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Often, fuel gases such as butane and natural gas (methane) are mixed with some foul-smelling impurities such as thiols (mercaptans) and hydrogen sulfide. Presumably, anything containing sulfur would burn to sulfur dioxide. The odor of sulfur dioxide is not easily noticed while burning such fuels, but I presume that the large amount of fuel gases burnt in the world would cause a significant amount of $\ce{SO2}$ emissions.

Why is this not usually brought up? Are the amounts actually so small that they are completely insignificant?

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    $\begingroup$ insignificant compared to release of SO2 due to burning of coal around the world, $\endgroup$ – Khan Sep 15 '16 at 4:48
  • $\begingroup$ The odorants might be partly responsible for the buildup of a white crust (corrosion?) around pilot-light nozzles, though. But as @Khan states, the amount of sulfur added is minuscule. $\endgroup$ – DrMoishe Pippik Sep 15 '16 at 23:56
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According to this North American Energy standards board publication , the total concentration of sulfur in natural gas, both natural and from oderant additives, must not exceed $\pu{70 ppbv}$. Concentrations are actually more commonly about a tenth of this. For example, from the same source, the Union Gas system typically contains about $\pu{5 ppbv}$ sulfur. Furthermore, the sulfur content of coal is many orders of magnitude higher than that of oderant-enriched natural gas at about $\pu{0.5 to 5\%}$ sulfur, and the worldwide combustion of coal is much greater than that of natural gas (although much of the sulfur from coal combustion is now scrubbed out at the source of combustion). Other fossil fuels like diesel also contain significant amounts of sulfur (regulatory sulfur content of diesel fuel in the US and EU was 10 ppm as of 2009).

The global atmospheric background concentration of $\ce{SO2}$, according to Owen, Lewis A.; Pickering, Kevin T (1997). An Introduction to Global Environmental Issues. Taylor & Francis. pp. 33–. ISBN 978-0-203-97400-1, is around $\pu{1 ppbv}$, meaning the sulfur content of the Union Gas product, for example, is only five times that that found throughout the Earth's atmosphere.

Summary - TL/DR:
Based on the background $\ce{SO2}$ concentration and the overwhelming sulfur emision source from the combustion of coal and other fossil fuels, the sulfur originating from natural gas oderant additives represents a negligible contribution to the global atmospheric $\ce{SO2}$ concentration.

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