Question 5 of 6: Flammability Diagram, Explosion Types, and Dust Explosions

Question 5: Flammability Diagram, Explosion Types, and Dust Explosions (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.

(a) Flammability diagram for butane

Part (a) —

Given. Combustion stoichiometry $C_4H_{10}+6.5\,O_2\rightarrow4\,CO_2+5\,H_2O$, i.e. $z=6.5$ mol O₂ consumed per mol butane.

Find. The lower flammable limit (LFL), upper flammable limit (UFL), and limiting oxygen concentration (LOC), and a flammability diagram showing the flammable region.

Approach. With only the balanced combustion equation given (no tabulated LFL/UFL), use the standard stoichiometry-based estimation: compute the stoichiometric fuel concentration in air $C_{st}$, then apply the empirical proportionality rules $LFL\approx0.55\,C_{st}$ and $UFL\approx3.5\,C_{st}$ (Crowl & Louvar), and $LOC=z\times LFL$.

1. Stoichiometric fuel concentration in air. For 1 mol fuel with $z$ mol O₂ (and the associated $3.76z$ mol N₂ from air): $$C_{st}=\frac{100}{1+4.76z}=\frac{100}{1+4.76(6.5)}=\boxed{3.13\%\ \text{fuel}}$$
2. Lower and upper flammable limits. $$LFL\approx0.55\,C_{st}=0.55(3.13)=\boxed{1.72\%}$$ $$UFL\approx3.5\,C_{st}=3.5(3.13)=\boxed{10.96\%}$$
3. Limiting oxygen concentration. $$LOC=z\times LFL=6.5(1.72)=\boxed{11.19\%\ O_2}$$

The calculated limits bracket the tabulated experimental values for butane reasonably well (literature: LFL ≈ 1.8%, UFL ≈ 8.4%, LOC ≈ 12%): the stoichiometry-based LFL and LOC estimates are close, while the UFL rule of thumb runs somewhat rich of the measured value, which is the well-documented weaker side of this estimation method — the 0.55/3.5 multipliers are fitted averages across many hydrocarbons and are more reliable for LFL than UFL. The diagram's four labelled regions (too lean, too rich, oxygen-starved, and flammable) are read directly off the air-dilution line and the LOC line.

(b) Deflagration vs. detonation

Part (b) — A deflagration is a subsonic combustion wave: the reaction front propagates by conductive/diffusive heat and mass transfer into the unburned mixture, at a flame speed below the local speed of sound, and the pressure rise it produces (typically up to about 8× the initial absolute pressure in a fully confined vessel) runs AHEAD of the reaction front as an ordinary pressure wave, not a shock. A detonation is a supersonic combustion wave: the reaction front is directly coupled to, and travels WITH, a leading shock wave that compresses and auto-ignites the unburned mixture just ahead of it (the Chapman–Jouguet mechanism), producing propagation speeds of order 1,500– 2,000 m/s and peak pressures of order 15–20× the initial pressure, far more destructive than a deflagration of the same fuel/air mixture. A deflagration can transition to a detonation (DDT) in a long, congested, or partially confined path (e.g. a pipe run with obstacles) as turbulence progressively accelerates the flame front until it outruns the speed of sound in the unburned gas.

(c) Conditions required for a dust explosion

Part (c) — A dust explosion requires the ordinary fire triangle (fuel, oxidiser, ignition source) PLUS two additional conditions unique to a combustible solid, together forming the "dust explosion pentagon": (1) combustible dust below a critical particle size (fine enough to burn essentially as fast as a gas once airborne); (2) an oxidiser, normally the oxygen in ambient air; (3) an ignition source of sufficient energy (spark, hot surface, friction, static discharge) to exceed the dust's minimum ignition energy; (4) dispersion — the dust must be suspended as a cloud within its explosible concentration range (between its minimum explosible concentration and an upper limit), not merely lying as a settled layer; and (5) confinement sufficient to allow pressure to build (an unconfined dust cloud typically produces a flash fire rather than a damaging overpressure). All five must be present simultaneously; removing any single one (e.g. housekeeping to prevent a settled-layer secondary dust cloud, or inerting to remove the oxidiser) prevents the explosion, the same control philosophy as Heinrich's domino chain in Question 1(a).