Some help on Compressed Air Energy Storage

[Evanish]

I was reading this article about different types of energy storage, and it gave this formula for compressed air.

Joules = P₀V₀ln(P/P₀)

Where
P₀ = Atmospheric pressure 10⁵ Pa
V₀ = Volume of air to be compressed in m³.
P = Pressure in tank when compressed in Pa.

Note: This formula is for Isothermal storage.

The reason for this post is because I want to make sure I'm understanding this formula correctly, and because I want to know if this formula is valid at all pressures. I'm guessing it's based on the ideal gas law, and at some pressure it starts to break down, but I don't know if that's true or at what pressures it becomes an issue. I don't know that much about this topic so I decided to ask here. Thanks.

 

[Simon Bridge]

You are correct, it is based on the ideal gas law and it will not work for some pressures (and some temperatures, and some densities) ... it is also only true for a constant temperature process, something that is tricky to set up: the process matters. It is usually easier to find out how the energy stored depends on pressure for a particular setup by measuring. Whether air is close enough to an ideal gas (and process close enough to isothermal) for the equation to be valid, depends on what you want to use the stored energy for. This sort of thing is often used for very rough back-of-envelope calculations... you can get an idea of the sorts of order of magnitude to expect.

 

[Baluncore]

There is a perfect fluid, a vacuum. Contained vacuum energy storage (CVES) involves a closed cylinder with a piston. As the piston is withdrawn, a vacuum is pulled in the cylinder. There is an advantage here over the pressure of a compressed gas in that the tension force applied to the piston as it is drawn remains reasonably constant. The force is determined by atmospheric pressure. The working fluid is as perfect as the vacuum.

Energy is being stored by creating the vacuum where there was once only atmosphere, the entire Earth's atmosphere rises ever so slightly, which is where the energy is actually stored.

 

[Evanish]

You are correct, it is based on the ideal gas law and it will not work for some pressures (and some temperatures, and some densities) ... it is also only true for a constant temperature process, something that is tricky to set up: the process matters. It is usually easier to find out how the energy stored depends on pressure for a particular setup by measuring. Whether air is close enough to an ideal gas (and process close enough to isothermal) for the equation to be valid, depends on what you want to use the stored energy for. This sort of thing is often used for very rough back-of-envelope calculations... you can get an idea of the sorts of order of magnitude to expect.

Thanks for the information. I guess what I'm most interested in is what the max energy/volume you can reasonably hope to get with a common gas like N₂. I've done some searching around and found this, but I'm still not really sure I understand all the practical limitations.

 

[Evanish]

There is a perfect fluid, a vacuum. Contained vacuum energy storage (CVES) involves a closed cylinder with a piston. As the piston is withdrawn, a vacuum is pulled in the cylinder. There is an advantage here over the pressure of a compressed gas in that the tension force applied to the piston as it is drawn remains reasonably constant. The force is determined by atmospheric pressure. The working fluid is as perfect as the vacuum.

Energy is being stored by creating the vacuum where there was once only atmosphere, the entire Earth's atmosphere rises ever so slightly, which is where the energy is actually stored.

Interesting idea. I've done some thinking on it. Normal atmospheric pressure is 14.7 psi. I think this defines the maximum force you can get from a vacuum. So doing a little math.

14.7 lb./in.² X 1550 in.²/m² = 22,785 lb./m²

22,785 lb./m² X 4.448221599999244 N/lb. = 101352.729155983 N/m²

So using w=df one m³ space can get you roughly 100,000 joules or .03 kwh per meter squared.

That doesn’t seem to be a very good energy per volume.

Let put this into context by seeing how much volume it would require to meet Hawaii’s energy storage need. I recently read http://www.technologyreview.com/news/534266/hawaiis-solar-push-strains-the-grid/ about them having such a need.

From this I know in November 2014 they generated 104 Gwh of renewable energy. Let's say they need to store 1% of that or 1.04Gwh. So that would be 1,040,000 kwh divided by .03 kwh equals roughly 35,000,000 m³. It seems a bit difficult. Maybe they could make use of some of their lava tubes to do it (not the cylinder thing of course but http://www.intelligentutility.com/article/15/01/cost-effective-mass-energy-storage-dare-compare).

 

[Baluncore]

I agree that: 1/36 kW.hr per m³ is a relatively poor energy content.
CVES is not a regional solution, it can be a fast and efficient local storage option.
There is more pressure difference possible above P_attm than there is below.

If the vacuum is created by removing air with a pump, it will be inefficient, as the pumped gas will significantly change temperature and pressure.
If the vacuum is “pulled” in a cylinder, there is no contained gas to change temperature and pressure, so it can be significantly more efficient.

 

[Simon Bridge]

Let put this into context by seeing how much volume it would require to meet Hawaii’s energy storage need.

Context is everything.
In fairness, this is the first time you have provided one. Before that you just asked about energy storage without mentioning scale or use.

I'm still not really sure I understand all the practical limitations.

...do you have another question?

 

[Evanish]

Context is everything.
In fairness, this is the first time you have provided one. Before that you just asked about energy storage without mentioning scale or use.

Sorry about that. I should have added more details about what I'm interested in. Mostly I'm interested in mass energy storage.

...do you have another question?

Sure, I have lots of questions. In regards to a storage system that operates in the Gwh range, what might a system that stores the most energy per dollar invested be like? For example at what pressures might it operate at and would it use normal air? I’ve done some searches on the subject but I can’t seem to find out such details about currently operating or planned facilities. Also, I’m interested in what types of underground formations can be used for compressed air energy storage. I’ve heard about salt caverns being used, but what about things like depleted oil wells? I understand that they can fill up with water. Does that mean they can’t be used?

 

[Simon Bridge]

Sure, I have lots of questions. In regards to a storage system that operates in the GWhr range, what might a system that stores the most energy per dollar invested be like?

Engineering question... it would be big.

For example at what pressures might it operate at and would it use normal air?

Normal air would be the cheapest, so there would be a strong motivation t use that. Pressures would depend on the containers available, the rate that they need to be able to draw the energy off, and how long the storage has to last.

I’ve done some searches on the subject but I can’t seem to find out such details about currently operating or planned facilities.

AFAIK, there are no currently operating or planned facilities.

Also, I’m interested in what types of underground formations can be used for compressed air energy storage. I’ve heard about salt caverns being used, but what about things like depleted oil wells? I understand that they can fill up with water. Does that mean they can’t be used?

No - you can use compressed air to drive the water out. In fact being filled with water may help them store more energy ... the energy is stored in the resulting higher sea-level. I suspect the main thing about used oil wells is that the oil companies are not keen to lose them in case some of the remaining oil becomes accessible ... also, oil does not generally come from a big airtight cavern underground.
Oneof the main engineering challenges using aral formation is that they tend to be porous ... you'd constantly lose energy.

 

[Evanish]

AFAIK, there are no currently operating or planned facilities.

Here is some information about the subject.
http://spectrum.ieee.org/energywise...ompressed-air-energy-storage-makes-a-comeback

http://www.greentechmedia.com/articles/read/texas-calls-for-317mw-of-compressed-air-energy-storage2

 

[Simon Bridge]

Oh I see what you are talking about ... these are gas turbine plants which use the pre-compressed air (compressed during low demand times - perhaps using energy from a nearby windfarm) rather than using the turbine to compress the air ... something like that?
I was thinking you meant to draw power more directly from the compressed air.

Huntorf and MacIntosh plants use natural "salt domes" to hold the compressed gas.
In principle, the compressed air could drive the generators directly ... but I don't think anyone is doing that.
Anyway, you'd have to make specific searches for the particular plants.

You may be better looking for academic papers on AA-CAES generation.

Aside: the equation in post #1 will be useless for these applications.
The air is not compressed by anything like an isothermal process, and, anyway, the particle number also changes.