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Marcus10

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I am trying to find the theoretical power required to compress nitrogen from a pressure P1 to P2, as well as the final temperature T2 after compression.

I found no formula that were anywhere near complete, but I found this tool, which tells me that from 300K@1Bar, I need 271.4kw (271kj/s) to compress 1 kilogram (0.2194 cubic meters at 300K, 1 Bar) of pure nitrogen per second to 200 Bar. So I started with:

The same tool says that the final temperature would be 1261.79K, but when I refer to http://www.nist.gov/data/PDFfiles/jpcrd39.pdf , I find that at 1200K @ 200 Bar, (the datasheet doesn't go beyond that temperature for that pressure) the enthalpy is 37.2324kj/mol, while at 300K @ 1 bar, enthalpy is 8.7166kj/mol, a difference of 28.5158kj/mol, or

So this doesn't add up. Even if I apply a 60% efficiency (i.e. break power of 271.4kj/kg / 0.60 = 452.33kj/kg), the enthalpy of the gas would have increased more than twice as much as the amount of energy consumed by the compressor.

Air being mostly nitrogen, I also tried this tool, which gives 374HP for 465cfm ft 2901 psi, i.e. 279kw for 1kg from 14.7psi to 200 bar, approximately the same as what I get with the first tool, still much less that 1,017.93kj/kg. It does not give any final temperature though.

So what went wrong? I don't want an "online tools" to do the work for me; I want to understand how it works and how to do it, and I want to know that the result I get is acceptable, i.e. not too much approximated. All formulae I fold rely on things like the Cp/Cv ratio being constant, or that PV=nRT, which are far from true in reality.

I tend to believe that the best way to get reliable results is to stick as much as possible to datasheets, rather than to general formula that give too inaccurate approximations. What is the proper procedure to determine the power required for compression, final pressure or final temperature given one of the others and the pressure and temperature of the gas before compression? Can I do that using only the data found in the datasheet?

Note that I am working with pure nitrogen only, not air nor a gas mixture. I also want to work with extreme temperature, at least as low as 100K and at least as high 800K, and also with high pressure differentials, so no PV=nRT or alike.

Can you help?

I found no formula that were anywhere near complete, but I found this tool, which tells me that from 300K@1Bar, I need 271.4kw (271kj/s) to compress 1 kilogram (0.2194 cubic meters at 300K, 1 Bar) of pure nitrogen per second to 200 Bar. So I started with:

271.4kj/s * 1kg/s = 271.4kj/kg.

The same tool says that the final temperature would be 1261.79K, but when I refer to http://www.nist.gov/data/PDFfiles/jpcrd39.pdf , I find that at 1200K @ 200 Bar, (the datasheet doesn't go beyond that temperature for that pressure) the enthalpy is 37.2324kj/mol, while at 300K @ 1 bar, enthalpy is 8.7166kj/mol, a difference of 28.5158kj/mol, or

28.5158kj/mol / (28.013g/mol * 1kg/1000g) =

28.5158kj/mol / (0.028013kg/mol) = 1,017.95kj/kg.

28.5158kj/mol / (0.028013kg/mol) = 1,017.95kj/kg.

So this doesn't add up. Even if I apply a 60% efficiency (i.e. break power of 271.4kj/kg / 0.60 = 452.33kj/kg), the enthalpy of the gas would have increased more than twice as much as the amount of energy consumed by the compressor.

Air being mostly nitrogen, I also tried this tool, which gives 374HP for 465cfm ft 2901 psi, i.e. 279kw for 1kg from 14.7psi to 200 bar, approximately the same as what I get with the first tool, still much less that 1,017.93kj/kg. It does not give any final temperature though.

So what went wrong? I don't want an "online tools" to do the work for me; I want to understand how it works and how to do it, and I want to know that the result I get is acceptable, i.e. not too much approximated. All formulae I fold rely on things like the Cp/Cv ratio being constant, or that PV=nRT, which are far from true in reality.

I tend to believe that the best way to get reliable results is to stick as much as possible to datasheets, rather than to general formula that give too inaccurate approximations. What is the proper procedure to determine the power required for compression, final pressure or final temperature given one of the others and the pressure and temperature of the gas before compression? Can I do that using only the data found in the datasheet?

Note that I am working with pure nitrogen only, not air nor a gas mixture. I also want to work with extreme temperature, at least as low as 100K and at least as high 800K, and also with high pressure differentials, so no PV=nRT or alike.

Can you help?

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