olga - modeling buried pipelines without femtherm_6620827_03

7/21/2019 OLGA - Modeling Buried Pipelines Without FEMTherm_6620827_03

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The standard OLGA model assumes that heat transfer flows with a constant flux in theradial direction. A series of concentric wall layers with given thicknesses and heat transferproperties are assumed for the pipe.

For a buried pipeline, the heat flux is not symmetrical. To simulate a buried pipeline inthe standard OLGA model, a pseudo-thickness of the soil is needed to account for theasymmetries of the system. It is also possible to simulate the heat transfer in a buriedpipeline with OLGA using FEMTherm, but this discussion will center on the use of thestandard OLGA model.

The equation for heat transfer in a buried pipeline is:

D

HD

kh soilsoil

2cosh

2

1

(1)

where: hsoil= heat transfer coefficient of soilksoil= thermal conductivity of soilD = outside diameter of buried pipeH = distance between top of soil and center of pipe

The term cosh-1(x) can be approximated by:

2

121 1ln)(cosh xxx forx> 1 (2)

For heat transfer for a series of concentric layers, the value of the heat transfer coefficientfor the soil is given by:

DDD

kh soilsoil

2ln2

(3)

where D2= Equivalent diameter of soil layer

Equating the values of hsoilfrom equations (1) and (3), and substituting the expression inequation (2) for the cosh-1(x) gives:

21

2

2 122

D

H

D

HDD (4)


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This expression gives the following values for D2/Das a function of H/D:

H/D D2/D

1.0 3.73

1.5 5.83

2.0 7.87

2.5 9.90

3.0 11.92

4.0 15.94

5.0 19.95

6.0 23.96

The equivalent thickness of the soil layer for use in the concentric layer calculation wouldbe:

)(5.0 2 DDtequiv (5)

where tequiv= equivalent thickness of soil layer for concentric layercalculations

It is useful to look at a ratio of the equivalent thickness to the burial depth. The burialdepth, BD, is defined as the distance from the top of the soil to the top of the pipe. Solvingequations (4) and (5) with the added relationship

DHBD 5.0 (6)

gives the following table:

BD/D tequiv/BD

0.5 2.73

1.0 2.421.5 2.29

2.0 2.23

2.5 2.18

3.5 2.13

4.5 2.11

5.5 2.09

As the burial depth increases, the ratio of the equivalent thickness of soil for the concentriclayer calculation to the burial depth approaches a value of 2.


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An alternative approach to modeling buried pipelines would be to assume that thethickness of the soil layer is equal to the burial depth. An equivalent value of the thermalconductivity of the soil would be calculated from equations (1) and (3) to account for theasymmetry of the soil layer. A comparison of the predictions done with this method vs.the equivalent soil thickness method shown above indicated that the two methods gavethe same steady state results. The equivalent thermal conductivity method, however,showed much more rapid cooling for shutdown cases, due to the decreased mass of thesoil layer. We recommend that the equivalent soil thickness method be used if theconcentric layer heat transfer model is used.

olga - modeling buried pipelines without femtherm_6620827_03

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