Interesting idea. It's not a bad concept, but there are some logistics to consider (it's not impossible to do this if one is "inventive").
As noted earlier, most home shop compressors use an oil-filled crankcase and even when they are new, there is oil in the compressed air... but let's assume that one has an oil-less home shop compressor (it just so happens that mine is oil-less, with a 60 gallon tank). While most home-shop compressors have a 20 gallon tank, let's assume that like me, you have a 60 gallon tank.
These figures are off the top of my head, so check my numbers: A US fluid gallon is defined as 231 cubic inches. So a 60 gallon tank is close enough to 8 cubic feet. My compressor, like most single stage home compressors, shuts off at 120 psi. Disregarding any post-compression cycle pressure drop from the gas temperature dropping (ideal case), no leak down, perfect gas, etc, and assuming we start at 14.7 psi, we would stuff a total of about 65.3 cubic feet of air in the tank. Assuming we're breathing it at very close to 14.7 psi, and assuming we tried very hard to suck all the air out with a regulator/respirator, we could get about 65.3 - 8 = 57.3 cubic feet of air out of that 60 gallon tank. (someone should check my math, but that sounds about right - one order of magnitude increase in pressure will give us one order of magnitude increase in mass given a constant volume and temperature) (Sorry; I'm too lazy right now to convert all this to SI units - ask if you need it converted and I will)
SCUBA guys, how long will that last at the surface (14.7 psi to keep the numbers consistent)? I can figure out a guess from 95th percentile respiration rate and volume, but you divers can prol tell us real quickly.
But note that I mentioned a respirator - you have to cycle all 57 cubic feet thru your lungs to get whatever duration (I'm guessing less than an hour). If you simply vent it into the closet, you will have to waste air - or your closet becomes a pressure tank. Also, there is the CO2 and transpired/respired H2O vapor problem...
We can make an improvised scrubber for the CO2 and we can deal with most of the H2O vapor in a similar fashion, so it's not impossible... also, we can easily make up a reliable (gravity is reliable) and accurate waste valve for the closet to keep a small positive pressure on (only a few inches of water column is plenty of positive pressure - 1/2 psi would probably be over kill and probably be hard on the average house construction). Forget the H2O vapor build up - let it get a little clammy in there (or icy, if it's sub freezing) for awhile - but breath thru a regulated respirator that wastes into the sealed closet and let the closet waste valve maintain the small over pressure.
Choosing my words carefully... the "commercial" systems rely on filtration and blowers and waste gates to provide fresh air (it requires a lot for circulated air - CO2, H2O, 3 days on pork and beans, etc...). Even a small room is onerous to handle with a manual blower, so power becomes required rather quickly. And... there are chemical weapons that destroy the filters - first attack, OK - second attack, best have changed filters...
I am very uncertain about bio agents and filters, but I assume that is primarily a particle size issue. Start with an off-the-shelf HEPA filter and go from there... and radioactive fallout *is* a particle size problem that is not very difficult to deal with over a moderate amount of time (days to weeks).
Pre-stored clean air is the surest method. Safely storing enough of it for ______ (you fill in the blank) and being able to effectively use it is probably not as simple as sucking on the end of an airline (the *blue* air hose in my house - blue for clean air and yellow for oiled air for air tools and yes, it's manifolded and valved up to be either-or with no back-siphonage of oiled air...).
Heck, it's an interesting proposition! But I'm not going any farther with it - risk management; I'm not dumping the effort into that. If I lived someplace with higher risks, sure, I'd compare it to other solutions - 120 psi is low and I can think of a number of inexpensive large volume storage methods.
Whew! And I was trying to be finished with thinking for the day... dang!
Regards,
Tom