[fox46]

You could use the exhausted air as it decompresses to cool the compressor and its output which will help increase its efficiency but since the exhausted air is at the same potential energy level as the surounding atmosphere, you cannot extract any more work from it.

It is similar to potential energy due to gravity that many students are learning about in physics. An object at a height relative to the ground has a potential energy due to gravity however, an object at ground level has no potential energy relative to the ground. You cannot extract any energy with out a potential or altitude difference. Another example is a hydro electric generator or waterwheel in a river. As long as water is flowing past it from one altitude or energy level to another you can use it to do work and turn the water wheel. But take that waterwheel and put it in a lake where all the water is at the same energy level and you cannot extract any work from it.

The air in your reservoir is at a higher energy level (pressure) than its surrounding atmosphere (the lake). As the air flows through your system (river) you can use it to do work- move actuators (turn the water wheel). But once it is exhausted to the atmosphere (returns to the lake) you can no longer extract any energy from it until you compress it again with the compressor (or pump the water back upstream)