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HalliburtonEngineer (Petroleum)
2 Mar 11 20:19
Can anybody explain why liquid CO2 has such a temperature dependant heat capacity, especially at lower pressure (~1,000 psi - see attached graph)?
From the PVT diagram I don't see any phase changes at the peak heat capacities.
I am planning a job where we will be injection liquid CO2 into an oil well, but because of wellhead limitations, the CO2 needs to be heated before entering the well.
HalliburtonEngineer (Petroleum)
2 Mar 11 20:21
The graph was not attached in the first post, here it is.
Helpful Member!  gruntguru (Mechanical)
2 Mar 11 21:06
Saturation temperature at 1000 psi is about 80 deg F so there is a phase change. (Approximate because I am reading off a metric chart and converting)

http://www.union.dk/media/CO2-GB.pdf
 

Engineering is the art of creating things you need, from things you can get.

iainuts (Mechanical)
2 Mar 11 21:59
Agreed with gruntguru. Critical pressure for CO2 is 1071 psia and temperature 87.9 F. So for the line showing 1000 psi, everything to the left of the asymptote is liquid, to the right is gas. Saturation temperature for CO2 at 1000 psia is 82.3 F.

There's better thermophysical properties data on the net from NIST here: http://webbook.nist.gov/chemistry/fluid/
HalliburtonEngineer (Petroleum)
2 Mar 11 22:22
Thanks, it make sense that there actual is a phase change from liquid to gas when the pressure is below Pc (1,071 psi), but what is then happening above Pc.
Why the increase in heat capacity even at 2,000 psi?
iainuts (Mechanical)
2 Mar 11 22:55
Above the critical pressure, there is too much molecular energy to allow for surface tension, so there is no longer a distinct liquid/gas phase. If you had a liquid such as CO2 in a tank and you slowly added heat, the pressure would rise along the saturation line and there would be a distinct liquid/gas phase separation provided by the surface tension until you got to the critical pressure. In other words, the liquid would be saturated (boiling) and the gas would be saturated (ready to condense)*. Once you get above critical pressure, surface tension disappears and what used to be gas and what used to be liquid could start to mix because there is no longer any surface tension providing a distinct liquid/gas boundary that separates the two.

However, there isn't any other distinction one can easily make between gas and liquid. Above the critical pressure, the molecules still act like liquid molecules and the fluid is relatively incompressible if cold enough, and the molecules act like gas molecules if they are very warm. But there's still an 'overlap' between the two phases such that as temperature decreases, the compressibility factor (Z) decreases meaning it becomes more and more incompressible (like a liquid). The closer you are to the critical pressure, the more distinct that transition is. Conversely, the farther you are away, the less distinct that transition is. So as pressure increases, the 'bump' in the line you see, becomes less distinct.

*Note in 'real life' there is rarely such a distinct separation. Generally, the liquid is subcooled in some areas and boiling in others while the gas is superheated in some areas and condensing in others.
gruntguru (Mechanical)
2 Mar 11 23:47
Have a look at the p,h diagram on page 10 of the link I posted. There is still a phase change from supercritical gas to liquid as you cool through the critical temperature.

The top edge is 120 bar (1740 psi). The spacing of the isotherms is proportional to the amount of heat required per unit temperature change (Cp). You can see this spacing is large in the 313 to 333K range resulting in the high Cp value.

Engineering is the art of creating things you need, from things you can get.

MortenA (Petroleum)
4 Mar 11 1:50
The NIST site is good - but the union site is easier to use since it contains all in one book and has a Moliere diagram smile

Best regards

Morten
Helpful Member!  ione (Mechanical)
4 Mar 11 6:12
The peak of specific heat (cp) at 2000 psig should be at 142 °F, that is shifted on the left in comparison to the graph you've reported. Please check also the curve at 5000 psig wat the NIST link supplied by ianuits (the one you've reported seems to be wrong).

At critical point specific heat reaches its absolute maximum. There are anyway pseudocritical points, characterized by pressure above the critical pressure and temperature above the critical temperature, exhibiting relative maximum values of the specific heat at this particular pressure.
 

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