Buried Pipeline Heat Transfer

[oskar11]

I am working on the following problem:

I have a buried pipeline at -5C which is causing a layer of soil X meters above it to freeze after a specified time period. The soil is initially at 5C and known is all the thermal data. In order to model this, I decided to consider the soil as a semi-infinite solid and consider the system to be 1-D transient.

The equation is: (T-To)/(Ts-To) = erfc(y/2sqrt(kt))

My problem is, as the pipeline causes the soil (and water) to freeze, it will create an insulating effect on the pipe... which I currently am not taking into account. Does anyone have any advice for me as to how to handle this situation?

 

[CRG]

The closest work I have done to what you are describing was calculating the depth of frost and depth of thaw in the arctic. Reference books was:
“Construction in Cold Regions,” McFadden & Bennett

Numeric method required the use of several graphs for some of the properties:
Soil conductivity, frozen or thawed
Dry density of soil
Moisture content of soil
Latent heat of fusion of the water
Soil thermal mass
Value from modified Berggren equation

References for the method:
Lunardini 1988
"Permafrost Engineering Design and Construction," Johnston 1981

 

[CRG]

Oops, obviously there were thermal conditions:
Degree days for freezing or thawing

 

[oskar11]

Thanks CRG. I'll try and find those from at a library on monday.

I am pretty new to this industry... and I would like to know if anyone with experience, could give me a rough estimate at how much frozen ground a pipeline like this would cause? Are we talking, 6", a couple feet, a couple of meters?

-5C pipe, 5C wet soil

Lets say I am looking for a relatively rough estimate for this calculation. Would the following be a sound method for determining the depth of frozen ground?

- find a heat transfer coefficient for the pipe and contents
- then use the htc to get a heat flux into the pipe
- using that heat flux, use fouriers law and get a temperature profile
- finally, using the temperature profile... just find the point at which T = 0C, and everything below that would be frozen.

This is assuming a linear temperature profile and a bunch of other simplifying assumptions, but for a rough estimate, would that result be terrible?

Thanks.

 

[oskar11]

Forgot to mention... but obviously the above method also assumes steady state, which I think is a decent assumption for the case I am working on.

 

[CRG]

Steady state makes it much easier. I incorrectly assumed transient. So what information do you need? If you give the dry soil density and the moisture content I can look up and give you the frozen and thawed thermal conductivity for typical soils. Also, I will need to know if it is fine grain or course grain. Either of the books I referenced above will have the typical properties for thermal conductivity of soils. I won’t be able to look up the data until Monday. With soils information, any good heat transfer book should give the method for the calculations. I use “Heat and Mass Transfer,” by Frank M. White. I don’t know if it’s the best; however, it the one I used in college and it good enough for me. You might even try Marks Standard Handbook for Mechanical Engineers, by Eugene Avallone and Theodor Baumeister. I would think that any engineering technical library will have Marks.

 

[CarlB]

This publication (Chapter 12) has some equations for heat transfer from buried pipes - may be a start.

http://www.ccb.org/docs/COETM/5_852_5.pdf

 

[sailoday28]

oskar11 (Chemical) Is your original equation for the transient, semi-infinite solid based on radial coordinates? If the pipe is buried deep enough, curvature has a big effect. ie, the surface area of the pipe and surface area of the ground will be greatly different.

 

[oskar11]

Yes, originally it was for a transient, semi-infinite solid based on radial coordinates. However, after some reasearch, it seems much too involved a question which I honestly do not have time for. Instead, I used a much simpler model just to get a general idea... and will hopefully be able to get a more accurate result at a later date. Thanks for all the help guys.