Baghouse Sizing, Emissions Monitoring and Gaseous Pollutant Behaviour: 18-Env-A5 Air Quality and Pollution Control Engineering, December 2016, Q5

Problem 5: Baghouse Sizing, Emissions Monitoring and Gaseous Pollutant Behaviour (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.

Part (i) — baghouse sizing.

Given.

Quantity	Value
Gas flow, $Q$	50,000 SCFM = 23.61 m³/s
Gas-to-cloth ratio, $u_0$	0.7 m/min (= 0.01167 m/s)
Inlet dust conc., $c_0$	10 g/m³ (= 0.010 kg/m³)
Cleaning cycle	reverse-flow, once per hour $\Rightarrow t=1$ h = 3,600 s at max loading
Bag size	10 in dia. × 15 ft, 39.09 ft²/bag = 3.632 m²/bag
Dust-cake constants	$K_1=350$ (paired with $u_0$ in m/min), $K_2=9\times10^4$ s⁻¹ (paired with $u_0$ in m/s, $c_0$ in kg/m³, $t$ in s)

Find. The number of bags required and the overall (maximum) pressure drop across the bags.

Approach. Size the total cloth area from $Q$ and the gas-to-cloth ratio, divide by one bag's area to get the bag count; then evaluate the given two-term pressure-drop model at the end of the 1-hour filtration cycle (worst case, just before cleaning).

Total cloth area needed. $$A_{total}=\dfrac{Q}{u_0}=\dfrac{23.61\ \text{m}^3/\text{s}}{0.01167\ \text{m/s}}=2{,}024\ \text{m}^2$$
Number of bags. $$n=\dfrac{A_{total}}{A_{bag}}=\dfrac{2{,}024}{3.632}=557.3 \Rightarrow \boxed{558\ \text{bags (round up)}}$$
Pressure drop — clean-cloth/support term. $K_1$'s stated units (N·min/m³) pair with $u_0$ in m/min: $$\Delta P_1 = K_1 u_0 = 350\times0.7 = 245\ \text{Pa}$$
Pressure drop — dust-cake term. $K_2$'s stated units (s⁻¹) require SI (m/s, kg/m³, s): $$\Delta P_2 = K_2\, c_0\, u_0^2\, t = 9\times10^4\times0.010\times(0.01167)^2\times3{,}600 = 441\ \text{Pa}$$
Total pressure drop. $$\boxed{\Delta P = \Delta P_1+\Delta P_2 = 245+441=686\ \text{Pa}}$$ Converting with the supplied factor ($0.0003391$ ft H₂O/Pa): $$686\times0.0003391=0.2328\ \text{ft H}_2\text{O}=2.79\ \text{in.\ H}_2\text{O}$$

Quantity	Result
Total cloth area required	2,024 m²
Number of bags	558
Pressure drop, clean-cloth term	245 Pa
Pressure drop, dust-cake term	441 Pa
Overall pressure drop	686 Pa ≈ 2.79 in. H₂O

[Figure not reproduced: Baghouse process schematic. See the official exam paper or the cited reference text.]

Reverse-air baghouse train for the lime kiln: dirty gas from the kiln enters the compartmentalised baghouse (558 Nomex bags sized above); the cloth layer plus the building dust cake capture ≥99% of the lime dust, which is dislodged by the once-per-hour reverse-air pulse into the hopper below, while clean gas exits to the stack.

Check: the two velocity figures the exam supplies for $u_0$ (0.7 m/min and 0.01167 m/s) are used deliberately — one per K-constant, matched to the units each constant is stated in; both terms independently evaluate to a physically reasonable pressure drop (100s of Pa), which is a strong self-consistency check on this pairing. The stated 99% removal target and the 162.8 °C/23.61 m³/s SCFM flow are not separate inputs to the bag-count or $\Delta P$ formulas as given — they describe the duty the sizing must satisfy, not additional terms in the two supplied equations.

Part (ii) — stack-emission monitoring techniques. Particulate: an in-stack opacity monitor / transmissometer continuously measures light attenuation across the duct as a real-time surrogate for particulate loading, used for continuous compliance demonstration. CO: a non-dispersive infrared (NDIR) analyser extracts a sample and measures infrared absorption at CO's characteristic wavelength — fast, selective and the standard reference method. SOₓ: a pulsed-fluorescence analyser excites SO₂ with UV light and measures the resulting fluorescence intensity, which is proportional to SO₂ concentration — highly sensitive and specific, and is EPA/CCME's reference method for continuous SO₂ monitoring.

Part (iii) — atmospheric behaviour of CO and SO₂. CO is chemically fairly stable in the lower troposphere; it is slowly oxidised to CO₂ primarily by reaction with the hydroxyl radical (OH), giving it an atmospheric residence time on the order of one to a few months, long enough to be transported regionally/hemispherically before removal — it does not readily form secondary particulate or acid deposition. SO₂, by contrast, is reactive: it oxidises in the atmosphere (both gas-phase, via OH, and in cloud droplets) to sulphate ($\text{SO}_4^{2-}$) aerosol and sulphuric acid over a period of hours to a few days, so its residence time is much shorter, but that same reactivity makes it the principal precursor of acid rain and fine secondary sulphate particulate, giving it a more regional (rather than global) impact than CO.

Topic: Fabric-filter (baghouse) sizing and continuous emissions monitoring.

Key relations: $A=Q/u_0$ (gas-to-cloth ratio sizing); $\Delta P=K_1u_0+K_2c_0u_0^2t$ (fabric-filter pressure-drop model, clean-cloth term + dust-cake term).

Why this works: the gas-to-cloth ratio is an empirical face-velocity limit below which the cloth+cake combination will not blind or re-entrain dust; the pressure-drop model is linear in the clean-media resistance and grows with the square of face velocity through the cake resistance, which is why baghouses are always operated at low face velocity relative to, say, a packed scrubber.

Common pitfall: using the same velocity unit for both $K_1$ and $K_2$ terms when the constants are stated in different unit systems, and forgetting that "the maximum pressure drop" corresponds to $t$ = the full time since the last cleaning cycle, not an average value.

Source: Cooper & Alley, Air Pollution Control: A Design Approach, 4th ed., Ch. 5 (Fabric Filters); CCME reference-method summaries for continuous emissions monitoring.

Question 5 of 7: Baghouse Sizing, Emissions Monitoring and Gaseous Pollutant Behaviour

Problem 5: Baghouse Sizing, Emissions Monitoring and Gaseous Pollutant Behaviour (20 marks)