CO2 enthalpy 2

[thermodynut]

1. Be kind, first post by engineering school dropout, now entrepeneur.
2. I'm working out a power-required calculation for a CO2 refrigerant heat pump. Consulting an old Handbook of Engineering Calculations by T.G. Hicks, I find he derives power requirements for the compressor from the total heat added by the compressor. In the example, using R12, the enthalpy of vapor at 128 deg F less the enthalpy of vapor at 40 deg F is contributed by the compressor, and he calculates the power requirement of the compressor from this difference (90.64 Btu/lb - 82.71 Btu/lb = 7.93 Btu/lb, then converted into horsepower and into kW/hr based on an assumed compressor and motor efficiency.
3. However, using CO2, according to the table I'm looking at from the internet, the enthalpy of vapor DECREASES as temperature increases, from 102.125 Btu/lb at 41 degF to 94.229 Btu/lb at 77 degF.
4. I don't think this means the compressor gives out free power, but how do I handle the reversed sign (heat is given out by the compressor) and how do I calculate a power requirement.

If all this shows my ignorance, as it well might, please give me helpful suggestions for developing the right tools to understand it!

 

[zdas04]

I'm just finishing a pretty detailed analysis of a CO2 sequestration project and I think you are reading the table wrong. I am looking at a p-h chart for CO2 and the constant temperature lines run from left to right as temperature increases. This means that for any given pressure, enthalpy is higher with a higher temperature.

Just as an aside, I used NIST data to get the enthalpy at each major step in a 5 stage compressor (pressure and temperature for suction, discharge, and inter-cooler of each stage). Using m Delta h I was able to match the hp from the compressor manufacturer to within 2%. This stuff does indeed work.

David

 

[thermodynut]

Thank you, David ... that's enough to get me going again to figure out the readings. Now I just have to find a better co2 table ... looks like the nist information is by subscription only, which I'm not ready to do yet ...

 

[insult2injury]

[URL unfurl="true"]http://webbook.nist.gov/chemistry/fluid/[/url] is free.

I2I

 

[zdas04]

The free NIST data is awesome. The $200 REFPROP is way beyond amazing.

David

 

[thermodynut]

Thanks for the nist free reference. It is indeed awesome, and I'll have to try REFPROP soon.

BUT: The CO2 enthalpy for vapor does seem to change at around 248 deg K , rising with temperature up to 248 and then falling.

According to the NIST table, at 247K it's 19.234kJ/mol; at 248K, 19.235; at 249K, 19.235, and thereafter it gets lower and lower: 250K, 19.234 etc. Graphically, it's a different shape than R22 vapor enthalpy, which continues to rise with rising temperature.

I'm back at my original problem: if the compressor heats the gas by compression to the point where the enthalpy begins to drop, how can the enthalpy figures be used to calculate power?

 

[jpankask]

I'll have to second that REFPROP is an excellent program. I purchased this from NIST for use on my master's report on the carbon dioxide refrigeration cycle. This can be used to do amazing things with spreadsheets!

 

[insult2injury]

From the attached figure, I'm not sure that I understand what you're saying. Perhaps there is an issue with the pressure/state of the conditions you are entering.

I2I

 

[iainuts]

Hi therm'
Step 1 - Start by considering an 'ideal' compressor which is isentropic. Locate your inlet condition using whatever database you have. I'd agree REFPROP is the best commercial tool for this I've seen. We have a proprietary one very similar to it that I like even better, but whatever database you have, you SHOULD be able to identify the state of the fluid at the inlet conditions to your compressor. That means taking pressure and temperature and locating BOTH enthalpy and entropy (ie: Hin(actual) and Sin(actual)). [NOTE: Find enthalpy and entropy on a per mass basis and you can get power later.] Once you have BOTH those values from your initial conditions you can move to the next step.

Step 2 would be to determine the ideal conditions given the outlet pressure. Remember you have all the initial conditions, so the outlet condition is that point where the pressure is equal to discharge pressure and entropy is equal to the inlet entropy. From that point you now should be able to determine the state of the CO2 on the outlet of an ideal compressor. That state provides you the temperature, enthalpy and density of the fluid. If you do this with REFPROP, I believe there's a method to pull these values back given a pressure and entropy. If you still don't understand how to do this, please explain what you have for a properties database (ie: charts, the web site previously mentioned, etc...).

Step 3 is to determine the ACTUAL conditions for your machine. For this you need the compressor's isentropic efficiency which is defined as:
u(%) = dH(ideal) / dH(actual)
or
u(%) = (Hout(ideal) – Hin(actual) ) / (Hout(actual) – Hin(actual) )
where u(%) is isentropic efficiency (%)
Hout(ideal) = Outlet enthalpy for the ideal cycle determined by step 2
Hin(actual) = Inlet enthalpy determined from step 1.
Remember, the values should be on a per unit mass basis, we can multiply by mass to get power later.
You should be able to obtain the efficiency from the mfg, or maybe describe the machine you have and someone here can suggest an efficiency. If it doesn't need to be too accurate, a ballpark value will be easy to come by.

To solve for Hout(actual):
Hout(actual) = (Hout(ideal) – Hin(actual) ) / u(%) + Hin(actual)
Now you have the actual outlet enthalpy. So the actual change in enthalpy for this machine will be dH(actual) = Hout(actual) - Hin(actual)

Note that with the actual outlet enthalpy and actual discharge pressure, you should then be able to determine the state of the fluid on the outlet. This includes temperature, density and actual entropy.

Step 5 is to solve for power if needed. Power is simply dH(actual) (mass flow rate). If you don’t know how to determine mass flow rate, just shout.

Hope that helps.

 

[thermodynut]

I2I, that's probably true ... just not sure how to enter the right conditions. When I get an isobaric chart of temperature vs enthalpy, it looks like one of the lines of the figure you posted. But the chart of Saturation properties does not: it shows enthalpy of liquid going up on the left side and the enthalpy of vapor going down as temperature rises above 248K.

Using

http://webbook.nist.gov/cgi/cbook.cgi?ID=C124389

then choosing Fluid Properties then choosing Saturation Properties - Temperature increments and giving a range of temperature from 220K - 300K at 1deg intervals. Then on the chart selecting Temperature Y axis and Enthalpy X axis.

Thanks for your continuing help ... I do realize my problems are certain to lie with some form of mistake and/or ignorance!

 

[25362]

Reading the NIS tables at 16.2 bar I found for the vapor enthapy as follows:

@ 247 K, 19.234 kJ/mol as you did, but then
@ 248 K, 19.287
@ 249 K, 19.339
@ 250 K, 19.390

 

[thermodynut]

iainuts, thank you for the details ... I think I must have been typing a response to I2I while you were typing yours. I'm going to be studying ....

 

[dcasto]

here's a quick look at a CO2 chiller loop

 

[thermodynut]

Thank you! Wow, very complete and much appreciated.

 

[dcasto]

its to let you see how the enthaphy changes across compressors and valves. Not a design for use.

 

[Shmulik]

http://www.chemicalogic.com/download/co2_mollier_chart_met.xls

http://www.chemicalogic.com/download/co2_mollier_chart_eng.pdf

 

[thermodynut]

Thank you, Shmulik, too!