Talk:Compressed-air energy storage

Discussion

The problem with your article on isothermal air compression is that it deals only in academics, not the day-to-day use of compressed air systems. Perhaps the greatest advantage of pneumatics is their safety: moving cutters can be safely cleared no other way. Material moved through pneumatic (pressure-vacuum) systems clear debris from shops so that fall accidents are far less likely. Air tools can be safely used in wet environments and explosive atmospheres where electric tools are out of the question. Air-powered vacuums can easily remove even the most dangerous radioactive materials and asbestos without the dangers of contamination seen with electrical power. Air agitated paint tanks give the finest finish ever seen. And the list goes on. The physics of compressed air use are by definition, appealing: I can think of no less efficient way to deliver power. But we use air tools constantly, particularly indexing lifts, jacks, nailers, scalers, and air-motor driven tools. Because rotary screw compressors are now on-par with diesel powered equipment in deep-shaft mines, using the exhaust for breathing air and to cool the hot environment is a real advantage. Why didn't anyone else think to mention that? —Preceding unsigned comment added by 209.244.31.59 (talk) 21:05, 17 April 2008 (UTC)

This article is about compressed-air energy storage, not use.--Dwane E Anderson (talk) 01:28, 26 January 2009 (UTC)

The Physics article seems completely wrong to me. By allowing the system to compress isothermally surely much of the energy is being lost? I'll check my thermo books tonightGreglocock 04:25, 21 March 2007 (UTC)

What about air-depression (you might call it fission as compression´s fusion)?

79.210.183.160 (talk) 13:19, 23 June 2009 (UTC)

Isothermal compression and expansion represent an ideal case where exactly the same amount of heat is released to the environment as must be reintroduced into the system during expansion. In practice the compressor and air tank will heat up during compression and the engine and tank will cool down during expansion unless very large heat exchangers are fitted or the system is very small or the power level is very small. In the ideal case no energy is lost, but in practice there is the loss of friction and losses to due with not being able to use exactly the isothermal cycle. It would be good to have some real measurements for the article. --Theosch 14:14, 22 March 2007 (UTC)

I suppose my confusion arises from my assumption that reversibility=efficiency, whhich does not apply to a system that in one cycle does no work. Either way, an adiabatic compression and expansion cycle also does no net work, and stores much more energy. I agree that an isothermal process probably bears a closer resemblance to the likely cycle of this process. Greglocock 01:36, 23 March 2007 (UTC)

66kw (~90hp) to move a average car is quite high. While 90hp may be required to accelerate quickly, modern vehicles in the US can maintain 60mph with approx 20hp or ~15kw. The quick math to prove this is simple: Assuming a standard highway fuel economy of 30mpg & an almost universally accepted bsfc (brake specific fuel consumption) of 0.53 lbs/(hr*hp) for modern gasoline engines, an engine traveling 60mph will consume approx 2 gal /hr of gasoline. Gas in the US has a specific gravity of 0.73-0.75 and thus weighs approx 6 lbs, thus the engine is consuming 12 lbs of gasoline per hour. Using a BSFC of 0.53, the a vehicle traveling 60mph @ 30mpg has an average power of 22hp or 16.9kw. If an air car compressor is a heat pump,could it supplement a homes central heating?--79.67.199.164 (talk) 17:41, 12 July 2008 (UTC)

OK now?

I think its ok now. Clarified both the scientific and layman understandings, and, it seems to me, that the large storage (at least if not used in its entirety, but only once filled, used during fluctuations or small cycles of emptying and refilling) is something near BOTH a reversible isothermal process and an isentropic (=reversible adiabatic) process. פשוט pashute ♫ (talk) 04:37, 16 March 2012 (UTC)

Undefined variables

The calculations are helpful, but impossible to understand with undefined variables. What are P_A and P_B? The article needs to be self-contained or contain references where terms are defined. —Preceding unsigned comment added by 68.7.105.15 (talk • contribs) 03:12, 27 December 2007 (UTC)

The notation should be clear for anyone who has completed a basic college course in thermodynamics; it is assumed that the reader has at least this level of prior knowledge. See the articles on ideal gas law and Boyle's law, referenced in the section. (You did read these supplemental articles, did you not?) The equations illustrate a simple, linear relationship between pressure and volume in an ideal gas under constant temperature conditions. P_A is the pressure at state "A" and P_B is the pressure at state "B", corresponding to volumes V_A and V_B, respectively. —Quicksilver^{T @} 06:13, 6 February 2008 (UTC)

I sort of agree, but on balance it is probably a reasonable whinge. I'll see if the other pages have a neat table I can steal.Greg Locock (talk) 06:47, 6 February 2008 (UTC)

Balance done. I think now the whole article is comprehensible. Ok now? פשוט pashute ♫ (talk) 05:17, 16 March 2012 (UTC)

Talk about pressurized caverns

This article talks mostly about the feasibility of compressed air cars. I'd love to see some discussion and math about using compressed air as a large-scale means to store energy. For example, storing the energy created by solar power during the day for use at night. --Gadlen (talk) 23:23, 18 January 2008 (UTC)

done a long time ago, and now clarified. פשוט pashute ♫ (talk) 05:17, 16 March 2012 (UTC)

Thanks for fixing things Greglock

Hey Greglock, this is happytrombonist16, the alter-ego of whatever ip address my computer was using when I posted the facts tag. I'm kinda new, so it's very possible that wasn't the right tag to use for that situation. However, it looks like you've fixed most of the things I had a problem with, so thanks! Happytrombonist16 (talk) 05:32, 27 January 2008 (UTC)

Agree. Thanks from me too! פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

Compressed air engine‎

At the moment air engine redirects to this page. There exists an article with the much better name Compressed air engine‎. Why don't we move the air engine stuff there, and leave the physics and storage side here? Greg Locock (talk) 09:45, 7 February 2008 (UTC)

Now its ok. Redirects to Pneumatic Motor - and here there's an expansion leading to there. (And external link there, to here). פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

CAES article is inadequate

The original focus of this article was on the use of compressed air energy storage for utility level power generation or grid energy storage. In my opinion the current version of this article focuses too much on the use of compressed air to power vehicles and not on power generation. Details like power output and storage time for the Mclntosh and Huntofr hybrid plants are missing. The section on types of compressed storage is inadequate and depends too much on the "German AACAES project information" which understates the efficiency of the hybrid CAES plants. The hybrid plants use the stored cooled compressed air to directly feed air into a gas turbine. This replaces the compressor that is powered directly by a normal gas turbine. The efficiency of a hybrid plant should be calculated by comparing the energy required to compress the stored air versus the energy required to run the compressor inline with the expansion turbine. See http://www.eere.energy.gov/de/compressed_air.html for details. —Preceding unsigned comment added by 68.2.181.124 (talk) 21:26, 27 March 2008 (UTC)

Apart from the above, this article is at present a mess with much duplication. I'll try to have a go later. Also there is a confusion of many articles all having to do in some way with this subject but inadequately linked. --Theosch (talk) 14:08, 4 April 2008 (UTC)

Fixed by now. פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

Physics check

The equations given in two sections of this article do not match. In one the specific energy is given per mole, in the other per N-m3. Probably an "n" missing somewhere. This needs to be checked and corrected.--Theosch (talk) 15:27, 4 April 2008 (UTC)

The clean-up looks okay to me. I noticed that an example of energy density was deleted. It would be good to replace that with a sourced example, say comparing the energy density with liquid fuels or batteries. --Mikiemike (talk) 22:25, 4 April 2008 (UTC)

I went through the energy density comparison referencing the appropriate Wikipedia battery page. Obviously liquid fuels are so much better there is little point in pointing this out. More interesting would be the comparison of using the same pressure vessels for compressed air storage or for storing fuel gases, e.g. CNG or hydrogen. --Theosch (talk) 15:15, 6 April 2008 (UTC)

I removed the "m³-N" units and values like "110 $\ln {\frac {P_{A}}{P_{B}}}$ kJ per m³" (instead of 100), because it wasn't clarified why they were used at all, they were used inconsistently, and the differences aren't that significant. W=pV ln(p1/p2) doesn't depend on temperature, so the "110 at 24°C" value has no sense, unless we measure the gas' volume at 0°C and use it (decompress isothermally) at 24°C. Maybe this is required when talking about energy density (I don't see why the decompressed volume is used anyway), so please correct me if I'm wrong. Tokenzero (talk) 12:27, 8 November 2008 (UTC)

100kJ * ln(20MPa/100kPa)=230 kJ and not 530 kJ as written in the article. please check., Jan 25 2012 — Preceding unsigned comment added by Kommentier (talk • contribs) 14:16, 25 January 2012 (UTC)

Please explain the error, I suspect you have use log base 10, not log base e. Greglocock (talk) 03:38, 26 January 2012 (UTC)

No you have to use log e but I accidentally pushed the log base ten button instead of the log base e (the buttons are right next to each other on my calculator) !! That is the author of the calculation rightly wrote: "Nevertheless it is useful to describe the maximum energy storable using the isothermal case, which works out to about 100 kJ/m3 [ ln(PA/PB)]. Thus if 1.0 m3 of ambient air is very slowly compressed into a 5 L bottle at 20 MPa, the potential energy stored is 530 kJ." The formula is from above where you take the integral over 1/V dV, which is ln V, i.e. the log over e, so I think the formula is right. now the typical air pressure is about 100kPa so 20MPa/100kPa=200 and now finally my calculator gives ln 200= 5.3. — Preceding unsigned comment added by Kommentier (talk • contribs) 10:24, 27 January 2012 (UTC)

Thanks! פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

Lake or ocean storage

At first sight this looks like an intelligent suggestion. But, I have never seen a reference to it, and certainly lake storage is rather odd. This is energetically equivalent to pumping water into the lake (to raise the water level) and then using it to generate power later on. But, it is more efficiewnt and cost effective to do this directly with water than with air. So, find some cites or I'll blow it away.Greg Locock (talk) 01:00, 29 April 2008 (UTC)

Lake or ocean storage: Response to need for citations & Additional Carnot comments

I added citations, including one relating to a patent (expired or about to expire). The patent covers the same material: underwater storage bags and their advantages. As for pumping water into a lake, that's not the correct analogy for understanding the energies: highly pressurized air is useful stored energy, water sitting in a high dam is also useful, but water in a lake can't do anything. The criticism, however, may point to other problems: for example, at extreme depth, effects relating to hydrostatic equilibrium and pressure gradient force could create problematic heating and cooling and potentially catastrophic "hammer" effects (like "water hammer" in domestic plumbing). (I'll try to add some math on this - into this talk section - if I can remember the appropriate integral calculus equation to use or have the patience to rough it out with a sums table.)

Add.: I found the barometric formula here [1]. The pressure at the top of a 1000 meter column of air is 88 percent of the pressure at the bottom (whatever that is - if sitting in ocean, 100 atm); at 330 meters (at more reasonable depth for the plastic bags), the pressure is 96 percent, pretty close. Still, temperature changes of 10 to 20 deg.C could be problematic. Anthony717 (talk) 11:45, 30 April 2008 (UTC)

Add.: Perhaps the ultimate (if far-fetched and merely illustrative) solution would be a detachment of (pressure-resistant) submarines to deliver and retrieve special "packages" from the underwater storage location. Each package would be a reinforced plastic bag containing air and sand, the sand for ballast. Ideas like this show the problem with CAES generally: the potential for energy storage is huge, but the engineering problems are equally huge. Anthony717 (talk) 11:45, 30 April 2008 (UTC)

Clearly, the deep water storage system has thermal efficiency disadvantages compared to adiabatic storage. (Though ... I suppose the air bags could be insulated with "wet suits" - good for perhaps 12 hours of storage.) Carnot efficiency can only be improved by complex staged pumping, possibly with large pressurized equalization chambers (or columns) containing the necessary heat exchangers. On the other hand, energy recovery is greatly simplified by the constant pressure of the source (the turbines can be optimized for a particular intake pressure and rate of flow). Also, the huge expense of mining is eliminated. Anthony717 (talk) 04:58, 30 April 2008 (UTC)

"As for pumping water into a lake, that's not the correct analogy for understanding the energies: highly pressurized air is useful stored energy, water sitting in a high dam is also useful, but water in a lake can't do anything. "

I suggest you do the maths. I am right. That is the work done in inflating the bag underwater is identically equal to the gain in potential energy of the water in the lake. Archimedes and all that. Anyway thanks for the refs, that is fine now. Greg Locock (talk) 05:56, 30 April 2008 (UTC)

The thing is that you have to get a permit and you need space to pump the water up to a high location creating potential energy, whereas with air storage, you put it IN the lake. Of course this is talking about using a small percentage of the lake. I know a kibbutz at the bottom of a large slope on a hill, with all of Jerusalem's cleaned sewage water passing below. They wanted to use the water to pump it up at night (low cost electricity) and retrieve it in the day (without converting it to electricity, just to push it to the fields!) but were not allowed because of nature preservation on the hill. That's probably the main issue with water storage.

The second issue of course is energy density. Are you sure that potential energy density of water storage is higher than compressed air?

Last but not least the energy losses: I'm not so clear that you can get better results from a hydroelectric system, vs. a pneumatic electric generator system, both in terms of energy loss, and in terms of cost effectiveness. It seems that the plastic bag solution may be very low cost, and give a good bang for the buck.

Of course, the hype many times (especially in the 2000-2010 decade) was much more than the actual results, and it is yet to be seen how serious these claims are. פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

Unexpected natural log

As an outsider, I found these formula's to be surprising and completely non-intuitive to the point that it would be great if someone with a good handle on them could add some text on the significance to the apparent fact (based on the ln function in the equation) that as you increase the pressure, the energy storage becomes less and less dramatic.

Intuitively, if I have a handpump that pumps in 1 liter of low pressure gas per stroke into a 1 cubic meter tank it takes me 1000 strokes to double the pressure, and then 2000 strokes to double the pressure again (both times I pump slowly and all heat conducts away). Not only did the second doubling of pressure take more strokes with my handpump, each stroke was significantly harder that during the first doubling of pressure, and yet, the formula for energy content claims the second doubling of pressure only added as much energy as the first doubling.

Instead I would expect the second doubling to provide ~4X the amount of energy since it was 2X the number of strokes at an average of 2X the force.
If the ln function is correct, I could also do some surprising things like take a 1 cubic meter tank that is at 3 atmospheres connected via a closed valve to a tank that at one atmosphere and calculate the energy. Then I could open the valve and hear a hiss and even drive a tiny turbine and power a flashlight while the tanks adjusted to be 2 tanks of 2 atmospheres each. Then if I recalculate the stored energy I would find the energy stored went up, not down because ln(3) < 2*ln(2). Are the formula's correct or am I wildly off the rails. If the formulas are correct, then some text about the implications of this would be a great addition.Johnkoger (talk) 04:08, 1 August 2009 (UTC)

The maths looks right. Intuitively, an isothermal system wastes a great deal of the expansion work, because you lose the energy that you put into warming the gas when you compress it. A 100% efficient expansion would be adiabatic, that is, there would be no heat transfer between the gas and the environment at any stage.

The problem with that is that you have to insulate the reservoir, and if you don't then the expansion process freezes up. This is the fundamental stupidity with the aircar proposal. Realistic systems that were not just investor scams spent a lot of effort using heat exchangers to prevent this. I suggest that a graph of the thermodynamics would improve this article. Greglocock (talk) 02:15, 2 August 2009 (UTC)

Greg, IMHO you didn't answer his question. Your just saying the math is correct.

Where is he wrong in his calculations? פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

.John, 1 cubic meter at 3 atmospheres has an uncompressed volume of 3 cubic meters. For your experiment to wind up with 2 tanks of one cubic meter each with 2 atmospheres, you would have to have started with a tank at 4 atmospheres, right? So if you start with 3 atmospheres, two tanks of one cubic meter each would wind up with 1.5 atmospheres each, and the corresponding formula would be ln(3) to 2*ln(1.5) (1.098 vs. .8109). So energy is reduced as expected. So with this correction, the math does not produce any "magic" energy results, right? I know it may still seems off somehow- counter-intuitive.

On that score, our intuition going astray when we have unclear or inaccurate images of the physics involved. There are two key culprits that trip us up:

1. You remarked that strokes of the pump are more difficult as the tank becomes more filled with air, so since we are doing more work, the energy must be going into the compressed air. Think about it. When you take the first pump it is like pushing a car on level pavement. Say you put the parking brake on after you add one atmosphere of pressure. The car is now on a modest hill. Take the brake off and hold the car. Are you doing work? You bet. Cells are contracting, and they are consuming energy and oxygen to keep your muscles rigid. But are you adding any energy to the car? Nope. So a good part of your effort in following 2000 strokes is simply the force needed to counteract the force of the compressed air trying to get out. The only thing you are adding is whatever exceeds the effort that is deducted simply to keep the air from going backwards- and this deduction gets larger and larger as you put more atmospheres in. It is as if you are pushing the car up a hill that gets steeper and steeper.
2. There is another source of confusion that didn't enter much into your example. We think of the energy being stored solely in the compressed air, when it isn't. We know about the refrigeration effect, but our imaginations don't really embrace the idea that the energy is both in the compressed air and disipated into the room. We intellectually know this fact- you yourself mentioned the heat lost during pumping- but our intuitions don't really catch on so fast. We kind of think of the energy as being in the tank- as if it were gasoline, when in fact it is stored both in the tank and in the elevated temperature of the room. This does not seem like any big deal until you talk about the incredibly low temperatures in CAES applications when large amounts of air is expanded. Then it is a huge shock about either the Non Green burning of Natural Gas, or the mind numbing complexity of adiabatic systems. J JMesserly (talk) 18:35, 14 April 2012 (UTC)

Guys, you didn't check John's calculations carefully. The adiabatic/isothermal issues are a red herring: as John said, he can do his compressions slowly enough to make the thermal considerations irrelevant. John, in fact your intuition is exactly correct and exactly matches the formula. Where you made your mistake is in evaluating the formula. Lets look closely at your example. Suppose you start with a tank of gas at ambient pressure P_a, and after 1000 strokes of your compressor you have increased the pressure to P_1 = 2 * P_a. The formula says the energy in the tank, E_1, is E_1=V*P_1*ln(P_1/P_a) = V*P_1*ln(2), since P_1/P_a=2. Now, put in another 2000 strokes, the pressure becomes P_2 = 2*P_1=4*P_a. The energy E_2 is now E_2=V*P_2*ln(P_2/P_a)=V*P_2*ln(4). How much have you increased the energy, i.e. what is E_2/E_1? Well, that is easy to calculate:

E_2/E_1 = P_2*ln(4) / (P_1*ln(2))

= P_2/P_1 * ln(4)/ln(2)

= 2 * ln(2^2)/ln(2)

= 2 * 2*ln(2)/ln(2)

= 4

So after your next 2000 strokes, the given formula says you have increased the energy by 4 times. Your intuition was bang on. You just didn't look at the formula correctly.

You may have been thinking you _added_ 4 times as much as you added the first time, i.e. that E_2-E_1 (the amount of energy you added) is 4 times the original energy you added (E_1). I.e. you might have expected E_2-E_1=4*E_1, or E_2=5*E_1. But this is not quite correct because you statement "2X the number of strokes at an average of 2X the force" is not quite correct: the "average of 2X the force" is not quite correct, but it is close (as you see from my calculations). On the other hand, this formula isn't quite correct. See my comments below. I will add them to the main page soon unless someone explains to me where I am wrong. On the other hand, the "correct" formula below complicates the analysis of your example quite a bit.— Preceding unsigned comment added by DavidIMcIntosh (talk • contribs) 19:11, 12 June 2014 (UTC)

CHARLES HODGES AND THE PORTER COMPOUND AIR LOCOMOTIVES

While tidying the "Types" section I removed the following unreferenced text: "see CHARLES HODGES AND THE PORTER COMPOUND AIR LOCOMOTIVES". If anyone knows what this relates to and can add a ref please do so. Cheers -- Timberframe (talk) 10:52, 21 April 2009 (UTC)

dispute over energy content

A similar proposal to the caisson method is being funded by EON - The reference quotes the energy content at a depth of about 1,970 feet,as some 6,945 MWh of energy for every cubic meter, however this is clearly wrong, since 1 cubic meter of air at that depth (600 meters) would contain 600m*gravity*1000kg/m^3 = 600*9.8*1000/(3600*1000000) = 0.0016 MWh

bear in mind, it is not the energy content of the air you are interested in. It is the energy contect of the 1 m3 of water than you have raised by 1 meter - this contains about 10 times the energy of the compressed air per se.

Are you suggesting that in an adiabatic process there would be any difference in the energy stored, whichever way you calculate it? Greglocock (talk) 02:40, 2 May 2009 (UTC)

Isothermal storage physics

Hi, I don't understand the formulas. The article says Energy W is a volume integral from V_A to V_B. But the volume of the vessel is constant all the time, may V means the amount of air at atmospheric pressure? 91.8.113.69 (talk) 21:56, 28 November 2010 (UTC)

I hope its clear now פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

way too academic

Compressed Air Energy Storage is a very specific term, applying to a particular approach to large scale energy storage within the utility industry. It's relatively simple. But the article as written dives right into all the talk about adiabatic, isothermal, etc. without first explaining the basis of how CAES projects (and there are currently two specific CAES projects operating) work. These more obscure engineering references might be discussed much further down, in the context of some of the R&D going on for CAES. — Preceding unsigned comment added by Onefinity (talk • contribs) 08:13, 5 January 2011 (UTC)

It wasn't really academic, just not written clearly, with different versions put together. פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

File:Minebw.jpg Nominated for speedy Deletion

An image used in this article, File:Minebw.jpg, has been nominated for speedy deletion at Wikimedia Commons for the following reason: Copyright violations What should I do? Don't panic; deletions can take a little longer at Commons than they do on Wikipedia. This gives you an opportunity to contest the deletion (although please review Commons guidelines before doing so). The best way to contest this form of deletion is by posting on the image talk page. If the image is non-free then you may need to upload it to Wikipedia (Commons does not allow fair use) If the image isn't freely licensed and there is no fair use rationale then it cannot be uploaded or used. If the image has already been deleted you may want to try Commons Undeletion Request This notification is provided by a Bot --CommonsNotificationBot (talk) 17:14, 3 October 2011 (UTC)

Seems bot gave it a kick. Maybe I'll get the time to fix this. פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

I suggest to translate this article in French language

I am looking to different energy storage process, and I think a french version of you article will be welcome, how can I proceed ahead ? — Preceding unsigned comment added by Mbariou (talk • contribs) 10:33, 7 November 2011 (UTC)

IMHO, open an article in French, and make it a stub, and in the talk page suggest it be translated from English. פשוט pashute ♫ (talk) 06:37, 16 March 2012 (UTC)

History: expansion needed tag removed

I added some material to the history section with cites in response to the expand section tag placed there. After making the additions, I removed the tag. If anyone feels further expansion is needed, feel free to restore it. There certainly have been many more announced projects and these were not mentioned. J JMesserly (talk) 17:45, 14 April 2012 (UTC)

Contested NYTIMES statement

Note on a retracted bit of info regarding salt dome capacities. In the Times article I cited, Wald wrote that the salt cavern could handle 5 times the 1100 psi pressure that McIntosh now uses. Others may see this and want to mention it as I did. I wound up retracting it because of an authoritative report in Gas Turbine World, Sept-Oct 2009, editor de Biasing states that the max allowable pressure is calculated at .9 of depth. So the ceiling of the McIntosh cavern at 1500 foot depth allows a max of only 1350psi. a reprint may be found at www.espcinc.com/library/GTW%20 ACAES%20Article.pdf. I suspect Wald is in error, but I don't know. Since it is contested, I pulled it. -J JMesserly (talk) 10:30, 17 April 2012 (UTC)

Trombe

I wonder why there is no mention of a trombe as a means of storing compressed air. — Preceding unsigned comment added by 83.240.200.90 (talk) 18:15, 3 December 2012 (UTC)

LightSail.com claims 70% round trip power efficiency using water mist cooling

Please see http://www.lightsail.com/tech.html and their CEO's Google Solve for X talk from a few days ago for the details, but I'm not sure which category (e.g. hybrid etc.) this fits into. so could someone please add it to the article? Apparently using water mist as a heat exchanger is a completely new idea bringing efficiency from 30% to 70%, and LightSail has patents on it. I'd feel more comfortable if an expert took a look at it before it was added. Neo Poz (talk) 23:15, 12 February 2013 (UTC)

History, sources for city wide installations?

Just came upon that article, interesting. I'm just very surprised to hear about Dresden, which is my hometown - I never heard of a pneumatic storage system installed there anywhere and I'm very tech interested. Can't find anything with Google as well. So is it possible to have a source for that??

RWE

Rheinisch-Westfälisches Elektrizitätswerk AG is developing 2 new systems; see ALACAES and ADELE. Ref 2: http://content.lib.utah.edu/utils/getfile/collection/etd2/id/86/filename/1430.pdf Mention in article KVDP (talk) 17:36, 24 July 2013 (UTC)

Math is correct, physics has small error?

Maybe its just late at night and I'm being stupid, but isn't the formula for the stored energy ignoring the work done by the ambient pressure, which should not be included in the calculation of the "stored" energy, as it is not recoverable?

Let's look at the situation of moving from state A: volume $V_{A}$, pressure $P_{A}$, to state B: volume $V_{B}$, pressure $P_{B}$, with constant temperature throughout. For simplicity, lets assume that $P_{A}$ is the ambient pressure. As has been pointed out, the pressure law yields $V_{A}P_{A}=V_{B}P_{B}$, and in fact for any intermediate state $V,P$ we have $V_{A}P_{A}=VP$. Now, suppose I start with a gas in a tube of cross section 1 at pressure $P_{A}$ and volume $V_{A}$, so the tube has length $V_{A}$. Lets put a plunger at one end. Initially, I put no force on the plunger (which has area 1), and the ambient pressure puts a force on the plunger of magnitude $P_{A}$. Now I put an infinitesimal force on the plunger and begin to slowly compress the gas. At any intermediate state, with the plunger at position $V$, so volume at $V$, and pressure at $P(V)=P_{A}V_{A}/V$, I maintain a force infinitesimally larger than what is required to maintain steady state. BUT, at such an intermediate state, ambient pressure always maintains a force of $P_{A}$, so the force that I must exert is

$F(V)=P_{A}\left({\frac {V_{A}}{V}}-1\right)$

Thus, the work that _I_ do in compressing the air (and this is the recoverable energy) is

${\begin{aligned}W_{A\to B}&=\int _{V_{A}}^{V_{B}}P_{A}\left({\frac {V_{A}}{V}}-1\right)dV\\&=P_{A}V_{A}\operatorname {ln} \left({\frac {V_{B}}{V_{A}}}\right)-P_{A}V_{B}+P_{A}V_{A}\\\end{aligned}}$

Now, typically we are wondering what the (recoverable, ideal) stored energy is in a tank, i.e. we know $V_{B}$, $P_{B}$ and $P_{A}$, but not $V_{A}$. Using $P_{A}V_{A}=P_{B}V_{B}$ (so, e.g. $V_{B}/V_{A}=P_{A}/P_{B}$ ), (changing sign to account for who's doing work on what...) we can write:

$RecoverableEnergy(V_{tank},P_{tank},P_{ambient})=V_{tank}P_{tank}\operatorname {ln} \left({\frac {P_{tank}}{P_{ambient}}}\right)-V_{tank}(P_{tank}-P_{ambient})$

The first term agrees with what in on the web page, but the web page ignores the fact that the ambient pressure would do work on the gas that is not recoverable (except if the tank were taken to outer space...), i.e. it ignores the second term. Writing the result in this format:

$RecoverableEnergy(V_{tank},P_{tank},P_{ambient})=V_{tank}\left(P_{tank}\operatorname {ln} \left({\frac {P_{tank}}{P_{ambient}}}\right)-P_{tank}+P_{ambient}\right)$

makes at least on property clear: linear in $V_{tank}$ (double the size of the tank, double the energy). If we want the formula in terms of gauge pressure, lets use $\rho =P_{ambient}$ for the ambient pressure, $p$ for the gauge pressure, and just $V$ for the volume of the tank. (By definition, $p=P-\rho$). Then the formula becomes:

$RecoverableEnergy(V,p,\rho )=V\left((p+\rho )\operatorname {ln} \left(1+{\frac {p}{\rho }}\right)-p\right)$

For $p<\rho$ , this has a nice Taylor series expansion.

$RecoverableEnergy(V,p,\rho )=V\left({\frac {1}{1\cdot 2}}{\frac {p^{2}}{\rho ^{1}}}-{\frac {1}{2\cdot 3}}{\frac {p^{3}}{\rho ^{2}}}+{\frac {1}{3\cdot 4}}{\frac {p^{4}}{\rho ^{3}}}-...\right)$

 — Preceding unsigned comment added by DavidIMcIntosh (talk • contribs) 02:28, 12 June 2014 (UTC)