Heat Transfer from a Burried Pipe 1

[ONEPOINT]

Hi,

I am trying to calculate the heat transfer rate from a burried pipe(depth=1meter, length=1000meters,high viscosity crude oil) when the surface ground temperature is -35C and
-22C.The fluid is stationary and its temperature is 5C.

There is a natural convection inside the pipe, a conduction transfer through the wall of the pipe and a conduction transfer mode from the surface of the pipe to the soil.

I am looking to find out the coefficient for heat conduction from a semi-infinite solid, and the coefficient for the natural convection that occurs inside the pipe.Is there anyone who could give me some tips about this?

Regards,

One Point

 

[torpen]

Hello,

I don't know empirical correlations for free convection inside horizontal cylinders.

Are you sure that there is advection within the pipe?
What is the value of the Rayleigh number Ra?
If Ra is less than a critical value heat transfer across the pipe occurs primarily by conduction across the fluid (no flow within the pipe).
Do you take into account the thermal inertia of the oil?

Regards,

Torpen.

 

[RossABQ]

Can't help you with the number-crunching, but I worked at a power plant that stored heated #5 - #6 heavy oil in above-ground tanks. The question always was how long the heaters could be out of service before there were problems, and also what type of heater was most effective.

We found through testing (heaters off) that there is a boundary layer that forms at the oil - tank wall interface that dramatically slows heat flow. Only 3 inches in from the wall, oil temperatures were virtually the same as in the middle of the tank after a full day in cold weather. I would not assume that there is a convective flow, although I do not know your pipe diameter; that would potentially make a big difference compared to a tank.

 

[BigInch]

You need to calculate the shape factor for the pipe in the semi-infinite solid, a function of the pipe's distance below ground. Most heat transfer texts, "Principles of Heat Transfer" F. Kreith & M. Bohn, for one, discuss the shape factor calculation in detail as well as forced convection and conduction across the wall film and through the pipe wall. If you can't find examples of those calculations, let me know. You should also consider the heat conduction of the backfill material, in both wet and dry conditions. Conduction of most soils is drastically affected by moisture content. Careful if you have a rainy and dry season, as you may never reach full thermal stability in either season.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[davefitz]

Nowadays, there are many finite elemetn computer programs taht can easily and economically simulate the problem you have defined.

Back in the 1970's we used the curves in the Kreith text, and those curves were copied from a 1930's set of curves from a german source. They were likely derived by the explicit solution of the 2 dimension conductive heat transfer diff eqn using separation of variables, etc. But those techniques dissapeared with bell bottom jeans.

As I recall, the ASHREA design book (1997 fundamentals) also has curves for buried pipes.

-35 C. Sounds like either the Athabascan oil sands or the Shell LNG project.

 

[telecomguy]

'fluid is stationary'
What do you call a pipe with no flow? A long skinny tank. Badumbum! ;o)

Is this an assumption to simplify the problem? or is the fluid truly stationary? Speaking from the gut, I would expect flow in the pipe to change the results substantially.

<tg>

 

[RossABQ]

I would bet the worst case for his design is when flow is lost (normal power goes down?) and the line needs to be kept warm by heat tracing.

 

[BigInch]

Its a standard group of calculations for a hot oil line where viscosity varies considerably with temperature. When the line is not working, cooling begins without a continuous reheating flow. Pipeline shutdown heat loss calculations for 1 day, 2 days, 3 days, 1 week, 2 weeks, maybe out to 3 months may be appropriate to determine how much power will be required for restarting flow.

For standard configurations finite element results are the same as the curves developed a long time ago, however finite element analysis is nice for predicting unusual configurations like a hot line on one side and an ambient temperature diluent line on the other half of the right of way under changing ambient temperature conditions. A 2-dimensional finite element spread sheet can easily handle it.

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[25362]

Cheremisinoff's Handbook of Heat and Mass Transfer -Vol 1- Heat Transfer Operations (Gulf) has a chapter 32 Titled: Estimation of heat losses from flows in buried pipes by Haim Bau, that may interest you.

 

[ONEPOINT]

Hi BigInch,

Thanks a lot for the suggestion oferred to me regarding the calculation of the heat rate loss from a buried pipe.

I still need some more help from you in this regards. Here is the task that I have to solve:

The pipe (NPS 24") is buried at 1 meter depth in soil. Ambient temperature is -35 C, the soil temperature is -5 C and the fluid ( oil flowing at 2.1336 m/s) has a temperature of 3C. So there is forced convection within the pipe and conduction from the outer surface of the pipe through the semi infinite solid(soil). In the text books of heat transfer, the calculation of the heat rate loss is usually given by the formula for conduction mode transfer through a semi infinite solid. In those equations a shape factor is considered and k of soil and delta T which is the difference between the temp. at the surface of the ground and the outers surface temp. of the pipe.

My first question is what temperatures should I choose in my case, given those given temperatures(Tambient,Tsoil,T fluid.)Should I choose for the soil surface temp,the -35C.This value is a measured temp for the ambient air in the winter time. Then, for the outside surface temperature of the buried pipe should I take an average between the fluid temp(3C) and the soil temperature(-5C) or an average between the fluid temperature(3C) and the soil surface temperature(-35C)?

The second question is related to the forced convection that is inside the pipe. Do I need to calculate the rate heat loss due to the forced convection from the fluid to the inside wall of the pipe? What kind of equations should I use for this forced convection mode transfer? Is this heat rate loss the same as that one obtained from the conduction formula given in text books for a conduction transfer through a semi infinite solid? This formula(conduction one) does not take into consideration what kind of flow regime is within the pipes. So it seems to me that for both stationary fluid or flowing fluid, the heat rate loss from the pipe would be the same, considering the same given temperatures, and K of soil...

I look forward to hearing from you..

Regards,

ONEPOINT

 

[BigInch]

Use the average bulk temperature of the fluid (3ºC) inside the radial distance to the inside of the fluid's wall film thickness and the soil temperature (-5ºC). The standard measurement point for air temperature is from inside a vented white box about 3.3 meters above the ground surface and ground surface temperatures are often quite higher than air temperatures taken that point.

Usually you will have a series of layers over which you must calculate the overall heat transfer coefficient,

1.) Heat transfer occurs from the average bulk temp fluid to the pipe wall across the fluid's wall film thickness to the pipe ID. The wall film thickness is affected by the flow reqime, laminar, laminar-turbulent, or turbulent.

You must calculate the Nusselt number to get the OTHC, across the wall film, usually by one of several correlations (Dittud-Boelter, Sieder-Tate, Petukhov-Popov, Sleicher-Rouse) depending on the Prandtl and Reynolds numbers of the flow. "Principles of Heat Transfer by F. Kreith and M.S Bohn discusses these extensively.

2.) Heat transfer from the ID to the OD of the pipe.

3.) Then from the OD pipe wall perhaps through a coating layer and into a sand backfill of about .3 m thickness immediately around the coating O.D.

4.) Then from the sand to the normal trench backfill, which continues up to the surface.

Since this is frozen ground for at least part time of the year, ice lensing below the pipe is likely to occur that may tend to lift the pipe and introduce associated stresses. The US Army Corps of Engineers has a website dedicated to Artic design and construction which you might find of interest as well as this technical manual for Artic Utility construction that you can download here,

http://www.usace.army.mil/publications/armytm/tm5-852-5/entire.pdf

BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com

 

[ONEPOINT]

Hi BigInch,

Thanks for your time and for your comprehensive answers. In the heat transfer text books that I have got, the rate heat loss calculations from buried pipes is done with the shape factor method that refers only to the conduction transfer mode through the soil.This method does not take into consideration the flow regime or the type of fluid that flows through the pipe.

So, in this case, it means that Q lost from the pipe would be the same if the oil is flowing or is not flowing.

I have done the calculations with this method for a 48" pipe buried at 1 meter and I have got 242 W/meter of pipe.The depth of the buried pipe(Z) is 1.509 meters from the surface of the ground to the centerline of the pipe.The temperature of the ground surface is -35C and the temperature at the outside surface of the pipe is -5C.

I have also tried to calculate the rate heat loss in the pipe. Forced convection and laminar flow (Re = 1650 and Pr = 13000). The properties of the fluid were considered at the bulk temperature of the fluid Tbulk = +3C.

The method used for calculating Nuselt number was Haunsen method for laminar flows in circular tubes. But this method does not specifically refers to the buried pipes.

The number that I got for Nu was 548 and then h = Nu*(k/D)= 57.6 W/m2*C. Then for one meter length of pipe As = 3.76 m2 and Q = 841 W.

So, if this is the rate heat loss that occurs inside the pipe by means of forced convection, why this value is different then that obtained by conduction through the soil?

What is lost from the fluid to the inside wall of the pipe should be the same with what is lost from the outside surface of the pipe through the soil. Could you please tell me if my above assumption is wrong?

Regards,

ONE POINT

 

[BigInch]

You should be able to equalize that with heat lost from pipe. You can't calculate the heat transfer across the pipe wall until you know the OHTC and have the total heat transfer calculated across all layers. Then figure the transfer between each layer, which should be different at the flux level (W/m2) but equal on a W/linear meter basis.

The shape factor should only adjust the diameter of the soil layer thickness you consider aroun the pipe such that you can consider the surrounding soil layer as a true cylinder, rather than some odd-shaped half-cylindrical-truncated at the top kinda' thing.

With that adjusted diameter, you can use the values for the soil as a completely cylindrical surrounding layer around the pipe.

Then calculate the overall heat transfer coefficient, including all of these,

the inner wall film,
the pipe steel,
anticorrosion coating,
bedding sand,
and adjusted backfill thickness.

If it was an unburried pipeline, you would have an exterior film coefficient from heat transferred from coating to air flowing past the OD, or if an offshore unburied pipeline, from coating to water flowing past at the speed of the current, etc. But its buried, so forget that.

Now using the OHTC and the temp inside the pipe and the temp at the outside of the adjusted backfill diameter (ground surface temp) calculate the W/m lost across all the insulation layers at once, ie. from inside pipe to ground surface. Then you should be able to go back and make each transfer between each individual layer balance.




BigInch-born in the trenches.

http://virtualpipeline.spaces.msn.com