Boyle's Law says that compression and temperature reduction are equivalents: PV = nrT
That is, increasing temperature is equivalent to increasing pressure, and vice versa: decreasing either is equivalent.
The problem with liquifying -- cooling -- a gas, is that:
1. You're removing thermal energy. Which itself cannot be usefully stored. So you're losing that unless it can be applied to some local low-quality heat process.
2. Re-gassifying the liquified air requires energy. If you've managed to store (some of) the removed heat, you can apply that. Otherwise, whatever you're using to introduce heat to the liquified air will itself get very* cold, very quickly, and eventually reach thermal equilibrium. Alternatively, you could apply a fuel-based heat source sufficient to boil off the liquid, but that's going to cost you energy.
Depending on the temperature of the freshly-generated gas, you're also going to be chilling whatever generating process you've got (probably gas turbine), which means both metal embrittlement and potential for frosting if there's any degree of water vapour in the air.
The more usual form of air-based energy storage, compressed air energy storage (CAES) likewise has problems with both heat loss and chilling on expansion. Compressing a gas heats it, and that heat will tend to escape to the environment, similarly to the case for chilling. On the energy-recovery side, expanding the gas to run a turbine will cool it (and the turbine) rapidly. Many CAES designs incorporate natural gas simply as a heating function to heat the freshly-expanded gas, meaning the storage system is not a no-fuel system, though it requires far less fuel than a conventional natural-gas generating plant.
The biggest issue I have with the system as described is that the re-expansion of liquified nitrogen isn't free, and requires a source of external heat. Given the phenomenally cold temperature of liquid nitrogen, any passive heating design will rapidly approach thermal equilibrium with the stored medium, limiting the rate of net energy release.
Liquificarion is a phase change and air is deviating strongly from ideal in the liquificarion process. The expansion process is also not cyclic so Carnot doesn't apply.
Boiling of LN2 results in a gas, which would then be used to drive a conventional turbine, with a "hot" (comparatively) and cold end, hence, a Carnot process.
Condensation of the (now gaseous) nitrogen within the turbine would all but certainly result in significant cavitation effects, as well as create a very low-pressure zone on the exhaust side of the turbine, which would probably not be conducive to normal operation.
Heat of vapourisation is not free, and would have to be supplied, somehow.
That is, increasing temperature is equivalent to increasing pressure, and vice versa: decreasing either is equivalent.
The problem with liquifying -- cooling -- a gas, is that:
1. You're removing thermal energy. Which itself cannot be usefully stored. So you're losing that unless it can be applied to some local low-quality heat process.
2. Re-gassifying the liquified air requires energy. If you've managed to store (some of) the removed heat, you can apply that. Otherwise, whatever you're using to introduce heat to the liquified air will itself get very* cold, very quickly, and eventually reach thermal equilibrium. Alternatively, you could apply a fuel-based heat source sufficient to boil off the liquid, but that's going to cost you energy.
Depending on the temperature of the freshly-generated gas, you're also going to be chilling whatever generating process you've got (probably gas turbine), which means both metal embrittlement and potential for frosting if there's any degree of water vapour in the air.
The more usual form of air-based energy storage, compressed air energy storage (CAES) likewise has problems with both heat loss and chilling on expansion. Compressing a gas heats it, and that heat will tend to escape to the environment, similarly to the case for chilling. On the energy-recovery side, expanding the gas to run a turbine will cool it (and the turbine) rapidly. Many CAES designs incorporate natural gas simply as a heating function to heat the freshly-expanded gas, meaning the storage system is not a no-fuel system, though it requires far less fuel than a conventional natural-gas generating plant.
The biggest issue I have with the system as described is that the re-expansion of liquified nitrogen isn't free, and requires a source of external heat. Given the phenomenally cold temperature of liquid nitrogen, any passive heating design will rapidly approach thermal equilibrium with the stored medium, limiting the rate of net energy release.