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# CO2 temperature rise after pumps

## CO2 temperature rise after pumps

(OP)
CO2 enters the first pump at 300psi 0C, exits at 850psi 30C, enters the second pump, exits at 1200psi 50C. What temperature would it exit the second pump at if the initial temp was 35C?

I've searched the forums, textbooks and after several attempts of calculating I don't think I have the right approach. Any suggestions would be very appreciated.

### RE: CO2 temperature rise after pumps

So, from those numbers, tell us how much energy is being input by pump_1 and by pump_2.

If temperature_2 and temperature_3 are the result of the energy of compression of the pumps, (and are not being regulated or cooled somehow), and if the flow rate remains the same.

Then, why do you not think the greater inlet temperature would yield a greater outlet temperature, if the pump energy difference did not change?

### RE: CO2 temperature rise after pumps

" I don't think I have the right approach"

Well what is your approach?? Then we might be able to comment.

CO2 is strange stuff and you're close to the phase boundary changes with your quoted pressures and temperatures.

Do you keep constant entropy?

BTW at the pressures and temperatures you're quoting, CO2 is normally regarded as vapour / gas, not a liquid. hence you're looking at compressors, not pumps

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

PV = NRT

### RE: CO2 temperature rise after pumps

(OP)
The CO2 does reach critical temperature and pressure in this system. At 30.95 C (304.1 K) and 1070 psi (7.38 MPa) the density [ρ] is 0.551 g/cm^3, this and the following data are from NIST:

Approaching it as an enthalpy problem hasn't got me anywhere because none of the ∆H = ∆U + ∆(PV) variables are constant.

The temperature rise is from the energy added to the system by the compressors/pumps. For simplicity can I assume the temperature differences can be directly converted to Joules, so a 30 C rise is 56973 added to the system?
(1 Joule is equal to 0.000526565076466 Celsius heat unit.)

### RE: CO2 temperature rise after pumps

(OP)
I've been leaning towards racookpe1978's approach. In that case can I consider it a linear system so if I raise the initial temperature by 35 C the final temperature will go up by 35 C also?

### RE: CO2 temperature rise after pumps

If your going to look at it from an energy added standpoint you will need to consider the flow rate and the temperature dependent specific heat of CO2. Here is a link to specific heat data: Link

Also, how accurate do you need the number? If +/- 5C is good enough and you are staying away from the phase transition then just take the current temp rises and be done with it.

### RE: CO2 temperature rise after pumps

(OP)
hendersdc, would you mind quickly explaining why flow rate and specific heat should be considered? I'm trying to develop an intuitive understanding of whats happening.

When you say "staying away from the phase transition"; it does reach critical temperature and pressure in the second booster. What effect does this have on the system?

+/- 5 C is good enough, did you land on this range because of the finite energy added to the system?

Thanks

### RE: CO2 temperature rise after pumps

"because none of the ∆H = ∆U + ∆(PV) variables are constant" - Like I said CO2 is strange stuff. If you go near the phase change line then it gets even weirder.

35 C and higher and you're in vapour phase so it will start to behave a bit more like a standard gas especially if you stay below 1070 psig.

As you're heading into 1200, then you're in super critical when it gets all weird again.

Remember - More details = better answers
Also: If you get a response it's polite to respond to it.

### RE: CO2 temperature rise after pumps

Flow rate and specific heat should be considered because the amount of energy it takes to raise a unit mass by unit temperature varies with temperature, there is no static 1C temp rise = X Joules conversion.

The phase transition comment goes along with what LittleInch is saying, behavior gets complicated.

### RE: CO2 temperature rise after pumps

The way I would proceed is to plot you initial results on a CO2 Mollier diagram and select the appropriate paths along the isothermal, isobaric, ientropic and isocharic lines to understand which exponents to use when applying the similar lines to determine the new conditions.

### RE: CO2 temperature rise after pumps

Oops I missed some info, "...which exponents in the Pv^n=C to use..."

### RE: CO2 temperature rise after pumps

chicopee:

That's what I was trying to get him to do. I don't know CO2, since my history is with steam systems. But - if it were steam - you would HAVE TO get the enthalpy staes at each point (before and after each compressor), then explicity look at the steam tables (CO2 tables) and determine the points on CO2's equivilent of the Moiller diagram before and after each compressor. Change the inlet temperature, then determine if that change in inlet temperature going into the first compressor is going to change the state in between, then determine if the same nbr 2 compressor is going to act the same way at the higher inlet temperature during compression. (Probably will, but that's like assuming water will behave the same way at 30 degrees F as it did at 34 degrees F. )

### RE: CO2 temperature rise after pumps

(OP)
I ran the physical experiment on Friday night, interestingly enough there was no temperature difference out of pump/compressor 2 when I heating up the initial temperature from 0 C to 35 C.

I used an inline gas heater with a PID loop, and there is a temperature sensor on the inlet of the pump system that verified I was indeed warming the gas up to 35 C

I'm still going to try to work it out on paper, thank you for all the help and comments.

### RE: CO2 temperature rise after pumps

Is the whole piping system (inlet, first and second compressor, outlet, and all connecting pipes and flanges very well insulated?

+0 deg C to +50 deg C, then +5 Deg C to +55 deg C (maybe) is "only" a 10% change in temperature, against a 4x times the pressure increase. Wouldn't take much heat loss in the pipes and flanges to "lose" 2-3 degrees of the potential increase at the outlet.

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