Yes, that is correct. But the end to end efficiency of Electricity -> H2 -> Electricity is much better than Electricity -> H2 -> CH4 -> Electricity. Hydrogen a

Yes, that is correct. But the end to end efficiency of Electricity -> H2 -> Electricity is much better than Electricity -> H2 -> CH4 -> Electricity. Hydrogen at 0°C and 100 Bar (~10MPa) has a density of 8.3447 kg/m^3. It has an energy density of 120 MJ/kg. So about 33 kWh/kg. So you end up with 278 kWh/m^3. Now of course you have to multiply this by the H2->Electricity efficiency. Let's be very pessimistic and take 0.6 or 60%, which is what a gas turbine plant can achieve today. You end up with 166 kWh/m^3 of usable electricity per cubic meter. One of many german gas storage facilities https://www.nafta-speicher.de/en/company https://www.nafta-speicher.de/en/company has a volume of 1.8e9 m^3. That translates into 300 Terawatt-Hours of storage capacity for just this one facility.