Air Consumption

Not my field, but surely if the exhaust line goes up to any sort of useful pressure then presumably it will inhibit your tools/equipment working effectively?
If the exhaust line is near atmospheric pressure then you are gaining nothing just a reservoir at atmospheric.
Or are you hoping to capture high pressure pulses from the exhaust line?
It sounds like a lose lose situation to me, bottom line is you don't get ow't for now't.
I reserve the right to be completely wrong here, I'm willing to learn.
Come to think of it steam engines can have several cylinders each working with lower pressure exhaust from the previous stage, so it may be feasible....
Try it and see
Del

What is your point in trying to capture exhaust. This is unusable air for anything but blowing dust away or unwanted bits of saw dust or materials such as that. But, there again if the valves are supplied with the proper mufflers as required to keep noise levels down, then the exhaust is defused and unusable anyway.

Listen to the cat and the fixer. I understand most plant managers want more bang for their buck when it comes to compressed air, or anything else for that matter, but a closed loop system as you describe will cost you in other ways. You have to have that difference of potential after your cylinders for proper cycling or a way to evacuate that exhaust without affecting the system. Any of this will cost you more in energy and equipment.

Consider this. If you want to improve efficiency in your system, pipe the exhaust of the cylinder to the intake of the compressor, with proper allowances for loss. As the cylinder exhausts, the compressor draws out the air. In a steam engine, this function is done by a condenser. Suction load on the compressor may be reduced, too.

I made a toy steam engine. I connected it to a small refrigerator compressor. When I used only pressure the steam engine ran slowly. When I connected the exhaust of the steam engine to the intake of the compressor, it sped up dramatically.