How can I estimate how far into a cave network breathing is possible?

I want two populations to coexist in a world with extensive tunnels carved into the rock. One population lives in the tunnels, coming out to trade and gather food. The other is aware of the tunnels but is wary of entering them.

I want the tunnels to go far enough that after a certain point there is insufficient air flow to maintain enough oxygen to breathe. The tunnel dwellers are well aware of this effect and know to only venture that far for short periods to avoid asphyxiation. To the surface dwellers they spread rumours that only the tunnel dwellers are capable of breathing the tunnel air, despite the fact that the regions where the tunnel dwellers live has perfectly breathable air for both populations (which are both human).

For tunnels that are mostly just over head height and arm span width, occasionally widening into rooms, after what distance into the tunnels would breathing no longer be sustainable? The tunnels are carved by humans, not by underground rivers, so they have no other end to create airflow from pressure differences.

Following Monty Wild's answer here is some further detail. The tunnels are carved horizontally into sandstone. The humans carry candles and oil lamps with them when travelling further into the tunnels. There are over 50 separate entrance tunnels each leading to its own main chamber after about 40 metres, in which small wood fires are kept burning for heating and cooking. Further tunnels continue from the main chamber, branching and opening into chambers for storage. Some of these tunnels connect the main chambers to each other, but there is no interconnection between tunnels further in than the main chambers. Each of the main chambers is about twice human height and about 300 metres square in floor area (a circle roughly 20 metres in diameter).

I'm looking to estimate whether a group of humans could survive in the main chambers, and if so how much further into the tunnels beyond they could travel before breathing became impossible.

posted over 9 years ago

trichoplax‭

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