At ETH Zurich, there is a project aiming at scaling compressed air storage to MWhs. [1]

The interesting part is that they are trying to make the storage adiabatic, i.e., they store the heat that is generated while compressing the air in a phase change material (i.e., a material that will become liquid when hot, since a lot of energy can be stored in phase transitions) and get the heat back to warm up the cold expanding gas on decompression.

The issue is that even with the phase change storage, heat will dissipate into the rock within a couple of days, making the whole process inefficient for long-term storage.

[1] https://www.ethz.ch/content/specialinterest/mavt/energy-tech...