Maybe I'm interpreting wrong, but I believe Eric said he requires a "water-cooled Air Compressor but the Bidder counterproposed the air-cooled Air Compressor".
There's a big difference in terminology when describing compressors. Perhaps Eric means something else, but what he wrote is that he wants a screw compressor with built-in (actually, probably cast) water jacket -- much like what has been traditionally manufactured in the reciprocating compressor field. His bidder quoted on a finned, air-cooled screw compressor. The intercooler and the aftercooler are something(s) completely apart. These can be either air-cooled or water cooled. In this case, I would suspect that Eric also wants water cooling in both coolers, taking advantage of the closer discharge air temperature approach to the cooler water. I think David Simpson is also working with this concept in his reply. I also suspect, like David, that this involves an oil-flooded screw - which is more practical and much more reliable and efficient than a dry one. Therefore, any intercooler is not employed. An aftercooler, however, will be needed with the customary bulky oil separation equipment.
I've not seen or heard of any jacketted oil-flooded screw compressor and I doubt if one could be justified for the simple reason(s) that David has pointed out. Perhaps two (2) screw compressors are planned in order to obtain what Eric describes as "two-stage", but I strongly doubt this also. I've also never seen a jacketted dry screw; the casting is very complicated and expensive to make - and in the majority of cases, not justified.
What I really suspect here is that the compressor specifications were prepared by someone who is applying what they believe to be analogous specifications between a reciprocating machine and a screw - when, in reality, there are few (if any) similarities. Eric should explain the lack of detailed basic data that the above posts have revealed and, as a consequence, we will probably find out the rest of the story - which will clear things up.
Art Montemayor
Spring, TX