A Solar Grand Plan??

[Matteo Martini]

I just came across into an interesting article of Scientific American, where it is proposed a "Solar Grand Plan", which could provide "a massive switch from coal, oil, natural gas and nuclear power plants to solar power plants could supply 69 percent of the U.S.’s electricity and 35 percent of its total energy by 2050"
The cost seems at first pretty huge (USD420Billions in 40 years), but, thinking again, this is what the US alone spend on oil every few months.

Here are some interesting passages:
- A vast area of photovoltaic cells would have to be erected in the Southwest. Excess daytime energy would be stored as compressed air in underground caverns to be tapped during nighttime hours;
- A new direct-current power transmission backbone would deliver solar electricity across the country;

Here is a link to the article:
http://www.sciam.com/article.cfm?id=a-solar-grand-plan&page=1

 

[BillC]

Thermodynamics isn't my area. But wouldn't pressurising air to 1100 psi (second page of the report) increase its temperature considerably? Then, as the air was stored underground until the off-peak period, it would cool down, at the cost of efficiency?

On what I do know more about, the report claims "HVDC lines lose far less energy than AC lines over the same span"; this is untrue. Line-loss in a high-voltage DC transmission system is less than AC, but it is not far less. The most common reasons for installing DC lines are to avoid synchronisation issues between weakly-coupled grids, to avoid reactive charging currents (which are a source of inefficiency, as well as resulting in high voltages), and occasionally, to reduce short-circuit currents.

 

[Dilb]

Thermodynamics isn't my area. But wouldn't pressurising air to 1100 psi (second page of the report) increase its temperature considerably? Then, as the air was stored underground until the off-peak period, it would cool down, at the cost of efficiency?

It depends on how quickly you compress it. If you partially compress a gas, then let it cool down, then compress it some more, you can do a lot less work to reach the same ultimate temperature and pressure. The limiting cases are an isothermal (constant temperature) compression and an adiabatic (perfectly insulated) compression.

The trade off is that to approximate an isothermal compression, you need a really big heat exchanger, or to run the process very slowly.

 

[INRM]

Why would you compress the air for use? Why not just store it in batteries?

INRM

 

[BillC]

Why would you compress the air for use? Why not just store it in batteries?

INRM

The energy storage density of batteries is rather low. A standard lead-acid 12V car battery might have a capacity of 60 ampere-hours, that is, 720 watt-hours or about 2.6 MJ. To supply over a peak period, you need a few kW per household for several hours, and hence more than a handful of batteries. For large quantities of power, the number of batteries becomes cumbersome, particularly when you factor in the finite lifetime of the individual batteries, and the inefficiencies of the charging cycle. These figures can be improved upon, but not by great leaps and bounds.

 

[shadron]

It depends on how quickly you compress it. If you partially compress a gas, then let it cool down, then compress it some more, you can do a lot less work to reach the same ultimate temperature and pressure. The limiting cases are an isothermal (constant temperature) compression and an adiabatic (perfectly insulated) compression.

The trade off is that to approximate an isothermal compression, you need a really big heat exchanger, or to run the process very slowly.

And, like all limiting cases, they aren't practically reachable in reality.

Isothermal isn't possible. Whether you compress a gas quickly or slowly, you are going to input the same amount of energy in heating it. The heat will be there, and will slowly leak (conduct) into the rock. That heat loss represents energy loss. So, you either have to cool the gas with a heat exchanger (and it needn't be all that huge; it only has to capture the lion's share of the compression energy which occurs right in the compressor), thus siphoning off the heat to use elsewhere, or you just let it go. In a daily cycle, there might not be too much loss into the rock; rock, like glass, not a good heat insulator, but not a good conductor either. Note also that when you reverse the cycle the gas is going to get cold - just as much cold as it heated up. Handling that will also take care. Perhaps with some planning this alternating source of heat and cold might be useful.

 

[shadron]

The need for a storage place has always been the buggaboo of alternate power schemes. Batteries are expensive, noxious, poisonous in several ways, and just plain dumb. For small users, the ideal sink for their excesses is teh energy grid - pump it out when you can, take some back when you can't. What is really needed is a way to send excess energy to other continents when we're in the sunlight, and draw from them when we aren't. Sounds like a job for super-conductors.

Where's research when we need it?

 

[bokonon]

Is compressed air a good storage reservoir for a heat exchanger? Is there something better for long-term storage? I was wondering how feasible it would be to store the heat that was extracted to cool structures in the summertime, and use it to heat them in the wintertime.

 

[shadron]

Is compressed air a good storage reservoir for a heat exchanger?

I think you mean good storage for an energy system. The heat exchanger is a way to extract heat and apply it somewhere.


The problem is one of scale. There are better solutions than compressed gas, but not in the scale that is required for the magnitude of the job. Lithium hydride batteries are very good, but very expensive, and have other drawbacks. In Colorado, Xcel Energy (our local supplier) has a pair of reservoirs, one a couple of hundred feet higher than the other. They use surplus energy to pump water to the upper reservoir, and then let it generate power in the reverse cycle. Even this is too small a scale for what they're talking about here, though, and it depends on a rather special, rare geological happenstance. At some point, if space elevators become possible, they might be able to store energy as potential by moving it to high(er) orbit, but I think if we ever get there our energy problems here will have been licked anyway.

I was wondering how feasible it would be to store the heat that was extracted to cool structures in the summertime, and use it to heat them in the wintertime.

That might certainly be possible. However, in the current scheme, the heat/cold cycle is daily, not yearly, so if you have use of one or the other in one season, it will be wasted in the other. What is needed is a constant use; so you perhaps use the heat exchanger to run a turbine, create electricity, and let the users of that determine whether they want to heat or cool with it.

 

[Dilb]

And, like all limiting cases, they aren't practically reachable in reality.

That's why I said you need big heat exchangers to approximate it.

Isothermal isn't possible. Whether you compress a gas quickly or slowly, you are going to input the same amount of energy in heating it.

Incorrect. There are two things going on as we compress a gas:
1) We reduce the volume it occupies.
2) We do work on it against it's pressure, which is added as heat to the gas.

1 causes an increase in pressure simply by having more gas in less space, i.e. Boyle's law. 2 causes an increase in pressure because of the increase in temperature, i.e. Gay-Lussac's law. If we start compressing the gas, the volume decreases and the temperature increases, both of which add to the work we do.
However, we can pause in the middle of our compression, and let it cool down. Then heat flows out of the gas, causing the temperature and pressure to drop. When we resume compression, we have less pressure to work against, so we don't need to do as much work to compress the gas the rest of the way.

If we could somehow manage an actual isothermal compression, we could have no energy losses, despite the fact that we transfer heat out of the gas during our compression. The trick is when we go to decompress our stored gas, it cools down when it expands. If we reverse our isothermal compressor, for an isothermal expansion, we could hypothetically get 100% of our energy back.

The problem is that an isothermal compression or expansion would literally take forever. To approximate it well, you need several stages of compression with effective (i.e. large) heat exchangers between each stage, to try and keep the gas from heating up too much.

 

[Dilb]

Is compressed air a good storage reservoir for a heat exchanger? Is there something better for long-term storage? I was wondering how feasible it would be to store the heat that was extracted to cool structures in the summertime, and use it to heat them in the wintertime.

I've seen that evaluated in a book, which unfortunately I've completely forgotten the title of. But the net result is that you need to start off with very large buildings (houses are nowhere near large enough), and then devote a lot of space to a very big, very well insulted tank, or otherwise you'll never keep the heat from leaking out during the 6 months.

 

[shadron]

Incorrect. There are two things going on as we compress a gas:
1) We reduce the volume it occupies.
2) We do work on it against it's pressure, which is added as heat to the gas.
1 causes an increase in pressure simply by having more gas in less space, i.e. Boyle's law. 2 causes an increase in pressure because of the increase in temperature, i.e. Gay-Lussac's law. If we start compressing the gas, the volume decreases and the temperature increases, both of which add to the work we do.
However, we can pause in the middle of our compression, and let it cool down. Then heat flows out of the gas, causing the temperature and pressure to drop. When we resume compression, we have less pressure to work against, so we don't need to do as much work to compress the gas the rest of the way.

OK, I get the gist of your argument, and I stand corrected. Unfortunately,

If we could somehow manage an actual isothermal compression, we could have no energy losses, despite the fact that we transfer heat out of the gas during our compression. The trick is when we go to decompress our stored gas, it cools down when it expands. If we reverse our isothermal compressor, for an isothermal expansion, we could hypothetically get 100% of our energy back.

As you note, we can't. The alternative is to insulate the chamber and do it adiabatically, which is also not completely possible, but is more feasible then the isothermic.

The problem is that an isothermal compression or expansion would literally take forever. To approximate it well, you need several stages of compression with effective (i.e. large) heat exchangers between each stage, to try and keep the gas from heating up too much.

Thanks for explaining that so that even an engineer can understand.

 

[Matteo Martini]

If we could somehow manage an actual isothermal compression, we could have no energy losses, despite the fact that we transfer heat out of the gas during our compression. The trick is when we go to decompress our stored gas, it cools down when it expands. If we reverse our isothermal compressor, for an isothermal expansion, we could hypothetically get 100% of our energy back.

The problem is that an isothermal compression or expansion would literally take forever. To approximate it well, you need several stages of compression with effective (i.e. large) heat exchangers between each stage, to try and keep the gas from heating up too much.

In page 3, they are talking about retaining heat efficiently in insulated tanks filled with molten salt

 

[Jimcalagon]

The need for a storage place has always been the buggaboo of alternate power schemes. Batteries are expensive, noxious, poisonous in several ways, and just plain dumb. For small users, the ideal sink for their excesses is teh energy grid - pump it out when you can, take some back when you can't. What is really needed is a way to send excess energy to other continents when we're in the sunlight, and draw from them when we aren't. Sounds like a job for super-conductors.

Where's research when we need it?

Maybe I'm being thick, but couldn't the energy be stored as potential energy - use the electricity generated to pump water to a high-altitude reservoir and then allow it to drain through turbines when power is needed (cf. the Dinorwic hydroelectric station in North Wales). Would this be too inefficient?

Or how about using the power to spin up thousands of flywheels (or one massive one ) which could be used to power dynamos when needed?

 

[DavidS]

Incorrect. There are two things going on as we compress a gas:
1) We reduce the volume it occupies.
2) We do work on it against it's pressure, which is added as heat to the gas.

Alas, also incorrect. The two essential things going on as we compress a gas are:
1) We reduce its volume
2) We raise its pressure
Any other effects are processing details.

We could, for example:
a) Isochoric cooling, which will reduce pressure at constant volume
b) Let the container collapse irreversibly to a smaller volume and the original pressure, which will extract no work.
c) Isochorically heat the gas back to the original temperature, which will raise the pressure above the original pressure.
The resulting fluid will be indistinguishable from gas "compressed" to the same conditions by any other process.

OK, so that's a bit nitpicky, but in the interest of thermodynamic literacy I take issue with the tail of your second point, "...work... is added as heat...".

Work is *NOT* heat. The work done on the gas does add energy to the gas, but that's not heat in the thermodynamic sense.

If we could somehow manage an actual isothermal compression, we could have no energy losses, despite the fact that we transfer heat out of the gas during our compression.

If you don't count the heat transfer to/from the gas as energy loss during isothermal compression, what *do* you count as an energy loss? Unless I'm missing something, that criteria lets in all processes -- the first law says we never have "energy losses" anyway.
Unless I'm missing your point, the second law says you'll lose *more* "energy" (ultimate work output) that way anyhow. The work input by adiabatic compression can be completely recovered as work output on adiabatic expansion, but if you let that input work energy "leak off" as heat you'll need another heat engine to turn it back into work again... at less than unit conversion efficiency.

The problem is that an isothermal compression or expansion would literally take forever. To approximate it well, you need several stages of compression with effective (i.e. large) heat exchangers between each stage, to try and keep the gas from heating up too much.

No, the number of stages is irrelevant. All that matters is that heat transfer occur quickly enough to maintain constant temperature. I agree that industrially practical implementations should be left as an exercise for the reader.

 

[Dilb]

Alas, also incorrect. The two essential things going on as we compress a gas are:
1) We reduce its volume
2) We raise its pressure
Any other effects are processing details.

If we're really getting pedantic, only 1) is necessary. But if we are using a compressor, my version is what happens.

We could, for example:
a) Isochoric cooling, which will reduce pressure at constant volume
b) Let the container collapse irreversibly to a smaller volume and the original pressure, which will extract no work.
c) Isochorically heat the gas back to the original temperature, which will raise the pressure above the original pressure.
The resulting fluid will be indistinguishable from gas "compressed" to the same conditions by any other process.

Strictly speaking, work will be extracted to accelerate the walls of the container, which is why it's an irreversible compression.

OK, so that's a bit nitpicky, but in the interest of thermodynamic literacy I take issue with the tail of your second point, "...work... is added as heat...".

Work is *NOT* heat. The work done on the gas does add energy to the gas, but that's not heat in the thermodynamic sense.

Yes, I should say the work done adds thermal energy to the gas, raising it's temperature. But for people who haven't studied thermodynamics, I don't think it's helpful to use the technically correct terms. If I was doing a thermodynamic analysis of the situation, sure, I'd be more careful.

If you don't count the heat transfer to/from the gas as energy loss during isothermal compression, what *do* you count as an energy loss? Unless I'm missing something, that criteria lets in all processes -- the first law says we never have "energy losses" anyway.
Unless I'm missing your point, the second law says you'll lose *more* "energy" (ultimate work output) that way anyhow. The work input by adiabatic compression can be completely recovered as work output on adiabatic expansion, but if you let that input work energy "leak off" as heat you'll need another heat engine to turn it back into work again... at less than unit conversion efficiency.

Again, this is a lack of vocabulary. So long as we don't have any non-isothermal heat transfer, in principle we have no real losses, and any energy we store in our compressed gas can be extracted. For people familiar with thermodynamics, I'd say we can have 100% exergy/free-energy efficiency.

In terms of energy, the energy given off as heat by an isothermal compression can be entirely recovered by the energy gained as heat during an isothermal expansion.

No, the number of stages is irrelevant. All that matters is that heat transfer occur quickly enough to maintain constant temperature. I agree that industrially practical implementations should be left as an exercise for the reader.

Again, technically yes, but a huge cylinder very slowly compressing down isn't how any real system actually works. Multistage compression, on the other hand, is used in all sorts of situations.

 

[BillC]

Maybe I'm being thick, but couldn't the energy be stored as potential energy - use the electricity generated to pump water to a high-altitude reservoir and then allow it to drain through turbines when power is needed (cf. the Dinorwic hydroelectric station in North Wales). Would this be too inefficient?

Or how about using the power to spin up thousands of flywheels (or one massive one ) which could be used to power dynamos when needed?

The cycle efficiency of a pumped-storage station is about 70%, if I recall. The largest flywheel generators I'm aware of (and there may be much bigger ones) are those at the JET research laboratory in Oxfordshire. They're good for 400MW -- but only for ten seconds. You're talking of a lot of flywheels.