How to calculate the boil-off rate of LO2?

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In summary: You will probably find that the heat flow is so small that it has no practical significance.In summary, the conversation discusses the use of a liquid oxygen tank and the concerns surrounding its saturation temperature and boil-off rate. The main factors to consider are the heat flow between the environment and the tank, the size of the vent valve, and the ullage space. Calculating the heat transfer rate can help determine the time it takes to reach saturation temperature and the amount of liquid lost when venting excess boil-off. However, these calculations may not have practical significance due to the small amount of heat flow involved.
  • #1
steves1080
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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!
 
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  • #2
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.
 
  • #3
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.
 

1. How do you calculate the boil-off rate of LO2?

The boil-off rate of LO2 can be calculated by multiplying the heat transfer coefficient, the surface area of the storage tank, and the temperature difference between the stored LO2 and its boiling point. This formula can be expressed as: Boil-off rate = Heat transfer coefficient x Surface area x (Stored LO2 temperature - Boiling point)

2. What is the heat transfer coefficient?

The heat transfer coefficient is a measure of how easily heat can pass through a material. It is affected by factors such as the type of material, its thickness, and the temperature difference between the two sides of the material. In the context of calculating the boil-off rate of LO2, a higher heat transfer coefficient means that more heat will be transferred from the stored LO2 into the surrounding environment, resulting in a higher boil-off rate.

3. How does the surface area of the storage tank affect the boil-off rate?

The surface area of the storage tank is an important factor in calculating the boil-off rate of LO2 because it determines the amount of surface area available for heat transfer to occur. A larger surface area means more heat can be transferred, resulting in a higher boil-off rate. It is important to accurately measure the surface area of the storage tank to ensure an accurate calculation of the boil-off rate.

4. What is the significance of the temperature difference between the stored LO2 and its boiling point in calculating the boil-off rate?

The temperature difference between the stored LO2 and its boiling point is a crucial factor in determining the boil-off rate. This is because the temperature difference directly affects the amount of heat that is transferred from the LO2 into the surrounding environment. A larger temperature difference will result in a higher boil-off rate, while a smaller temperature difference will result in a lower boil-off rate.

5. Are there any other factors that can affect the accuracy of the calculated boil-off rate?

Yes, there are other factors that can affect the accuracy of the calculated boil-off rate, such as the insulation of the storage tank and the ambient temperature. Insufficient insulation of the storage tank can result in a higher boil-off rate, while a higher ambient temperature can also increase the rate of heat transfer and result in a higher boil-off rate. It is important to consider these factors when calculating the boil-off rate of LO2.

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