At least in the western US (my oldest son, being a petroleum engineer explained to me patiently) there is no gap as such remianing when the oil or gas is depleted. There is no cavern remaining, only a sandstone or sand shale rock formation that is now void of it's previous contents. Often, this void refills with undergound water. This water is usually extremely salty and corrosive, being the remnants of an ancient sea that covered 2/3's of the western US during the formation of the rock strata. The engineers are now experimenting with injecting carbon dioxide gas in liquid form into depleted oil fields. This would accomplish stabilizing the depleted field as well as storing greehouse gases for thousands of years... (Obviously, I nodded knowingly, as one does when their child explains something)...