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"Apex will need a small amount of natural gas to heat the air it compresses to maximize turbine output."

As far as I understand they need to heat up the turbine as air (a gas) cools down upon (adiabatic) expansion.

And while accumulating / compressing air in ground lacunae, pumping it into the storage, we are just heating up the ground.

Am I right in my understanding of the process thermodynamic ?

Sounds correct to me. It sounds like they're hoping the compressive heating effects will be dispersed through a large enough volume to be negligible. Whereas the expansive cooling will be concentrated at the point of exit.
You are correct, the article has a typo and should state 'decompresses' instead of 'compresses.'
> and the system can fill the cavern with air while generating electricity. You can't charge and discharge a battery at the same time.

Umm, does this seem as pointless to everyone everyone else as me?

It's a very strange statement. There's no reason to do it, and you can easily do it anyway with your multiple batteries.
The article, and the comments here, are missing an important fact that really helps clarify how these compressed-air energy storage systems work:

These systems use the compressed air as input into a natural gas turbine. You can think of the underground storage as a giant intercooler that stores the output of the first (compressor) half of a natural gas turbine, and then feeds that compressed air into the second (combustion) half.

See a good explanation here: http://energystorage.org/compressed-air-energy-storage-caes

Glad to see something about houston on HN regardless of what the startup is doing! Woot woot