# Compressed air energy storage

1. Nov 14, 2014

### Stanley514

What defines how much energy we could store in some gas by compressing it to a certain volume by applying a certain pressure? The compessability coefficient? Is there some gases which allow to store more energy than air? Which gas has the largest compressibility coefficient?

2. Nov 15, 2014

### Doug Huffman

Yes, look to specific gas constant derivable from atomic number and molar mass.

3. Nov 15, 2014

### Staff: Mentor

At low pressures (in the ideal gas region), at a given temperature and pressure, all gases have the same molar volume. So, per mole, they all have the same amount of energy stored. At higher pressures (beyond the ideal gas region), the properties of individual gases begin to differ because of intermolecular interactions.

Chet

4. Nov 15, 2014

### Philip Wood

A gas (assumed ideal) stores no more energy when compressed than before compression, if we compress it isothermally. This is because, for an ideal gas, the internal energy depends only on temperature.

Yet if we allow the gas to expand isothermally, back to its original pressure and volume, it can clearly do work. The energy comes, not from the compressed gas, but from the surroundings, in the form of heat flowing into the working gas and maintaining its temperature, which would otherwise drop. This amount of energy was given to the surroundings as heat when we compressed the gas isothermally in the first place. If we hadn't allowed this heat to flow out, the gas temperature would have risen.

So, strictly, it's not the compressed gas that stores the energy enabling work to be done. It's the surroundings.

Sorry if you didn't want to know this, but I have an Ancient-Mariner-like compulsion to tell people.

5. Nov 15, 2014

### RonL

Your excellent post almost compels me to start a thread and get myself in hot water:D

6. Nov 16, 2014

### Philip Wood

Thank you for your kind comment. Made my day! Maybe a new thread could look into entropy aspects...

7. Nov 16, 2014

### RonL

Treat me tender now, I'm in early stage recovery from a, Von Neumann/Shannon induced coma

8. Nov 16, 2014

### Staff: Mentor

See, I would have quibbled with part of it:
Yes, if they operated isothermally that would be correct. But neither a pump nor an air motor operate isothermally: They operate adiabatically. The heat flow comes after the work is already done. That's why pumps get hot and air motors get cold.

9. Nov 16, 2014

### Philip Wood

Guilty as charged. But in mitigation (1) The basic point I was making still stands: provided the gas is allowed to cool between compression and expansion, it doesn't have any more energy after compression and cooling than before compression. (2) I chose to consider isothermal changes because they're easier to describe than adiabatic compression followed by cooling, followed by adiabatic expansion (followed by heat inflow). What's more, the theoretical efficiency (work out/work in) is, I think 100% for the isothermal case, whereas for the practical case heat is having to flow through finite temperature differences (e.g. when the compressed gas cools off) so we've lost reversibility and efficiency. Trust a physicist to want to deal with an ideal case that isn't used in the real world...

10. Nov 16, 2014

### RonL

Hot water time:p why cool the compressed air after compression ? let the temperature rise in the receiver and at peak temperature, pressure, and volume, any moisture brought in at intake can become steam, adding to discharge volume that drives the motor.
If motor and compressor are designed to be a single unit, resistance to compression can take place at a small diameter and energy transfer that drives the motor function, takes place at a larger diameter, an easy 5:1 leverage of energy application.
All energy that goes into bringing the system to design speed and temperature, stays in the system, after that it becomes close to a single shot exchange of intake/discharge. let the mind see Hero's Turbine with some modern day materials and design work.

11. Nov 16, 2014

### Staff: Mentor

And I'm an engineer, but we're on the same page overall. ;)

12. Nov 16, 2014

### Staff: Mentor

Depends on the application. If you are driving an air-powered car or even pumping-up its tires, you want the air to be cool otherwise it cools down as you drive and you lose pressure/energy!

13. Nov 17, 2014

### marcophys

Taking an airgun with a soda bottle cartridge.
The gas cools as it expands.
What is supplying the energy to blast the pellet out of the barrel?
Is it the amount of heat lost?

14. Nov 17, 2014

### Philip Wood

Marcophys. No. I'd imagine that the expansion is so quick as to be almost adiabatic. So the energy comes, this time, from the internal energy of the gas. But it's not extra energy that we stored in the gas during compression because there isn't any extra energy! If the gas temperature (and hence internal energy) had been raised during compression, the extra energy would soon have escaped as heat into the surroundings.

In fact the gas's internal energy after the expansion is less than before we compressed it in the first place. The gas is cooled by the expansion. After the expansion heat gradually flows back into the gas from the surroundings [I'm assuming here that the surroundings are at the same temperature throughout, and that the gas was at this temperature when we started to compress it.]

Last edited: Nov 17, 2014
15. Nov 17, 2014

### marcophys

If the cartridge was heated prior to use (theoretically)...... as the liquid gas temperature rises, the gas escapes with more energy?
Or does it?

If it does..... what would happen if the ambient temperature was colder or hotter than the liquid gas?

Ie. Does the liquid gas, at change of state, behave differently in a hotter or colder atmosphere?

16. Nov 17, 2014

### RonL

The atmosphere conditions will only have an affect on how quickly the liquid gas absorbs heat.
If you heat the cartridge, yes you will increase the energy of the gas inside.

17. Nov 17, 2014

### RonL

If using compressed air as energy storage and reapplication in some form of work production, there has to be a mechanism of compression and also expansion. The time of storage will determine how large a system needs to be and how well it is insulated. It seems to me that making use of that heat energy that exists prior to compression, is a matter of how well the process is micromanaged and how far the final expansion is carried out.
As for tires, that is a static condition, I have truck tires that are holding pressure after 20+ years, with no additional air added (they do show signs of lowering pressure, but not much).
My mental block seems to be if air is not allowed to cool, will it not give back the same energy put into it during compression, if the expansion system will provide the complete process to take place ?
In my mind a ram effect at intake and an expansion discharge into a draft behind some moving object, should have some slight positive value, no?

18. Nov 17, 2014

### marcophys

I understand..... thanks :)

19. Nov 17, 2014

### RonL

Keep in mind, heat will increase pressure, but it also weakens material strength of the container......"THINK TWICE" and always do the research:D

20. Nov 17, 2014

### marcophys

But perhaps something like "don't try heating pressurised vessels, as they will explode" should have been included.

It's difficult, because many badly setup experiments can be the cause of injury.

Boy dies in explosion, after heating a pressurised gas cannister, under a Bunsen burner."

I guess it could happen, and probably has happened in some experiment or other, that was being discussed on a forum.

I will take more care in future ;)

21. Nov 19, 2014

### Philip Wood

I considered the ideal cycle: adiabatic compression of gas from $V_{hi}$ to $V_{lo}$, compressed gas allowed to cool to temperature of surroundings, adiabatic expansion of gas from $V_{lo}$ back to $V_{hi}$, decompressed gas taking in heat from surroundings. The gas is assumed to start and finish at the temperature of its surroundings. I find
$$\frac{work\ out\ during\ expansion}{work\ in\ during\ compression} = \left(\frac{V_{hi}}{V_{lo}}\right)^{(1-\gamma)}.$$
$\gamma$ is $\frac{c_p}{c_v}$, the ratio of molar heat capacities of the gas.
For a diatomic gases, like oxygen and nitrogen, $\gamma = 1.40$, so for a compression ratio of 10,
$$\frac{work\ out\ during\ expansion}{work\ in\ during\ compression} = 10^{-0.4} = 0.40.$$
For monatomic gases, like argon, $\gamma = 1.67$, so for a compression ratio of 10,
$$\frac{work\ out\ during\ expansion}{work\ in\ during\ compression} = 10^{-0.67} = 0.21.$$
These poor figures are because we throw away energy in the form of heat in stage 2. We get the same amount of work as we put in, though, if we are prepared to compress the gas so slowly, and let it expand so slowly, that the processes are isothermal.

22. Nov 19, 2014

### RonL

My question then, would it not be an isothermal cycle, if I compress air then expand through reaction ports without allowing the air to cool between the two processes?

23. Nov 19, 2014

### Philip Wood

I'm afraid I don't know what a 'reaction port' is. Is it a hole between two vessels? If so, then, no work would be done by an ideal gas expanding into another vessel. But I've probably misunderstood.
But if the temperature never changes throughout, then it's isothermal!

24. Nov 19, 2014

### RonL

As in too many cases, maybe not the proper term a wedge shaped chamber that transmits pressure energy between a fixed surface and a surface in motion, or two surfaces moving in opposite directions. (would reaction chamber be better?).
My thoughts are based on a pressure tank that is insulated (best possible method) preventing the least amount of heat loss and a compressor that builds pressure into said tank.
If the process is started, then consider a 1,000 RPM for 10 minutes, the final state is a tank with 10,000 compressor cycles, then as an estimate of 150psi, the final temperature might be 350 F or more.

My thoughts are, a large volume of air with almost the same potential energy as put into it, along with moisture from the surroundings being raised to a steam of higher potential.

A proper design should be able to take efficiency to a very high percentage.

I had best limit my final comment to: The best possible design, puts the compressor inside the receiver tank which in turn also functions as a drive motor.:)

25. Nov 19, 2014

### Philip Wood

I'm afraid I'm not competent to comment, except to say that this looks like neither of the idealised cases I considered. No reason why it should! Certainly not isothermal, as you're raising the temperature. Approximately adiabatic if it's insulated, but it looks as if you're trying to recoup the energy stored in the gas, rather than throwing it away, as I did. I was considering the case of a compressed gas being used to do work at some time in the future, well after it's cooled down. Very best wishes.