sqrt(1 + 0.0001 * x)
    sz = 0.06 * x / math.sqrt(1 + 0.0015 * x)
    return Q / (math.pi * u * sy * sz) * math.exp(-H**2 / (2 * sz**2)) * 1e6   # ug/m3
best = max(range(100, 20001, 50), key=conc)
for x in (500, 1000, best, 5000):
    print(f"x = {x:5d} m: C = {conc(x):7.1f} ug/m3")
print(f"maximum ground-level concentration at about {best} m downwind")
# x =   500 m: C =   217.2 ug/m3
# x =  1000 m: C =   630.1 ug/m3
# x =  1050 m: C =   631.2 ug/m3
# x =  5000 m: C =   159.8 ug/m3
# maximum ground-level concentration at about 1050 m downwind

Concentration is zero at the stack base, peaks about 1 km downwind where the plume first reaches the ground, then falls. 631 µg/m³ of SO₂ (1-hour) is far above India's 24-h standard of 80 µg/m³ — this source needs a scrubber or a taller stack.

Common mistakes

Applications

Key takeaways

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