Emission Rate from Stack Concentration

Concentration says how dirty the exhaust is; emission rate says how much pollutant is actually reaching the atmosphere, and only the second one is a quantity of anything. Multiply them: 250 mg/m³ leaving a stack that moves 20 m³/s is $250 \times 10^{-6} \times 20 = 5 \times 10^{-3}$ kg/s, which is 5 g/s or 18 kg/h. That number is the source strength every dispersion model asks for and the quantity most permit limits are written against, precisely because it cannot be improved by adding air.

The whole difficulty is basis matching, and it is worth being pedantic about it because the errors are large and invisible. A concentration reported dry, at a standard temperature, corrected to a reference oxygen, is a number about a hypothetical gas stream. The flow it must be multiplied by has to describe that same hypothetical stream. Multiplying an oxygen-corrected concentration by the actual wet flow double-counts the dilution and can be wrong by a factor of two, and the answer will look entirely reasonable on the page. The reliable habit is to write the basis beside every number in the calculation — dry standard cubic metres at 25 °C corrected to 3 % O₂, or actual cubic metres at stack conditions — and to refuse to multiply two numbers whose labels do not match.

Standard conditions are themselves a trap, because there is no single standard. US EPA methods use 20 °C and 101.325 kPa, industrial hygiene and most ppm-to-mg/m³ conversions use 25 °C, European emission limits use 0 °C, and the gas industry has its own. Between 0 and 25 °C the volume of a given amount of gas differs by 9 %, so a flow carried across a reference-state boundary without correction carries a 9 % error straight into the emission rate. Converting between them is just the ideal gas law, $Q_2 = Q_1 T_2/T_1$ at constant pressure, and it takes ten seconds. Not doing it takes a re-test.

One more thing worth knowing: permits do not always want mass per unit time. Combustion sources are frequently limited on a heat-input basis, in ng/J or lb per million BTU, because that normalises for the size of the unit and cannot be gamed by either dilution or throughput. Getting from this equation's answer to that basis needs the fuel firing rate and its heating value, and the arithmetic is a simple division — but the reason the regulator asked for it is worth remembering. Every step in the reporting chain, from oxygen correction to heat-input normalisation, exists to defeat a way of making an emission look smaller without emitting less.