what would be the benefit to it being heated by the earth during storage?
all the temperature management here looks to just be counteracting the temperature changes that naturally occur when you compress or expand a gas. i imagine if you compressed it and then pumped hot air into water-filled caverns you'd get some negative effects of thermal shock.
Hot air should have higher pressure, so theoretically you could get more displacement. But your pumps also have to work harder to create a pressure differential. Hard to say which effect would be bigger.
all the temperature management here looks to just be counteracting the temperature changes that naturally occur when you compress or expand a gas. i imagine if you compressed it and then pumped hot air into water-filled caverns you'd get some negative effects of thermal shock.