there are some soil thermal conductivity values, as for the pipe, that should be no problem with google, you need to know what kinda metal you're dealing with
My problem doesn't concern directly the accuracy of ground thermal conductivity i'll use : i think a mean value between all the available papers data is enough to begin. (I'll study the temperature dependence of the ground thermal conductivty later...)
My quesstion is related to the geometrical difficulty of this kind of problem. To be clearer, i've a 2 meters buried pipe which will be blowdowned from 175 bar to 5 bar in 8 minutes. Length is about 400 meters. I've a fluid dynamics/thermodynamics model for the transient compressible flow of gas in pipe. I have to include, in this model, heat transfers (gas-pipewall and pipewall-ground). I don't know how to calculate heat transfer between ground and pipe because there's no symmetry : there's 2 meters of ground above the pipe and a lots of kilometers of ground below the pipe. Which ground volume have to be taken into account in the ground energy balances ? Is there a way to make this problem easier ?
I think your geometric symmetry above and below the pipe is not really a problem. The heat transfer will be symmetrical, conforming to the pipe. You should model the pipe as a cylindrical sink with heat flowing from the ground to the pipe and see what your temperature profile is from r=0 to r=2 meters. You will probably have thermal equilibrium within the 2 meters of cover.
Perhaps the bigger problem will probably be in determining the heat transfer coefficient(s) between the pipe and the ground, because (if I don’t miss my guess) that pipe is cathodically protected with a coating that insulates the steel from the ground. You will need to find a coefficient(s) that accounts for your type and thickness of coating as well as for the steel and soil.
This topic has been discussed numerous times on Eng-Tips. The moisture content of the soil will make a huge difference. Do an advanced search on this site using the key words “soil thermal conductivity” and read what has been said in the posts. Let us know if you do not find what you are looking for.
If yoour simulation tool includes an option for insulating layers - why not try with a 2 m think "insulation" layer with properties similar to the soil? Maybe its thick enough so that the outer edge will not change conditions too far ways from ambient?
"When you're up to your armpits in aligators, its hard to remember that you started out to drain the swamp".
You are going from 175 bar to 5 bar in 8 minutes and you're trying to determine flow transient behaviour. Assuming that the gas starts at near ground temperature then in 8 minutes the vast majority of the BTU's of the temperature change of the gas will leave with the vented gas. The thermal-affected zone at the end of the 8 minutes is unlikely to extend through the pipe coating let alone meters or kilometers into the earth. An hour after the event (assuming that the 5 bar gas remains in the pipe "at rest") some small amount of sensible heat will have been transfered from the soil to the gas in the pipe, but at best it is a third-order effect compared to the flow-related temperature and pressure transients.
If you see a 200C temperature change from the blowdown and a 0.1C temperature change from convection to earth (within the 8 minutes) most people would successfully ignore the temperature change to earth and use adiabatic calculations.
For a time period on the order of 8 minutes , the effect of the 2 m soil is essentially the same as an infinite sink. There should be no real need to differentiate between top layer and infinite bottom layer for relatively fast transients such as this. The time period for the soil dynamics is on the order of D^2*rho*Cp/k, where D is the 2m depth.
The original published solution curves for the buried pipe problem was by Schlicting, and many older conduction heat transfer texts have these curves. Similar curves are also presented in the ASHRAE handbook. But the modern engineering method is to model it in a finite element program.
Are you sure that the pipes are in direct contact with the ground and not in some tunnel,chase or insulated in some type jacket? I would never bury heating pipes in direct contact with the soil- this would be a stupid practice.
