Underwater Compressed Air Engineering
The system has an air reservoir at the bottom of deep water, with a compressed air pipe from the compressor/turbine set at the surface connected to its top.
There’s a barrier floating on the surface of the water in the tank, which is a cylinder with a vertical axis. The barrier need not be a tight fit in the cylinder: you are trying to reduce the rate of dissolution, not necessarily to prevent it entirely. The smaller the surface area of water exposed to the air, the less will dissolve in a given period. The longer the narrow part of the path from the air to the bulk of the water, the more slowly the air will dissolve because it can only dissolve as fast as the air that’s already dissolved diffuses away – so the barrier has a fairly wide “skirt.”[1]
The barrier would have to be a very loose fit, or it would be very susceptible to fouling.
You could also have a closed bottom with a pipe (as shown) to let the water in and out, wide enough for fouling not to be an issue over the life of the system, but much narrower than the diameter of the reservoir, to reduce the rate of loss of air. Air in solution would have to diffuse along the pipe to escape. The pipe in the diagram has two double bends, so that it neither sucks up debris from the bottom, nor does it collect any debris falling from above.
Possible Hazards
The most obvious hazard is the possibility of a catastrophic failure of containment of the compressed air, resulting in an enormous bubble rising rapidly to the surface, expanding rapidly as it does so, due to the decreasing pressure of the surrounding water. It would probably be wise to enact an exclusion zone for shipping above any large installation of this kind – and possibly limit the size of any single reservoir, to keep the size of the exclusion zone within bounds.
At sites with multiple reservoirs, it would be important to ensure that the failure of one reservoir would not cause failures in neighbouring reservoirs.
Choice of Materials for Vessels
Low cost, long expectation of life in (sea)water, and adequate strength are the main criteria. My guess is that glass-fibre reinforced concrete [2] would be a good choice, but I don’t know whether something else might be better. Weight isn’t an issue in service – in fact holding the vessel down when it’s full of air is more of an issue than holding it up when it’s empty! (But doesn't require any greater mechanical strength in 1000m or more of water than in 100m.) However, weight is a possible issue during construction.
A Size Comparison
There are many ships (supertankers, container ships, cruise liners) of 200,000 tonnes plus [3]. A vessel of that displacement (that is, the same size as the underwater part of the ship) at a depth of 1,000m would store ~2.5 GWh. At 200m it would store ~350 MWh. These vessels would be very much cheaper than those ships – much simpler, and without the above-water part.
There’s no magic about the 200,000 tonnes size; the vessels could be very much larger or very much smaller than that.
Other Details
If the system is too far offshore for the pump-turbine-generator unit to be onshore, it would probably be supported like a deep-sea oil rig, with floats well below low tide wave trough level, legs from them to support the platform well above high tide wave peak level, and anchor cables in permanent tension.
Storing Other Gases
The same technology could also be used for storing other gases, such as hydrogen or methane. You might still recover the compression energy as well as the fuel value of the gases. This might or might not be worthwhile, depending on the scale of the operation.
[1] See: Solubility of Air in Water and Diffusion Coefficients of Gases in Water.
[2] See Glass Fibre Reinforced Concrete. That article doesn’t mention coated glass fibres, only alkali-resistant ones. The concrete cladding on the external insulation on our house has coated glass fibre reinforcement! For more information see Strength properties of coated E-glass fibres in concrete (this is a .pdf and may be downloaded and saved rather than displayed, depending on your browser settings) and E-Glass Fibre.
[3] See List of largest ships by gross tonnage.