How to calculate the boil-off rate of LO2?

[steves1080]

Hi everybody,

I am an entry-level engineer working on a launch pad and so far I have little experience with cryogenics. We have a 80,000 gallon capacity liquid oxygen tank on site, and it is generally filled to about 75% full, but varies depending on what is going on. What I am wondering is a couple of different things:

1- I understand that if the liquid oxygen has reached its saturation point, it is going to be warmer than liquid below its saturation temp due to a higher heat flux. What I do not understand is how to determine the time it takes to reach this saturation temperature. If the pressure inside the vessel never exceeds 3 psig in standby conditions and there is no temp sensor, is there even any way to know this?

2- How would one determine the amount of liquid that would be lost if the vent was opened to atmosphere to rid some of this excess boil-off and effectively "cool" the liquid to a lower temperature? In addition, how could you determine the amount of time this takes? I know it will have something to do with energy/heat transfer, size of the outlet piping of the vent, and ullage space above the liquid inside the tank, but I can't seem to make sense enough of it to figure out where to start.

Thanks in advance for any help on either of these questions!

 

[mfb]

You need some way to determine heat flow between the environment and your oxygen tank. This will determine the heating rate (together with heat capacity of liquid oxygen and the container) and boiling rate (together with heat of vaporization).

size of the outlet piping of the vent, and ullage space above the liquid inside the tank

I don't think they are so significant.

 

[Chestermiller]

I'm guessing there is a vent valve on the tank that maintains the pressure in the tank at 3 psig. The temperature of the O2 in the tank should be ~ the equilibrium temperature corresponding to a pressure of 3 psig (~18 psia). I think this temperature is about -170 C. Of course, a small amount of heat will be flowing through the insulation, driven by the temperature driving force between the outside temperature (~20C) and the inside temperature (-170C). This heat flow causes a small amount of O2 to vaporize and be vented, such that the temperature within the tank is maintained constant. As mfb indicated, you need to be able to estimate the rate of heat transfer from the outside to the inside. The liquid-side heat transfer will probably not be the limiting factor. If you have enough insulation, the air side heat transfer will not be the rate limiting factor either. To get an upper bound estimate of the heat flow, you use the heat conduction equation, based on the overall temperature driving force, the thickness of the insulation, and the surface area available for heat transfer. You need to consider the air-side heat transfer resistance to see how that compares with the resistance through the insulation, and recalculate the heat flow if it is significant.