How do steampunk civilizations get lifting gas?
Inspired by the above question I was tempted to suggest collecting the gases rising from public toilets.
I know that human gaseous emissions contain varying proportions of oxygen, nitrogen, carbon dioxide, hydrogen and methane.
https://en.wikipedia.org/wiki/Flatulence#Production,_composition,_and_smell
Some of these are lighter than air and some are heavier than air.
Judging by answers to this question https://chemistry.stackexchange.com/questions/61140/why-dont-heavy-and-light-gases-separate-in-the-atmosphere it would be possible to engineer an environment that allows the gases to separate.
Question
By removing turbulence due to draughts, can I rely on the lighter gases such as hydrogen and methane rising from the toilets where they can be collected. Will the heavier sink to the floor where they can be drained away? If not, how can I most efficiently separate them in situ without using chemistry or endangering the clientele?