Evaluation of thermal transfer processes and back-fill material around buried high voltage power

110 Pages·2016·3.53 MB·English

by  Sundberg, J.

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Evaluation of thermal transfer processes and back-fill material around buried high
voltage power cables
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Evaluation of thermal transfer
processes and back-fill material
around buried high voltage power
cables

Jan Sundberg

Department of Civil and Environmental Engineering
Division of GeoEngineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Gothenburg, Sweden 2015
Report 2016:5

1 (51)
Chalmers, Civil and Environmental Engineering, Report 2016:5 2 (51)
Evaluation of thermal transfer processes and back-fill material around buried high
voltage power cables

Jan Sundberg

© Jan Sundberg

Report / Department of Civil and Environmental Engineering, Chalmers University of
Technology, 2015
Report 2016:5
ISNN 1652-9162

Department of Civil and Environmental Engineering
Division of GeoEngineering
Chalmers University of Technology
SE-412 96 Göteborg
Sweden
Telephone: + 46 (0)31-772 1000

Chalmers, Civil and Environmental Engineering, Report 2016:5 3 (51)
Content
Glossary and definitions ................................................................................................ 6
1 Introduction and objectives .................................................................................... 9
1.1 General ........................................................................................................... 9
1.2 Factors affecting the thermal design ............................................................. 10
1.3 Objectives ..................................................................................................... 11
2 Thermal transport in soil ...................................................................................... 12
2.1 Thermal transport mechanisms ..................................................................... 12
2.2 Influence of various characteristics ............................................................... 13
2.2.1 Mineral content ...................................................................................... 13
2.2.2 Porosity and water content .................................................................... 13
2.2.3 Temperature .......................................................................................... 15
2.2.4 Anisotropy ............................................................................................. 17
2.3 Determination of thermal properties .............................................................. 17
2.3.1 Experimental methods ........................................................................... 17
2.3.2 Theoretical methods .............................................................................. 19
3 Thermal processes around buried power cables .................................................. 20
3.1 Ampacity of buried cables ............................................................................. 20
3.2 Thermal resistivity around buried cables ....................................................... 20
3.3 Coupled thermal and moisture transport ....................................................... 21
3.3.1 Overview ............................................................................................... 21
3.3.2 Important parameters ............................................................................ 22
3.3.3 Experimental laboratory studies ............................................................. 23
3.3.4 Experimental field studies ...................................................................... 28
4 Critical conditions in the nature ............................................................................ 29
4.1 Ground temperatures in Sweden .................................................................. 29
4.1.1 General .................................................................................................. 29
4.1.2 Results .................................................................................................. 29
4.2 Soil types ...................................................................................................... 33
4.3 Groundwater level......................................................................................... 35
4.4 Summary ...................................................................................................... 37
5 Cable back-fill ...................................................................................................... 38
5.1 Introduction ................................................................................................... 38
5.2 General demands on back-fill material .......................................................... 39
5.3 Desirable thermo dynamic properties............................................................ 40
6 Discussion ........................................................................................................... 41
Chalmers, Civil and Environmental Engineering, Report 2016:5 4 (51)
6.1 Thermal transport and drying out effects ....................................................... 41
6.1.1 Influence of hysteresis and water content .............................................. 41
6.1.2 Influence of geometry and boundary conditions in laboratory studies .... 42
6.1.3 Discussion of the experimental field studies .......................................... 43
6.1.4 Comparison with backfill in SW-link ....................................................... 45
6.1.5 Definition of the dry zone ....................................................................... 45
6.2 Ground temperature in Sweden .................................................................... 46
7 Conclusions ......................................................................................................... 48
8 References .......................................................................................................... 50

Appendix 1: pF curves and grain size distribution, Gouda et al. 1997
Appendix 2: Field experiments, Gouda et al. 1997
Appendix 3: Location and description of the SLU experimental sites Asa and Jädraås
Appendix 4: Classification of Sweden in geographic regions
Appendix 5: Literature review

Chalmers, Civil and Environmental Engineering, Report 2016:5 5 (51)
Glossary and definitions

Thermal transport
• Thermal resistivity, Rho ((m∙K)/W): a material´s resistance to transport thermal
energy. The thermal resistivity is the inverse of the thermal conductivity R=1/λ.
• Thermal conductivity, λ (W/(m∙K)): the ability for a material to transport
thermal energy
• (Volumetric) Heat capacity, C (J/(m3∙K)): a materials ability to store thermal
energy C=ρ∙c, ρ=density (kg/m3), c=specific heat capacity (J/(kg∙K))
• Thermal diffusivity, κ (m2/s): the ability of a material to level temperature
differences

The thermal properties are related to each other as follows:

κ = λ/(ρ∙c) = λ/C =1/(Rho∙C)

Structure of porous media
The principal structure of soils, or other porous media, can be expressed by the figure
below. It consists of solid soil particles (V ) and pore volume (V ) and related masses
s p
(m). The pore volume is in nature filled with partly water and air above the ground
water table. Below the ground water table the pores are completely filled with water. A
well compacted soil has a lower pore volume (higher density) compared to a non-
compacted soil. The relationship between the pore volume and the total volume is the
porosity (V /V). The degree of water saturation (S) is a measure of how large part of
p r
the pore volume that is filled with water (S=V /V ). In the figure below the porosity is
r w p
about 60% and about 2/3 of the pore volume is filled with water (S≈65%). See also
r
Figure 2.

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The density can relate to different mass-volume relationships, e.g. the dry density is the
relation between the dry solid mass (m ) and the total volume (V). The water content
s
can be expressed in several common way meaning quite different things. It is therefore
necessary to define the water content in a proper way. Normally the water content
relates to the mass of water (m ) and the total mass (m) but in geotechnical papers it is
w
common to relate to the dry mass (m ) instead of the total mass which can be confusing
s
if it is not clearly expressed (the latter definitions implies a possible water content
exceeding 100%). A third possibility is a definition per volume. Some definitions are
clarified below:

Density of solid particles, ρ (kg/m ) ρ = m /V
s 3 s s s
Bulk density, ρ (kg/m ) ρ = m/V = ρ ∙(1+w)
3 d
Dry density, ρd (kg/m ) ρ = m /V = ρ∙(1/(1+w))
3 d s
Water content, w (%) w = m /m
h h w
Water ratio, w (%) (or water content) w = m /m
w s
Volumetric water content, ϴ (%) ϴ = V /V = (ρ /ρ )∙w = n∙S
w d w r
Porosity, n (%) n = V /V = 1- ρ /ρ
p d s
Degree of water saturation, S (%) S = V /V
r r w p

Water retention
Below the ground water table the pore system is saturated with water. Above the ground
water table the water content is lower. The water retention capacity influence the water
content in relation to the suction head (distance above ground water table) under steady
state conditions.
In the Figure below water retention curves (or pF curves) are illustrated for different
soils from sand to clay. The groundwater table can be assumed to be at pF=0 on the
vertical scale (in reality it corresponds 1 cm above the ground water table). The pF scale
(left vertical scale) is linear and corresponds to a logarithmic scale with the negative
pressure (or suction head) expressed as cm water table (right scale): e.g. pF=2
corresponds to 100 cm since log10(100)=2. The curves are sorted on clay content. The
lowest curve (1) is a clean sand and the uppermost curve has the highest clay content.
The horizontal scale express the water content, commonly expressed as volumetric
water content. This is quite convenient since it also gives information about the porosity
of the soil since porosity is equal to volumetric water content at full water saturation
(pF=0).

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The water retention capacity (or pF curves) for different soil types, from a sand to a clay, sorted
by the clay content; 1: low, 10: high (Andersson & Wiklert, 1972).

Hydraulic transport
The hydraulic conductivity describes the ability for a material to transport water in a
saturated pore system. The unsaturated hydraulic conductivity corresponds to
unsaturated conditions and is much lower the saturated ditto for a specified soil type.
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1 Introduction and objectives

1.1 General
The thermal processes around buried power cables control the temperature of the cable
and the size of the possible electric power transmission. At low temperature and
stationary conditions the heat transport is controlled mainly by the thermal resistivity of
the backfill and the surrounding soil. At high temperature the thermal processes are
much more complicated and includes vapor diffusion in the direction of the thermal
gradient and a balanced suction of water in the opposite direction.

If the suction of water cannot balance the vapor diffusion, the soil around the cable is
drying out and the thermal resistivity is significantly increased. The temperature rise
may damage the cable or, in extreme cases, destroy the cable.

This report is focused on the state of knowledge of the thermal processes around power
cables and cable back-fill material.

In Appendix 5 there is a literature review with focus on the thermal processes around
cables.

Some definitions (SI units) on thermal properties:

• Thermal conductivity, λ (W/(m∙K)): the ability for a material to transport
thermal energy
• Thermal resistivity, Rho ((m∙K)/W): a material´s resistance to transport thermal
energy. The thermal resistivity is the inverse of the thermal conductivity R=1/λ.
• (Volumetric) Heat capacity, C (J/(m3∙K)): a materials ability to store thermal
energy C=ρ∙c, ρ=density (kg/m3), c=specific heat capacity (J/(kg∙K))
• Thermal diffusivity, κ (m2/s): the ability of a material to level temperature
differences

The thermal properties are related to each other as follows:

κ = λ/(ρ∙c) = λ/C =1/(Rho∙C)

Other glossary and definitions are described in the section “Glossary and definitions”.

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