Water Correlation Between Temperature & Pressure 2

[vpl]

Somebody asked me this, and I don't know where to go find the information. Maybe one of you could point me to a reference?...

Is there a correlation between temperature and pressure for water? I know it's basically incompressible, but not entirely. The person who asked me said he had heard it was 100 psi/ degree F (he was wanting confirmation of the formula).

The volume is fixed (it's a steel pressure vessel), the water is sub-cooled (starting around 550 degrees) with pressure around 2000 psig.

If this is something obvious, please feel free to berate me -- I just am failing open.

Thanks

 

[MortenA]

We have been around this resently i think.

I seem to recall that its a lot more than 100 PSI/deg F (assuming the vessel 100% filled and temp rising) if you keep the volume 100% unchanged (no bulging or anything).

I dont have databook here, but find the expansion coef. for water and the compressibility for water and you should get the result fairly easy

Best Reagrds

Morten

 

[butelja]

The bulk modulus of water is approximately 300,000 psi. I don't have a steam table that has subcooled condensate at 2,000 psig, so I've approximated using specific volume of the liquid at saturated conditions.

At 550 °F, the specific volume of the liquid is 0.0218 ft^3/lb. At 600 °F, the specific volume of the liquid is 0.0236 ft^3/lb. This is an increase in volume of 8.257% for a 50 °F temperature change. To compress the water by 8.257% (to keep constant volume) would require a pressure increase of (300,000 psi)*(8.257%) = ~25,000 psi. Dividing this by the 50 °F temperature change gives ~500 PSI/°F.

These are rough numbers. The compressibility of water will be nonlinear for large pressure changes. Container thermal expansion and compliance will tend to slightly lower the numbers. At lower temperatures (~100 °F), the numbers work out closer to ~100 psi/°F. Hydrocarbons in schedule 40 carbon steel pipe are ~70 psi/°F. The bottom line is, don't heat liquid full sealed containers unless they are rated for very high pressures.

 

[vpl]

Thanks butelja! This is more than what I was looking for. I really appreciate your taking the time to look into this for me.

 

[Haf]

Morten mentioned that a question of this sort has been asked before. TBENNE asked a similar question "Pressure Change in Vessel" on Jan. 3 with the last response coming on Jan. 21. You may want to check out that thread if you can find it.

Morten and butelja (among others) addressed the question. Most impressively, they seem to be giving about the same answer they gave last time.

Haf