Pressure due to Temp Change in Liquid Full System 1

[sshep]

My Friends,

I am asked to build a spreadsheet (or equivalent tool) for our mechanical engineering manager which can calculate the pressure in a liquid full system as a function of temperature, given an initial condition of temperature and pressure. For his needs it must be as rigorous as possible. Typical engineering assumptions (incompressible liquid, fixed volume, etc) cannot be used. Such a correlation would need to include:

1) Rho calculations for water as f(T,P)- i.e. the pressure dependency is an issue as it will require more rigorous solution of a water EOS rather than a simplified coefficient of expansion as per thermal relief sizing.
2) Volume changes of vessel as f(T,P)- i.e. thermal expansion and modulous of elasticity.

As this has probably been done many times before (I think even I have for incident investigations, etc), I am asking if anyone knows of a either a tool, example, or partial calculation such as Excel addin for water Rho(T,P), vessel volume change as f(T,P), etc. Anything that saves me a completely from scratch development is appreciated.

best wishes,
Sean

 

[Latexman]

Will this software be required to handle different vessels (different dimensions and head types)? Or, will it be used for one vessel, as inferred in your post? If only one vessel, I recommend collecting real data and developing a correlation.

Good luck,
Latexman

 

[sshep]

The request is for a general tool, although the vessel can be approximated as a cylinder. We pressure test suspected exchangers with condensate that is cooled (as best we can) but can't get to ambient with the mobile equopment we have. Sadly, this situation is frequent for maintenance activities, but is not really a problem in plant construction because we make better cooling provisions and often save the hyrdotest water for use in other equipment (stays ambient).

I am concerned that there will be problems with making a general tool. With my simple model (fixed volume), even small temperature drops (the usual situation) lead to results that don't match well- i.e a few degC temp drop and you are in a vacuum. This does not seem to be the case from plant observations. I will add volume changes for the cylindrical vessel (T and P) and see if it helps.

Thanks,
sshep

 

[zdas04]

I didn't respond the first time I read this because the boundaries that you put around the problem are impossible to solve. The gross level answer is to look at the coefficient of thermal expansion and the bulk modulus. The combination of these two terms for water results in a pressure change of about 100 psi/°F for clean, deaerated water. The number is not exactly 100 psi, but it is very close. Then you have to factor in contaminants which can dramatically change the compressibility (i.e. 1/bulk modulus) of the fluid. Non-rigid piping changes the results completely. In a system of any size, the temperature change will not be homogeneous so while the part in the sun might be heating and trying to increase pressure, the part underground could be cooling and trying to decrease pressure. Then you have to consider that the compressibility is a function of total liquid volume, but the expansion is localized to where the temperature begins changing.

You want a rigorous EOS-based GENERAL tool for this? Not in this lifetime. For vessel that is liquid full and blocked in, the 100 psi/°F number is safe and reasonably representative. You can apply more precision than that for a very carefully defined system, but you are not going to successfully make it a general-purpose calculator that works everywhere.


David Simpson, PE
MuleShoe Engineering

http://www.muleshoe-eng.com

Please see FAQ731-376 for tips on how to make the best use of Eng-Tips Fora.

"It is always a poor idea to ask your Bridge Club for medical advice or a collection of geek engineers for legal advice"