Tank bottoms heat loss

[georgeverghese]

Does anyone have the theory, derivation and/or expressions for the heat loss through the bottom of a heated storage tank sitting on the ground.

For example, a heated storage tank holding molten bitumen at 150-170degC, sitting on a layer of sand say 300mm thick followed by a semi infinite depth of wet earth.

Thanks in advance.

 

[IRstuff]

You could certainly brute force it and treat the wet earth as fixed thermal sink. Then, it's just conduction through the sand layer.

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[georgeverghese]

It may be difficult to justify additional CAPEX based on a scenario where the temp drops from 170degC to 20degC or so in just 300mm of sand - in reality would imagine it takes a greater depth than that. While the true depth to exponentially (??) decay to ambient may be difficult to guess, think the depth at which the temp drop get to say half the total drop may be easier to picture ( ie a drop of 0.5x(170-20) = 75degC delta T).
Am hoping someone out there might have something more exact.

 

[IRstuff]

I think you have your numbers off. 300 mm of sand works out to 0.8W/m^2-K, which is about 1/10th the transfer coefficient from the sides of the tank to ambient air.

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[lilliput1]

Heat loss to ground would be mostly around the perimeter. Typically for slab on grade house perimeter insulation consist of 2 ft vertical down + 2 ft horizontal towards interior of 2 inch thick rigid foam insulation.

 

[IRstuff]

"half the total drop may be easier to picture ( ie a drop of 0.5x(170-20) = 75degC delta T)"

This is where the problem is. "half the total drop" means that 75C or 100C is measurable on an interior or external surface; this means HIGH heat transfer, e.g., 75C against 25C wet soil is a huge heat loss. Likewise, 100C on the inside wall of the tank means a huge heat loss. Only when the temperature delta is fully dropped across the wall, liner, and insulation, AND you have a low heat transfer coefficient do you have optimal insulation.

Another example, your hot water heater with warm to the touch outside is losing measurable heat. When sufficient insulation is added, the outside wall will feel exactly like the external ambient and little heat is lost.

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[georgeverghese]

IRstuff - That may be one approach: to neglect any resistance to heat transfer from the earth and assume all resistance to enable a reasonable heat loss is to be derived purely from the sand layer and any other engineered insulating layers (the 300mm layer is quoted for discussion purposes only ; the actual thickness may be thicker). Dont remember what we had on the vertical side of the tank which was buried, but the same approach as above may be defended.

There may also be a significant film resistance due to natural convection on the inside of the tank that would need to be accounted for also.

Thanks folks