What do you assume the percent remaining is if not mass?
Yes, the assumption in the charts is that the O2 concentration at the start is 21% by weight, 21% by mole or 210,000 ppm (all the same thing). Safe assumption is that in this case we can treat the opened keg the same way. Notice the scale is not linear in these graphs. After 2 purges we are down to at least 75,000ppm or 7.5% (total by weight) air. Probably close to if not lower percentage than you would get by opening the lid, maybe using the charts in this situation will end up conservative by a purge, two stretching it.
you are both somewhat correct.
I am with Magic Matt in saying that a half-empty keg is likely to have a lot more air getting in than a full keg, and therefore will require a few more purges than a full keg to get to the same purge level. Each purge will reduce oxygen by the same ratio, regardless of total volume. So if you start with say 1L of air in half-full keg, vs. 0.125L of air in another, say full keg and each purge reduces it by say a factor of 2, it will take 3 purge cycle on first keg to get to the same amount of air as second keg.
But because we are normalizing ppm by the mass of beer in the keg, there's another factor of 2 for half-empty keg (less beer to adsorb oxygen), so you would need 4 more purge cycles for half-full keg with 1L of air in headspace to get to the same ppm as in full keg with 0.125L of air in headspace.
But I don't think you need 12 purges either. In your example above, I don't see how you get that 21% oxygen in headspace is 210,000 ppm. That's not correct - you need to normalize oxygen to beer (water) in the keg. The idea is most oxygen will get dissolved into beer eventually, so when someone says you want to keep oxygen <1 ppm say, it's oxygen to liquid ratio.
You need to calculate weight of oxygen in grams (1 L of air would contain 1/22.4*0.22 moles of oxygen, or about 0.3 grams), divided by 10kg or so (half full keg, 2.5 Gallons) of beer, or about 30 ppm.
So if you want to get below 1 ppm of oxygen, and each purge cuts amount of oxygen in half you will need 2^5=32, or 5 purges at ~14 psi or so.
If you started with say ~10L of air, or 300ppm (completely filled half of the keg with air), you will need another 3-4 purges or total of say 9 purges to get down below 1ppm. So maybe 12 purges is a bit of an overkill.
Matt, Doug - check my math please.
[EDIT: some people like techbrau advocate getting to below 0.15 ppm of oxygen in packaging, which means another ~3 purges, so maybe 12 or more purges is then justified from this perspective]