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Why do CAES systems have intercoolers after every compression stage?

Isn't it a waste of work, since the air will cool anyway in the storage cavern?

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    $\begingroup$ have you looked at different compression processes (adiabatic, isothermal) and their energy needs? What attempts have you made to answer the question yourself, where are you stuck? $\endgroup$ – mart Jun 29 '16 at 14:31
  • $\begingroup$ Because PV = nRT. 'nuff said $\endgroup$ – Carl Witthoft Jun 30 '16 at 13:00
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Not just CAES system, intercooling is desired for multi stage compressors in general, if you checked this diagrams of isentropic, polytropic and isothermal compression processes between the same pressure limits you can see that the curve that requires minimum power (area to the left of the process curve) for the same inlet and outlet conditions is the curve on the left (isothermal compression)

enter image description here

So, by removing sufficient heat from the compression process say by constant cooling of the compressor casing you can get close the isothermal path. But since cooling the casing won't be much effective in removing heat another technique is used which is stage intercooling, and here in this figure you can see the saved power by splitting the compression process into two stages with intercooling in between:

enter image description here

Isn't it a waste of work, since the air will anyway cool in the storage cavern.

I hope it's clear now that it's not a waste of work (at the contrary). And it won't be much of a storage system without a proper thermal insulation to minimize the heat loss during the hours of storage.

(Figures are from Cengel's book of Thermodynamics - An Engineering Approach)

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    $\begingroup$ Two additional points: (1) without intercooling, you have to design a compressor and storage system that can withstand higher temperatures, and (2) you would also have to produce a higher pressure at the output of the compressor, since the pressure would decrease at constant volume as the stored air cooled down. An intercooler can reduce the volume as the air cools while flowing through it, and maintain the pressure, as in the diagram above. $\endgroup$ – alephzero Jun 29 '16 at 19:15
  • $\begingroup$ It might be worth explaining that reversible processes like adiabatic/isothermal expansion/compression are 100% efficient. Also, an intercooler requires a reheater to work correctly. $\endgroup$ – Aron Jun 30 '16 at 5:20
  • $\begingroup$ @Aron What reheater? $\endgroup$ – Algo Jun 30 '16 at 8:33
  • $\begingroup$ @Algo On (adiabatic) decompression, the gas will cool significantly. A heater is often used if the gas needs to be quickly decompressed. $\endgroup$ – Aron Jun 30 '16 at 8:51
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It would be a waste of work, if the air did not cool in the storage cavern!

But as you say, it does cool, hence you'll have less pressure available when expanding the air than the pressure you needed to work against when compressing it. The excess pressure could be avoided by compressing in isothermal mode, and as Algo said you approximate isothermal by putting an intercooler between two isentropic compressors.

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