Control of Gas and Vapour Emissions — Cyclones, Adsorption and Incineration: 18-Env-A5 Air Quality and Pollution Control Engineering, December 2014, Q7

Question 7: Control of Gas and Vapour Emissions — Cyclones, Adsorption and Incineration (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) Cyclone Cut Diameter and Collection Efficiencies

Given. A large-diameter cyclone removing grain dust:

Given data
Quantity	Symbol	Value
Particle diameters	$[d_p]$	20, 40, 60, 80 µm
Inlet width	$B_c$	0.3 m
Inlet gas velocity	$v_i$	25 m/s
Particle density	$\rho_p$	1100 kg/m³
Gas viscosity	$\mu_g$	$1.9\times10^{-5}$ kg/(m·s)

Find. The theoretical cut diameter $[d_p]_{cut}$, and the fractional collection efficiency at each of the four particle sizes from the "50% η" curve.

Approach. Compute $[d_p]_{cut}$ directly from the supplied formula, then read the collection efficiency at each of the four given particle sizes off the specified "50% η" curve (plotted against actual particle size, not a normalized ratio).

Compute the theoretical cut diameter. $$[d_p]_{cut} = \sqrt{\frac{9\mu_g B_c}{2\pi v_i \rho_p}} = \sqrt{\frac{9(1.9\times10^{-5})(0.3)}{2\pi(25)(1100)}} = \boxed{17.2\ \mu\text{m}}.$$
Read the "50% η" curve at each given particle size. The chart's x-axis is the actual particle diameter (log scale, 10–100 µm) with three efficiency curves; the question specifies using the rightmost, dotted "50% η" curve (lowest efficiency for a given size — the correct choice for a large, lower-efficiency cyclone). Reading the calibrated chart (Fig. 7.1) at each of the four sizes gives the values in the table below.

[Figure not reproduced: Cyclone fractional collection efficiency vs. particle size, curves C1, C2 and 50% eta. See the official exam paper or the cited reference text.]

Fig. 7.1 — Source chart: fractional collection efficiency vs. particle size for three cyclone curves (C1, C2, 50% η). Per the question, the dotted "50% η" curve (rightmost, i.e. lowest efficiency for a given size, appropriate for a large-diameter/coarser-cut cyclone) is read at d_p = 20, 40, 60, 80 µm.

Quantity	Value
Theoretical cut diameter, $[d_p]_{cut}$	17.2 µm
Efficiency at $d_p=20\ \mu\text{m}$	≈ 4%
Efficiency at $d_p=40\ \mu\text{m}$	≈ 8%
Efficiency at $d_p=60\ \mu\text{m}$	≈ 24%
Efficiency at $d_p=80\ \mu\text{m}$	≈ 70%

Check: the printed "50% η" curve is read directly against actual particle size, as the question instructs, and no rescaling by $[d_p]_{cut}$ is applied. Note the resulting readings are internally consistent with the curve's own name only in the sense that its OWN 50%-efficiency crossing (log-interpolating between the 60 and 80 µm reads above) falls near 70 µm — about four times the 17.2 µm theoretical cut diameter from the idealized Lapple-type formula. This gap is expected, not an error: the formula gives an idealized inertial-separation cut size, while the printed curve is an empirical performance curve for an actual (coarser-cutting, lower-efficiency) large-diameter cyclone, which is precisely why the question specifies using this particular curve rather than the theoretical value alone. Chart reads carry the usual ±5% engineering tolerance of a value read off a printed curve.

(ii) Adsorption System for VOC Emission Control

A common industrial application is fixed-bed activated-carbon adsorption to recover a solvent vapour (e.g., toluene) from a paint-booth or printing-press exhaust before it is released to atmosphere. VOC-laden air is drawn through a bed of granular activated carbon; the toluene molecules are physically adsorbed onto the carbon's internal surface (specific surface area on the order of 1000 m²/g) while clean air passes through to the stack. Once the bed approaches saturation (detected by a rise in outlet VOC concentration, i.e. breakthrough), the airflow is switched to a second, freshly regenerated bed (a lead-lag pair keeps the system running continuously), and the saturated bed is regenerated in place with low-pressure steam, which desorbs the toluene. The steam/toluene vapour mixture is condensed and gravity-separated in a decanter (toluene is only weakly water-soluble), recovering the toluene for reuse or resale and regenerating the carbon bed for the next cycle.

Fig. 7.2 — Fixed-bed activated-carbon adsorption schematic with steam regeneration and solvent recovery.

(iii) Incineration System — Thermal Oxidizer Design for 99.9% Efficiency

A representative example is a thermal (direct-flame) oxidizer treating a solvent-laden process exhaust (e.g., from a coating or resin-curing line). Reliable destruction of organic vapours to a guaranteed 99.9% destruction/removal efficiency (DRE) is governed by the classical "three T's" of combustion: Temperature — the combustion chamber is maintained at 980–1100 °C (well above the auto-ignition temperature of the target compounds, with margin for the least-reactive species present), typically sustained by an auxiliary natural-gas burner supplementing the process stream's own heating value; Time (residence time) — the chamber is sized so that combustion gases spend a minimum of 0.75–1.0 s at the design temperature before exiting, ensuring the oxidation reactions run to completion rather than being quenched partway; Turbulence — burner and chamber geometry are designed to thoroughly mix the waste gas with combustion air and the flame zone (baffled or swirl-inducing chamber inlets), eliminating cold, unmixed pockets that would otherwise bypass complete oxidation. A recuperative or regenerative heat exchanger commonly preheats incoming process air with the hot exhaust, both reducing auxiliary fuel consumption and, for regenerative systems, extending effective residence time. Continuous monitoring of chamber temperature (interlocked to a fuel/waste-feed cutoff on any temperature excursion below the validated minimum) and periodic stack testing against a CO or THC (total hydrocarbon) surrogate together provide ongoing assurance that the 99.9% DRE demonstrated during commissioning is being sustained in routine operation.

Concept & Theory

Topic. Inertial (cyclone) particulate separation theory vs. empirical performance curves, activated-carbon vapour recovery, and thermal-oxidizer destruction efficiency.

Key relations. Lapple-type cut diameter $[d_p]_{cut}=\sqrt{9\mu_g B_c/(2\pi v_i\rho_p)}$; adsorption breakthrough governed by the carbon bed's equilibrium isotherm and empty-bed contact time; thermal DRE controlled by the "three T's" (temperature, time, turbulence), with Arrhenius-type destruction kinetics meaning DRE is exponentially sensitive to chamber temperature.

Why this works. A cyclone separates by centrifugal force overcoming drag, exactly analogous in form to gravity settling (Question 1's underlying Stokes balance) but with a much larger effective "g" from the swirling flow, which is why cyclones handle far smaller particles than a simple settling chamber at the same footprint; activated carbon works because Van der Waals physisorption onto an enormous internal surface area is reversible with heat, which is what makes steam regeneration (rather than disposal) economically attractive; and thermal oxidation works because virtually any organic compound will fully oxidize to CO₂ and H₂O given enough temperature, time and mixing, which is why the three-T's framework transfers unchanged across almost any VOC destruction application.

Common pitfall. Assuming a higher chamber temperature alone guarantees higher DRE — without adequate residence time and turbulence to bring every parcel of waste gas to that temperature, cold/unmixed pockets can still bypass destruction even in a chamber whose bulk average temperature looks adequate on the control-room readout.

Source. Cooper & Alley, Air Pollution Control, ch. 6 (cyclones), ch. 9 (adsorption) and ch. 7 (thermal incineration, the three T's).

Question 7 of 7: Control of Gas and Vapour Emissions — Cyclones, Adsorption and Incineration

Question 7: Control of Gas and Vapour Emissions — Cyclones, Adsorption and Incineration (20 marks)

(i) Cyclone Cut Diameter and Collection Efficiencies

(ii) Adsorption System for VOC Emission Control

(iii) Incineration System — Thermal Oxidizer Design for 99.9% Efficiency