The authors of the paper estimate gravity batteries like the one above could operate at a cost of between USD $1 and $10 per Kilowatt-hour with the capacity to generate from 10 to 70 Terrawatt-hours of electricity.

That's got to be wrong. An operating cost of $1 to $10 per kWh produced -- it that's what it's supposed to mean -- isn't remotely competitive. The cost per kWh produced needs to be at most a few cents more than the cost of the electricity used to store the energy. OTOH, if it's meant to refer to the capital cost of storage capacity, I have a hard time believing it could possibly be as low as $1 per kWh of storage capacity. Even $10 would be low enough to revolutionize the energy storage market.

As to the figure of 10 to 70 TWh of storage capacity, I could believe that if it's the projected total for all abandoned mines in the US. Gravity storage of this type should be good for about 6 kWh of storage capacity per cubic meter of tunnel volume per kilometer of shaft depth. Few coal mines have shaft depths greater than 2 km. That would mean ~12 kWh per cubic meter of tunnel volume at that depth. It would require a billion cubic meters, or one cubic kilometer, of tunnel volume at 2 km depth to give 12 terawatt-hours of storage capacity.

One hundred thousand kilometers of tunnels, if the average tunnel cross section is 10 m^2. That would be one hellofa coal mine.

Given the risk of flooding, wouldn't it be reasonable to see which of these mines could be converted to pumped storage hydroelectric facilities?