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To those who think it sounds impossible, remember that methane is CH4 and a good amount of the energy released is attributable to those hydrogens getting together with oxygen. So you are basically subtracting the yield from carbon.

Wouldn’t it be a lot better though to somehow turn CH4 into hydrogen and carbon, bury the carbon or use it for uses that don’t end up in the atmosphere, and burn the hydrogen alone or use it in fuel cells? Fuel cells might get you to pretty good energy yields.