Would we be able to breathe inside a 20 km deep hole?

Let’s say we find a way to survive the massive heat that would be found on such a depth. Or let’s say that God Almighty managed to dig this hole and make it not outstandigly warm. Air pressure increases as we go down. Would we be able, then, to breath down there? On which height this would start to become an issue?

From this paper, "Barometric hazards within the context of deep-level mining,"Journal of The South African Institute of Mining and Metallurgy July 2005, Volume 105, comes the following quote on potential barotrauma in deep mines:

The Van der Linde paper is: VAN DER LINDE, A., VAN RENSBURG, J.P., and KIELBLOCK, A.J. “The physiological
effects of daily atmospheric pressure oscillations on workers in deep-level mines.” Research Report No. 9/86, Johannesburg: Chamber of Mines of South Africa. 1986

There are accounts that suggest that ambient pressure at the lowest levels of some of the South African Deep Levels mines, such as Mponeng or TauTona, over 3900 meters deep, reaches roughly twice that of sea level. That strikes me as really, really high, given the authors of the previous paper note that,

A paper where the authors attempted to model ambient pressures in deep mines may be found here. Tan, A., Zhang, T.X., and Wu, S.T., “Pressure and Density of Air in Mines,” Indian Journal of Radio and Space Physics, Vol. 37, February 2008, 64-67. They did not come to a figure of double sea level pressure, but they did note cites that claimed such.

I’d start to be a bit worried about susceptibility to O2 toxicity, 20,000 m down, and if we believe the South Africa estimate, an increase in 2.2 atmospheres of pressure. For those who scuba dive, do you really start getting ‘narced’ at (2.2 atm X ~32 ft seawater) 70 feet down?

Typically at 100 feet or greater, but each person is different (but 70 is way below where one could expect that) . This is nitrogen narcosis, a drunk like feeling, the dreaded ‘bends’ is a different thing which has to do with decompression.

It’s a lot more than that due to the exponential nature of pressure vs. altitude: going down twice as far more than doubles the pressure increase because you have to support both the original air column and the additional air column from the increased depth.

If this calculator is to believed, the pressure increase at 5 km down is 68%, while at 20 km down it’s 409%.

Derp. They even mentioned its exponential nature in one of the papers I mentioned. It pays to read, I guess. 4.09 x 32 is 130 ish feet, and though the closest I’ve come to scuba is reading Shadow Divers and seeing “Open Water,” 130 feet is starting to get serious on compressed air.

Plus at 130 feet if you’ve only got a single 80 cubic foot tank you’re going to go through it in around 10 minutes, while miners could be expected to spend many hours at depth. I assume they’d work a 12 hour shift to minimize time lost in transporting workers up and down the elevators.

I’ve been on air down to 110 ft, with no observed ill effects or narcosis - though of course self-diagnosing nitrogen narcosis is pretty difficult. But from tech diving and hardhat diving I’ve read about - there’s no issue with being at 4 atm pressure for several hours - the problem is in returning to 1 atm. They usually have to stage their way back up over several hours to avoid decompression sickness and barotrauma.

I felt a pleasant effect about at 100 ft it was not overly noticeable but also hard to deny too FWIW & YMMV