Well, I'm no physicist, so I'm not nearly as smart as you fellows, but here's some homespun wisdom from down beneath the decks where we actually build and run real compressors for pay and fun. We get our hands greasy, we don't have fancy degrees, and we are mostly not even lowly engineering types, etc. :-) We do on occasion support the pumping of a hell of a lot of reasonably dry and pure compressed air, though.
Two-stage compressors invariably have an intercooler between stage 1 and stage 2. (It's that finned pipe between the exhaust of 1 and the intake of 2). Typically it wraps around by the fan/flywheel on your reciprocating pump so that cooling air blows across those fins. Fins help a lot. :-) yes, it's copper. Now THATS your intercooler...boys and girls, this is not a turbocharger setup on your Subaru. "INTER" = between stages of compression. This helps stage one ram a more dense charge of air into stage two of your "two stage compressor"...got it?
Well designed 2 stage compressors then ALSO have an after-cooler. That's a second heat exchanger (which drops the temperature of the full pressure air charge as close to ambient or below, as much as your wallet can afford). It does this by dumping the heat back to the ambient surroundings. This is pretty critical because the air leaving the exhaust at stage two is pretty hot - say about 130-150F at 100PSI if ambient was about 80f or so... The reason this is so critical is more than just pure efficiency, (though that is important.) The hidden reason is critical because aftercooling the compressed charge will condense (some of) the accumulated moisture out of that air. You really REALLY want to do this before your air goes to your accumulator. If you don't all that water will quickly fill up your accumulator, reduce total air volume, rust out your tank, pollute your downstream devices with moisture+oil+rust laden air and generally make your life miserable. This is bad. Shorty gets a call from engineering types if this water shows up above decks. Bad bad bad. :-/
Now a decent after cooler can easily drop the temp from 135F to ambient, which will condense a fair amount of the water right out of that hot charge. Fancy refrigerated types can do even better. Smart physicist types can figure dew point and saturation and relative humidity and so forth to figure out how much moisture will actually condense. (You might have to ask a lowly engineer type to help you with the calculations and/or using real world experience, but we won't tell anybody that you asked :-)
How much water? You smarter guys and gals will probably feel the need to figure that out, but it really doesn't matter how much since there will be literally gallons and gallons of it over time! That's bad. Just trust old Shorty here and plan on removing it. The first line of defense to do that is simple. Somewhere between the output of your stage two after cooler and your accumulator, you should have a moisture separator/trap. (I like to put them upstream of a one way tank check valve. It sounds like your existing compressor has a nominal trap, but plan on doing better by taking a few tips from Shorty)
A fair amount of that moisture your after-cooler condensed will collect right there in the trap, if you build the system right. To do that, put a self venting trap UPSTREAM of your accumulator unloader valve. Lay out your after-cooler output pipes to run 100% downhill to the trap and 100% uphill from the trap to the accumulator. Shorty was taught in his little bit of schooling that water runs downhill. Laid out this way, all that water will condense in the after-cooler and drain right down to that separator. Of course, every time your pump rests the pressure in this part of the system will drop. When it does, the trap will automatically self-vent that moisture, saving you trip to the compressor ever few hours to accomplish the otherwise onerous task of remembering to drain your trap. So what you say? Well, if you don't drain it REGULARLY, The trap will quickly fill up and become useless, blowing that water right back into your accumulator. (This is bad. Water above decks, etc. shouting swearing ensigns calling on red phone, etc.)
Shorty does want to point out that none of the above addresses downstream air purity of the functional air charge. That's a whole 'nother ball game which you must also address in your system design.
p.s. Some nonsense in the original thread to ignore. 1.) Real he-man compressors don't have "rubber seals" in them. Rubber is non-existent in compressors and it seals in general. 2.) The intercooler is located between pump stages...got it? The heat exchanger between the pump and accumulator is called an AFTERcooler. 3.) You cannot "ignore the moisture", it is not negligible. 4.) Standards for air purity are well defined within the compressor industry - and breathable gas purity is among the highest and therefore most expensive standard to accomplish. Don't guess about this. Oil laden air is dangerous - even fatal - as a breathable gas. 5.) there is a direct relationship between required purity of air and dollars you must spend...and it goes in the direction you might expect.
Shorty says "use the world wide inter web and Goggles to search out compressor design and engineering sources." There are lots of them with real heavy-duty Physicist quality info, calculators and stuff where they talk about bars and cycles and torrs and relative humidity and air grades and everything. Of course you physicist types will have to deign to speak with lowly engineering types and so forth to get the real scoop on how to get there, but relax. They don't bite.
Cheers from the boiler room!
Shorty