Excess Air from Flue Gas Oxygen

Burn a fuel with exactly the air the chemistry requires and the flue gas contains no oxygen at all. Every molecule of oxygen you find afterwards arrived in air that was not needed, so the leftover oxygen is a direct measure of the surplus. Since that surplus air is 20.9 % oxygen and the rest of it, mostly nitrogen, passes through unchanged, the excess air works out as $EA = O_2/(20.9 - O_2)$: the oxygen measured, divided by the part of the sample that is not excess air. Five percent oxygen in the flue gas means $5/15.9 = 0.314$, or 31 % excess air. It is a two-second calculation off any combustion analyser and it is the most useful single number in boiler tuning.

Why it matters is stack loss. Every cubic metre of air beyond stoichiometric is heated from ambient to stack temperature and thrown out of the chimney, and that heat comes out of the fuel bill. As a rough figure, each 15 % of excess air costs about a percentage point of thermal efficiency on a typical boiler, and the effect compounds with stack temperature: the same surplus air is far more expensive on a 260 °C stack than on a 150 °C one. Sensible operating bands are 10 to 15 % excess air on natural gas, 15 to 25 % on oil, and 20 to 40 % on coal, with the fuel's ability to mix with air setting the floor. Anything far above the band means either the air-fuel ratio is set badly or tramp air is leaking into the boiler casing and the breeching, and a reading that climbs steadily at fixed firing rate is almost always the second one.

The relation carries an approximation worth naming. It assumes combustion is complete, so that all the fuel's carbon and hydrogen have taken their oxygen and the only oxygen left is surplus. Near stoichiometric that stops being true: mixing is never perfect, some fuel finds no oxygen while some oxygen finds no fuel, and carbon monoxide appears in the flue while oxygen is still being measured. The equation then reads low on the true air requirement and dangerously high on the efficiency. This is exactly why modern burner controls trim to carbon monoxide rather than to oxygen once the excess air is below about 15 %: CO is the direct evidence of unburned fuel, and oxygen alone cannot see it. The refined form of this equation subtracts half the CO from the oxygen for that reason.

Two practical cautions. The reading must be on a dry basis, which is what a conventional analyser with a chiller or a permeation dryer gives you; a wet in-situ zirconia cell reads a lower oxygen because water vapour is diluting the sample, and putting that number into this equation under-states the excess air. And use 20.9 rather than 21 for consistency with the emission-correction convention — the difference is under half a percent and matters mainly because mixing the two constants across a report invites a reviewer to ask which other constants were improvised. Finally, remember what excess air is not: it is not a measure of combustion quality, only of quantity. A burner can run at a textbook 12 % excess air and still make carbon monoxide if the flame is impinging or the atomisation is poor.