RE: What is the most efficient air compression method?
Screw is the most variable. You can "download" it (like throttling down) to 10~20% while maintaining a practical efficiency. It has to spin faster than centrifugal tho. This is talking about air conditioning plants. System efficiency is enhanced since energy is saved when only a small portion of the building is in use.
While you have no specific application, gravitational has to be the most efficient both theorectical and actual.
Clement