This is energy storage. That is fine. You put energy in, and later you take the same energy back (apart from process losses). Of course you can do that.
It is not at all the same as trying to use something as an energy source, which is what you were claiming could be done.
in way it is... but not quite...
It is a variable volume storage system (VVSS) that used ambient pressure to maintain constant pressure in the vessel as it is being exploited.
The ambient water pressure is being used to maintain that pressure as the volume inside the tank reduces due to exporting the air pressure to the surface..
But this is not the full story IMO... there is something else that could improve this system. upon.
From what I understand the VVSS is fed pressure from the surface using mechanical pumps when they recharge it.
It must be economically viable to do so, other wise they wouldn't be doing it.
To improve on it's economics I would be looking at delivering pressure harvested from the ambient pressure instead of pumping it down from the surface.
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Say you establish a large Bulk VVSS down about 1000 meters. ( 1472 psi)
You sink down pressure harvesting VVSS submersibles to top it up by docking with the Bulk VVSS.
The energy cost to go down by sinking is negligible.
No need for mechanical pumping at the surface.
All pressure to the bulk storage VVSS is harvested from ambient pressure.
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If designed properly the submersible VVSS could be recycled and used over and over again...to top up the bulk storage.
It would have to sink lower than the Bulk VVSS so that it has the pressure stored that is higher when rising to dock with the bulk VVSS and transfer harvested pressure.
How much compressed air is needed to float the submersible to the surface?
This could be provided by releasing a small quantity from the stored air pressure. Just like submarines do.
End result:
A constant air pressure of 1472 psi delivered to the surface....from the bulk VVSS via tubing or pipes. All of which is supported and provided by harvested ambient water pressure.