olga buried pipe

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umptions

Thermal calculations for the wall rest on the assumption that radial heat conduction through the concentric walls is

the dominating phenomenon. The heat flux may be calculated in two ways:

The heat flux through the pipe wall layers is calculated by the code with user-defined thermal conductivities,specific heat capacities and densities for each wall layer.

The heat flux is determined by a user-defined overall heat transfer coefficient.

The former is recommended since the heat storage capacity in the wall is often significant. It is preferred to include a

dynamic calculation of the temperatures of individual wall layers in a transient simulation.

The latter option will save some CPU time, but should be used with care and preferably in steady state situations

only.

Figure A: Illustration of a buried pipe

Buried pipelines may be modelled with the soil as the outermost wall layer. The f irst method of calculating the heat

flux (where heat flux is a function of wall properties) should then always be used due to the large thermal mass of

the soil.

The thickness of the composite soil layer is based on an equivalent heat transfer coefficient for the soil for a pipeline

burial of a particular depth. Theoretically, the equivalent heat transfer coefficient from the outer surface of a buried

pipeline to the top of the soil can be calculated to be:

(a)

where:

D = outer diameter of buried pipe

H = distance from centre of pipe to top of soil

lsoil = soil heat conductivity

hsoil = overall heat transfer coefficient for soil

The term cosh-1 (x) can be expressed mathematically as follows:

cosh-1 (x) = ln ( x + ( x2 - 1 ) 0.5 ) for x ³ 1

Página 1 de 3Thermal computations - Methods and assumptions

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The adjusted thermal conductivity of the soil layer can be determined using the expression below for a known value

of the soil thermal conductivity:

(b)

where:

Rsi = inner radius of soil layer (=outer radius of pipe wall)

Rso = outer radius of soil layer

ksoil = input value of soil conductivity

The specific heat capacity of the soil may be adjusted as follows in order to predict the transient heat transferaccurately:

(c)

where:

Cp input = input value of soil thermal capacity

Cp soil = soil thermal capacity

Heat transfer at steady state conditions depends only on the outer soil layer radius R so and on ksoil. However, fordynamic situations, a good soil discretization is important in order to obtain a rel iable temperature profile across the

wall layer. Alternatively, the Solid bundle module may be used in such a situation.

iabatic wall temperature correction term

OLGA applies adiabatic wall temperature correction to the wall surface temperature (TWS) when the liquid volume

fraction (HOL) is less than 5% (AL > 0.95). The definition of adiabatic wall temperature is:

The temperature assumed by a wall in a moving fluid stream when there is no heat transfer between the wall and the

stream.

The temperature correction is given by:

where:

= adiabatic correction term for the wall surface temperature

= smoothing factor

= gas viscosity

= average gas velocity


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= gas heat conductivity

The correction term applies when the liquid volume fraction is less than 0.05.

Note that considerable amount of energy is added to the inner wall surface when high gas velocity appears. The

physical argument for this is high radial velocity gradient . That is: Gas velocity gradient perpendicular to the

flow direction (see Figure B). The gas velocity is zero at the inner wall and increases the further you go from the wall

to the centre of the pipeline. This causes the actual fluid temperature to be at the highest at the wall and decrease

towards the centre of the pipeline.

Figure B: Gas velocity and temperature profiles

ase changing materials

The model for simulating phase changing materials accounts for latent heat of fusion and the difference in thermalproperties for unfrozen and frozen materials. Thermal conductivity and heat capacity are given for three ranges,

above the melting point, below the melting point and in the transition zone.

For heat capacity, the value specified in CAPACITY is used for all temperatures above the melting point. A multiplier

(HCAPMULT) is used below the melting point. If the FUISIONMULT key is different from 0, a step wise function is

used for heat capacity having the value equal to FUSIONMULT*CAPACITY in the phase changing region. If the

FUSIONMULT key is 0, linear interpolation is performed between 1 and HCAPMULT. The FUSIONMULT key takes

the latent heat of fusion (additional energy added or withdrawn for a phase change) into consideration.

The example below describes how the latent heat of fusion is calculated in a situation with a wet soil material. In the

example, we use a phase changing region from -1 to 0 C. This gives one multiplier between -1 and 0 C to account

for the latent heat of fusion, while another multiplier is used below -1 C for the frozen soil. The soil is assumed to

have a dry density 1900 kg/m3, with 10% water weight/dry soil weight. The moist unfrozen heat capacity is 1067

J/kgC (0.255 btu/lbF) and the frozen heat capacity is 876 J/kgC (0.209 btu/lbF). The latent heat of fusion is (190

kg/m3*333 kJ/kg)/(2090 kg/m3) = 30.27 kJ/kg. This gives:

HCAPMULT = 876/1067 = 0.82

FUSIONMULT = (30270+1067)/1067 = 29.4

Thermal conductivity given in CONDUCTIVITY is used directly for temperatures above the melting point. A

conductivity multiplier (CONDMULT) is used for temperatures below the melting point. Linear interpolation is used in

between.


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olga buried pipe

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