What is the limit of liquid propane in a tank?

[tpv]

TL;DR Summary

how much liquid can one put in a propane tank without the tank exploding?

The Propane industry mandates that a tank not be filled more than 80%. The question I have is this: how do I calculate the limit of liquid propane in a standard 3800 liter tank given a 30 degree rise in temperature (from 273 K to 303 K) such that it will not rupture the tank? For example, can I exceed the "80% fill rule" and put in 95% without fear of compromising the tank?

The tank is rated at 250 psi with a 4:1 safety factor. The pressure relief valve is assumed stuck shut. From what I've found on the web, the thermal expansion of liquid propane is 0.003 per degree K. Thus, if I understand correctly, 30 degrees should result in a 9% increase. If the tank was initially filled to 92%, then the liquid should expand to fill the tank, and, presumably, the expanding liquid will subsequently exceed the 1000 psi mark and burst the tank. Or, will the combination of vapor pressure and liquid compromise the tank before this point? Or am I missing something altogether? Does expanding liquid propane have the ability to exceed 1000 psi once it fills its container?

Thanks.

 

[Dullard]

The vapor pressure is a function of the temperature. As long as there is vapor, the tank pressure won't exceed the vapor pressure (assuming a reasonable temp change rate). When the volume of the liquid equals the volume of the tank, all of the vapor will have become liquid. Any additional temperature increase will rapidly elevate the pressure. I can't think of any reason that liquid propane wouldn't exceed 1000 PSI.

 

[gmax137]

The tank is rated at 250 psi with a 4:1 safety factor.

This does not mean it is "safe" to pump the tank up to 1000 psi. The "4:1 safety factor" accounts for things beyond your ability to control or observe, which may or may not be present in your particular tank.

 

[tpv]

Thanks, Dullard and gmax137.
From what you said, and from what else I gather, as the temperature increases, the vapour pressure will increase, but remain initially irrelevant to the problem. When the temp hits + 26 C, the tank will be 100% liquid. Presumably the pressure in the tank at this temp will be about what the vapor pressure would have been, had there been any vapor. The charts for propane give a vapor pressure of about 135 psi at 26 C. At this point, since the tank is all liquid, the bulk modulus of propane becomes the critical factor. I found that for propane K is roughly 0.22 GPa (depends on temperature). The equations are as follows:

dV = 1.003 dT (V = volume, T = temp)
K = dp/ (dV/Vo) (k = bulk modulus, p = pressure, Vo = initial volume of tank)
Hence,
dT = Vo/(1.003 K) x dp

k=0.22 GPa,
dp = 1000 -135 psi = 865 psi = .006 GPa

Plugging in the numbers, we get:
dT = 3800/(1.003 x .22) x .006 = 102 degrees

In this case, the propane expansion will not cause the internal pressure to reach 1000 psi unless the temperature rises another 102 degrees, or reaches a full 128 degrees.

However, since the critical temperature of propane is only 96 C, presumably the moment the temperature hits 96, all the liquid will attempt to turn into a vapor at this point, and the pressure will rise drastically immediately.

Therefore, there is no risk of a propane tank ever reaching an internal pressure of 1000 psi unless it is being heated by an external heat source and the temperature rises above 96 Celsius.

Am I missing anything?

 

[tpv]

My humblest apologies. I made a terrible mistake. The above equation dV = 1.003 dT is incorrect. The incompatibility of the units should have told me this equation was wrong. The proper equation is:

dV/Vo = 0.003 (1/degree K) dT (where V = volume, Vo = initial volume of the tank, and T = Temperature)

This makes the volume of the tank fall out of the end result (as expected). And the final equation is much cleaner:

dP = (95.7 psi/degree K) dT

With this equation, the internal pressure of the liquid propane will hit 1000 psi after only a 9 degree rise in temperature, or at 35 C.

In summary,
From 0 C to 26 C, the liquid expands from 92% to 100%.
At 26 C, the liquid fills the tank, and the pressure is 135 psi.
from 26 to 35 C, the liquid pressure increases from 135 psi to 1000 psi.

There is a real and definite risk of a propane tank exploding if it is over filled.