PRESSURE CHANGE IN VESSEL 4

[TBENNE]

A 5 Gallon Pressure Vessel(non-vented) is completely filled with Diesel Fuel #2.The vessel is pressurized to 500 psig, the temperature of the Diesel is 90 Degrees F. If the Diesel is heated to say 140 Degrees F, What is the equation to calculate the pressure rise?

 

[MortenA]

You have to find the expansion coefficeint of the diesel oil. Normally there will be a linear coefficent. Then it should be fairly easy to calculate the volume expansion, then you have to find the liquid compressibility, that would enable you to calculate the pressure rise when you assue a constant volume.

You need a databook for those two constants.

A general equation would look something like this:

expansion coeeficient: a (ft3/deg F)
Compressibility: b (ft3/psi)

at constant volume: dP (psi) = a*dT/b

Best Regards

Morten

 

[MJCronin]

TBENNE,

Is this some kind of homework problem !!???

I cannot immagine any kind of real or practical use for such a set-up.....but, I can imagine this being a homework problem dreamed up by an instructor

Come back and tell us this is real !!??

MJC

 

[MortenA]

If it is a homework problem it wont be the first time on these pages This was perhaps a bit more obvious than normally.

Best Regards

Morten

 

[TBENNE]

Morten / MJC,

No, this is not a homework question.

We are a division of JohnCrane Mechanical Seals.We manufacture the Seal Lubricator Systems that supply the barrier fluid to "cool" and "lubricate" the seal(s).

This question relates to a unit we built. This unit uses Diesel Fuel as the barrier fluid (to "lubricate" the seal).
It is stored and circulated through a pressure vessel. The question had been posed as to what pressure increase would be seen in this unit with increased temperature.

I still have not found the answer or information.

Regards, Tom

 

[butelja]

If your vessel is completely liquid full, the pressure rise will be very great. For diesel fuel in schedule 40 piping, the pressure rise is on the order of 60-70 PSIG for every 1 (ONE!) °F. This translates into thousands of PSI in your case. I have a Mathcad worksheet for piping that can calculate this, but the answers are largely academic. The reason is that no matter what combinations of fluid and piping material are, the answer is a very large pressure rise for a very small temperature rise.

 

[MortenA]

Dear Tom

I think my first post covers is EXCEPT for the coefficients. Try to find them in a databook.

Now in order to make up for my impollite insinuations i even checked google for you (

http://www.google.com)

a great search engine.

I found a chevron datapage:

http://www.chevron.com/prodserv/fuels/bulletin/diesel/L2_4_6_rf.htm

Here the linear thermal expansion coefficient is 0.00046 /deg F


The compressability is however more difficult. I took the first reference that i could find (not quite sure its diesel no. 2 but it is diesel). The value i found at this link

http://www.amesim.com/de/pdf/fuel_113.pdf

is approx 1/15000 bar = 1/217500 psi

A 50 def F temp increase should therefore lead to a increase in pressure of 0.00046*50*217500 psi=5000 psi pressure increase (the correspond OK with Butelja's rule of thumb where 1 def F means 60-70 psi increase since .00046*217500 equals 100 psi/deg F).

Best Regards

Morten

PS: Try a seach engine like GOOGLE if you are looking for physical properties. I used the search terms "expansion coeeficient diesel" and "bulk modulus diesel" to find these sites

 

[mgp]

I'm a bit curious about how this device is supposed to work.

If this vessel is pressurized to 500psig and part of a closed circuit there must be a reason for this pressure (it must be higher than that of the secondary side of the seal i suppose)

Then how is the pressure maintained in case of a leakage thru the seal? If there is nothing to maintain this pressure, then the system will be useless after the first incidence of leakage, because there's no overpressure left.

On the other hand if there is something to maintain this pressure, then there is also the possibility to allow relieving any overpressure, fex. thru a thermal relief valve.

Another possibility could be to allow a volume of nitrogen at the top of the vessel large enough to cope for thermal expansion of the diesel and large enough to maintain pressure in case of a seal leakage. Same system is used on accumulator backup vessels for hydraulic systems, enabling emergency hydraulic operation if the power unit breaks down.

Also consider that should the pressure rise to abnormal levels, there's a good chance the seal will be blown away (into where it wasn't meant to go) possibly before the vessel bursts.

Regards
Mogens

 

[owg]

You folks have all answered the question very well. What remains is academic interest. I would just add that although the pressure of the diesel will increase, the volume of the container will increase due to temperature and pressure. Back to practice - of course some form of thermal pressure relief will be needed as a minimum, either inherent in the system, or by way of a thermal relief valve. Also, depending on the details of the design, overpressure relief in the event of fire may also be required. This could remove the need for separate thermal relief.

 

[butelja]

OWG,

The Mathcad spreadsheet I mentioned in my earlier post does take the pressure expansion as well as the thermal expansion of the container into account. The algebra equating the volume change of the fluid as a function of pressure and temperature to the volume change of the container as a function of pressure and temperature gets a little messy.

 

[TBENNE]

Gents,

We built a small vessel from 2" pipe for actual testing, the 60-70 PSI increase / 1Degree rise is almost exact

Pressure is maintained to the vessel through a "piston pot",
with different areas on each side of the piston, thus creating a +10% differential on the lubricator side(reference pressure from the inboard side of seal is on opposite side of piston)

Thanks, Tom