Burial of pipes

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

For a buried pipeline, the heat flux is not symmetrical. To simulate a buried pipeline in the standard OLGA model, a pseudo-thickness of the soil is needed to account for the asymmetries of the system. It is also possible to simulate the heat transfer in a buried pipeline using the use of the standard OLGA model.

The equation for heat transfer in a buried pipeline is:

where: hsoil = heat transfer coefficient of soil

ksoil = 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:

for

For heat transfer for a series of concentric layers,

where: D2 = equivalent diameter of soil layer

Equating the values of hsoil from equations (1) and (3), and substituting the expression in equation (2) for the coshgives:

This expression gives the following values for

H/D

1.0

1.5

2.0

2.5

3.0

4.0

5.0

6.0

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

the heat flux is not symmetrical. To simulate a buried pipeline in the standard OLGA model, a thickness of the soil is needed to account for the asymmetries of the system. It is also possible to simulate

the heat transfer in a buried pipeline using the enhanced soil heat transfer module, but this discussion will center on

The equation for heat transfer in a buried pipeline is:

= heat transfer coefficient of soil = thermal conductivity of soil

= outside diameter of buried pipe = distance between top of soil and center of pipe

(x) can be approximated by:

for x > 1

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

quivalent diameter of soil layer

from equations (1) and (3), and substituting the expression in equation (2) for the cosh

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

D2/D

3.73

5.83

7.87

9.90

11.92

15.94

19.95

23.96

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

the heat flux is not symmetrical. To simulate a buried pipeline in the standard OLGA model, a thickness of the soil is needed to account for the asymmetries of the system. It is also possible to simulate

the enhanced soil heat transfer module, but this discussion will center on

(1)

(2)

the value of the heat transfer coefficient for the soil is given by:

(3)

from equations (1) and (3), and substituting the expression in equation (2) for the cosh-1

(x)

(4)

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

where: tequiv = equivalent thickness of soil layer for concentric layer calculations

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

Gives the following table:

BD/D

0.5

1.0

1.5

2.0

2.5

3.5

4.5

5.5

As the burial depth increases, the ratio of the equivalent thickness of soil for the concentric layer burial depth approaches a value of 2.

Please note that the equivalent thickness calculated by this method use the rigorous logarithmic diameter ratio calculation method. Since OLGA uses a linearized approximation to this method, the soilseveral sub-layers for the OLGA calculations in order to minimize the error due to the linear approximation. Please refer to the section on heat transfer layers for a discussion of this subject.

An alternative approach to modeling buto the burial depth. An equivalent value of the thermal conductivity of the soil would be calculated from equations (1) and (3) to account for the asymmetry of the soil layer.equivalent soil thickness method shown above indicated that the two methods gave the same steady state results. The equivalent thermal conductivity method, however, showed much more rapid coolinthe decreased mass of the soil layer. We recommend that the equivalent soil thickness method be used if the concentric layer heat transfer model is used.

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

= equivalent thickness of soil layer for concentric layer calculations

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

Tequiv/BD

2.73

2.42

2.29

2.23

2.18

2.13

2.11

2.09

As the burial depth increases, the ratio of the equivalent thickness of soil for the concentric layer calculation to the

Please note that the equivalent thickness calculated by this method use the rigorous logarithmic diameter ratio calculation method. Since OLGA uses a linearized approximation to this method, the soil should be broken into

layers for the OLGA calculations in order to minimize the error due to the linear approximation. Please refer to the section on heat transfer layers for a discussion of this subject.

An alternative approach to modeling buried pipelines would be to assume that the thickness of the soil layer is equal to the burial depth. An equivalent value of the thermal conductivity of the soil would be calculated from equations (1) and (3) to account for the asymmetry 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 gave the same steady state results. The equivalent thermal conductivity method, however, showed much more rapid cooling for shutdown cases, due to the decreased mass of the soil layer. We recommend that the equivalent soil thickness method be used if the concentric layer heat transfer model is used.

(5)

= equivalent thickness of soil layer for concentric layer calculations

, is defined as the distance from the top of the soil to the top of the pipe. Solving equations (4) and (5) with the added relationship

(6)

calculation to the

Please note that the equivalent thickness calculated by this method use the rigorous logarithmic diameter ratio should be broken into

layers for the OLGA calculations in order to minimize the error due to the linear approximation. Please

ried pipelines would be to assume that the thickness of the soil layer is equal to the burial depth. An equivalent value of the thermal conductivity of the soil would be calculated from equations (1)

A comparison of the predictions done with this method vs. the equivalent soil thickness method shown above indicated that the two methods gave the same steady state results.

g for shutdown cases, due to the decreased mass of the soil layer. We recommend that the equivalent soil thickness method be used if the