What factors determine the energy storage capacity of compressed gases?

[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?

 

[Doug Huffman]

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

 

[Chestermiller]

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?

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

 

[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.

 

[RonL]

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.

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

 

[Philip Wood]

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

 

[RonL]

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

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

 

[russ_watters]

See, I would have quibbled with part of it:

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.

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.

 

[Philip Wood]

The heat flow comes after the work is already done.

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...

 

[RonL]

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...

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.

 

[russ_watters]

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...

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

 

[russ_watters]

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.

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!

 

[marcophys]

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.

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?

 

[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.]

 

[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?

 

[RonL]

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?

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.

 

[RonL]

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!

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?

 

[marcophys]

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

I understand... thanks :)

 

[RonL]

I understand... thanks :)

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

 

[marcophys]

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

Yes... I thought about this... do I put a warning in... and does that distract the reader, when the question was theoretical.
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.

I can picture the headline:
"Boy Dead After Reading Physics Forum
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 ;)

 

[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.

 

[RonL]

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.

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?

 

[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!

 

[RonL]

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!

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.:)

 

[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.

 

[RonL]

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.

Thanks Philip,
It is not a design you will find in a textbook or even in the patent office files (I suspect) and it seems to involve several different things, anyway I hope I haven't strayed to far off topic of compressed air energy storage, it all boils down to what happens with the heat:)

 

[CWatters]

Many years ago I flew model aircraft powered by compressed C02. In winter the tank and engine would get cold enough for ice to form on the outside and power would drop off. I wondered if this would be a difficult problem to overcome if we ever started to build compressed air powered cars. Would the engine and tank need massive fins and forced air to stop the things freezing up in winter?

 

[RonL]

Many years ago I flew model aircraft powered by compressed C02. In winter the tank and engine would get cold enough for ice to form on the outside and power would drop off. I wondered if this would be a difficult problem to overcome if we ever started to build compressed air powered cars. Would the engine and tank need massive fins and forced air to stop the things freezing up in winter?

The mind-set of the general population is being swayed in general, to a more responsible trend of thinking, that excessive waste of energy is no longer a trivial matter.
In my opinion, engineering could develop a method of hybrid use of compressed air and electric powered transportation, that engages the fact that the largest portion of needs are on very short power duration's.
Compressed air is a less desirable method in colder conditions, for the very reason you mention, but in my mind, if heat of compression is retained in a captive method, it can eliminate to a great extent what you are saying is a potential problem.

Between compressed air power and electric power, the ability to build both into the same single unit as a prime mover has possibilities that are (hopefully) starting to be looked at and considered by engineers.
Just my thoughts and will not be high power, high speed, dream machines for the uber-wealthy :)

 

[CWatters]

Shouldn't be too hard to do a back of the envelope calculation... Google says that a pure electric car like the Tesla needs about 180Wh per mile. Average commute by car in the UK is 10 miles (20 including return). So you need at least 3.6KWh of energy. Perhaps double for safety? Let's call it 6kWh or 21MJ.

Lets say you use water to store the "heat of compression" as you called it. We can work out how much water you have to carry..

Energy = mass * shc * DeltaT

or

mass = Energy / (sch * DeltaT)

If the water temperature can range from 20 to 100C that's a delta of 80C.

Mass = 21*10^6 / (4181 * 80)

= 64Kg of water

That would store enough heat (to decompress air) for about 30-40 miles.

 

[RonL]

Shouldn't be too hard to do a back of the envelope calculation... Google says that a pure electric car like the Tesla needs about 180Wh per mile. Average commute by car in the UK is 10 miles (20 including return). So you need at least 3.6KWh of energy. Perhaps double for safety? Let's call it 6kWh or 21MJ.

Lets say you use water to store the "heat of compression" as you called it. We can work out how much water you have to carry..

Energy = mass * shc * DeltaT

or

mass = Energy / (sch * DeltaT)

If the water temperature can range from 20 to 100C that's a delta of 80C.

Mass = 21*10^6 / (4181 * 80)

= 64Kg of water

That would store enough heat (to decompress air) for about 30-40 miles.

The mention of water brings to my mind, the thoughts of "hot water rockets" at Bonneville :) water can store a greater amount of heat.
A 200 to 300 Kg power system, should be a good weight budget for a short distance auto.

My main thought about energy storage in compressed air is something along the line of, 30 C @ compressor intake, then as pressure increases in the reservoir temperature rises to 200 C or greater, at this higher temperature a volume of air (and steam ?) equal to compressor volume is ejected through an expansion drive design that has a final temperature of just above freezing and pressure near 0 psi.
Insulating to prevent heat loss from the reservoir, gives the ability to use hotter air to drive the compressor bringing in cooler air. A very fine line between how much energy is needed at the compressor as opposed to how much is applied at the expansion transfer point.

 

[RonL]

I wonder if anyone can see a closeness to Maxwell's thought experiment ?
If the compressor is equal to the Demon function and the receiver transmits energy back to the compressor, the force of gravity is an added component not considered by Maxwell's thought experiment.
Just a thought.

 

[Stanley514]

Why we can store much more energy in compressed gas than in compressed spring? Is it because gas is more compressible than spring?
What relation exist between matter deformability and energy storage?

 

[Philip Wood]

Again I re-iterate (from post 4) that you're not storing energy in compressed air unless your method of storage involves raising the temperature of the air (and then, to use the energy, letting it cool again).

But, moving on, what does it mean to say that more energy is stored is stored in a gas than a spring? How much gas are you comparing with how much spring? Please note, I'm not trying to nitpick. I genuinely don't know how one would make a quantitative comparison.

 

[Stanley514]

Again I re-iterate (from post 4) that you're not storing energy in compressed air unless your method of storage involves raising the temperature of the air (and then, to use the energy, letting it cool again).

But, moving on, what does it mean to say that more energy is stored is stored in a gas than a spring? How much gas are you comparing with how much spring? Please note, I'm not trying to nitpick. I genuinely don't know how one would make a quantitative comparison.

It really depend on spring.

Carbon nanotube springs

are springs made of carbon nanotubes (CNTs). They are an alternate form of high density, lightweight, reversible energy storage based on the elastic deformations of CNTs. Many previous studies on the mechanical properties of CNTs have revealed that they possesses high stiffness, strength and flexibility. The Young's modulus of CNTs is 1 TPa and they have the ability to sustain reversible tensile strains of 6%[1] and the mechanical springs based on these structures are likely to surpass the current energy storage capabilities of existing steel springs and provide a viable alternative to electrochemical batteries. The obtainable energy density is predicted to be highest under tensile loading, with an energy density in the springs themselves about 2500 times greater than the energy density that can be reached in steel springs, and 10 times greater than the energy density of lithium-ion batteries..

http://en.wikipedia.org/wiki/Carbon_nanotube_springs
So, why carbon nanotube springs have better energy density than steel springs?

 

[RonL]

Why we can store much more energy in compressed gas than in compressed spring? Is it because gas is more compressible than spring?
What relation exist between matter deformability and energy storage?

You will find weight might be the biggest factor in why either would be considered for a particular function.

 

[Philip Wood]

So, why carbon nanotube springs have better energy density than steel springs?

The energy stored due to tensile stress per unit volume of solid is u = \frac{1}{2}Y \epsilon^2 in which Y is the Young modulus and \epsilon is the strain.

Both factors, Y and maximum possible elastic \epsilon are different for the two materials. The carbon-carbon covalent bonds exert more force per unit increase in separation of the atoms than the metallically bonded atoms in steel, leading to the nanotubes having a greater Young modulus than steel. Also, much larger strains can be suffered by the nanotubes than by steel before the material ceases to deform elastically. This is because the metallic bonding (pooled electrons) in the steel allows planes of atoms in crystals to slip over each other (promoted by the presence of dislocations) under moderate stress. This can't happen in the covalently bonded nanotubes, though they do break eventually under VERY large stress.