THESIS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
Insulation materials in
district heating pipes
Environmental and thermal performance of
polyethylene terephthalate and polyurethane foam
Sara Mangs
Department of Chemical and Biological Engineering
CHALMERS UNIVERSITY OF TECHNOLOGY
Göteborg, Sweden 2005
Insulation materials in district heating pipes : Environmental and thermal performance
of polyethylene terephthalate and polyurethane foam
SARA MANGS
ISBN 91-7291-700-8
© SARA MANGS, andra reviderade upplagan 2014, tidigare utgiven 2005.
Doktorsavhandlingar vid Chalmers tekniska högskola
Ny serie nr 2382
ISSN 0346-718X
Chemical Environmental Science
Chalmers University of Technology
SE-412 96 Göteborg
Sweden
Telephone +46 (0)31 772 1000
Cover: Close-up of PET foam
Printed by Chalmers reproservice, Göteborg, Sweden, 2005
Insulation materials in district heating pipes
Environmental and thermal performance of
polyethylene terephthalate and polyurethane foam
SARA MANGS
Department of Chemical and Biological Engineering
Chalmers University of Technology
SE-412 96 Göteborg, Sweden
ABSTRACT
District heating can contribute to increased energy efficiency in society. The
environmental impact can be reduced by minimising the heat losses in the district
heating pipes during distribution of the heat to the customers. Today, the most
commonly used type of district heating pipe has a steel or copper media pipe,
surrounded by polyurethane (PUR) foam insulation and a protective outer casing of
polyethylene. The heat losses increase over time due to diffusion of blowing agents
out of and air into the insulating foam. In this thesis, the long-term environmental and
thermal performance of different insulating materials was studied. The diffusion
mechanisms of cyclopentane, a commonly used blowing agent in PUR foam, were
compared to those of a new gas, 1,1,1,3,3-pentafluorobutane (HFC-365mfc). The
performance of polyethylene terephthalate (PET) foam as a possible replacement
alternative to PUR foam was also investigated. The environmental impact from global
warming, acidification and resource depletion was studied for the first three phases
(pipe production, network construction and network use) of the life-cycle of different
pipe alternatives by means of life-cycle assessment (LCA). The LCA-study of PET
foam insulated pipes is theoretical, since only foam boards can be produced today.
The diffusion characteristics of HFC-365mfc in PUR foam were found to be similar to
those of cyclopentane. District heating pipes insulated with HFC-365mfc blown PUR
foam may have less environmental impacts due to heat losses than cyclopentane
blown foam, but the high global warming potential of HFC-365mfc render its use
questionable. If it is assumed that the entire HFC-365mfc content in the PUR foam
were to be released to the atmosphere, the use of this gas for pipe insulation can not
be justified as an option to cyclopentane blown foam.
The determined effective diffusion and solubility coefficients of blowing agents and
air are lower in PET foam than in PUR foam. The environmental performance of
pipes insulated with high-density carbon dioxide blown PET foam (157 kg·m3) is
similar to pipes insulated with carbon dioxide blown PUR foam (86 kg·m3). If PET
foam of lower density could be produced, it would be a potential competitor to pipes
insulated with cyclopentane blown PUR foam. A future trend towards increased
recycling of PET can be expected in Europe, possibly as a result of increased PET
consumption and current regulations. Recycled PET has also the advantage of a lower
price than virgin PET and PUR.
Keywords: District heating pipe, insulation, polyurethane foam, polyethylene
terephthtalate foam, mass transport, thermal performance, cyclopentane,
1,1,1,3,3-pentafluorobutane, HFC-365mfc
LIST OF PUBLICATIONS
This thesis is based on the work contained in the following papers, referred to by
Roman numerals in the text:
I
Diffusion of cyclopentane in polyurethane foam at different temperatures
and implications for district heating pipes
Maria E. Olsson, Ulf Jarfelt, Morgan Fröling, Sara Mangs and Olle Ramnäs
Journal of Cellular plastics, 38 (2002) 177-188
II
Transport of 1,1,1,3,3-pentafluorobutane (HFC-365mfc) in rigid
polyurethane foam and polyethylene
Sara Mangs, Morgan Fröling, Olle Ramnäs and Ulf Jarfelt
Cellular Polymers, 21 (2002) 155-164
III
PET (polyethylene terephthtalate) foam as insulation material for district
heating pipes
Sara Mangs, Olle Ramnäs and Ulf Jarfelt
Proceedings of The 9th International Symposium on District Heating and
Cooling, Espoo Finland, August 30-31, 2004
IV
Mass transport of cell gases in carbon dioxide blown PET (polyethylene
terephthtalate) foam insulation
Sara Mangs, Olle Ramnäs and Ulf Jarfelt
Cellular Polymers, 24 (2005) 115-126
V
Environmental comparison of DH pipes - PET and PUR foam insulated
district heating pipes
Sara Mangs, Camilla Persson, Morgan Fröling, Olle Ramnäs and Ulf Jarfelt
Euroheat and Power, 3 (2006)26-31
CONTENTS
1 INTRODUCTION ..................................................................................................... 1
1.1 Goal and scope ..................................................................................................... 1
1.2 Outline of the thesis ............................................................................................. 2
1.3 The research group ............................................................................................... 2
2 DISTRICT HEATING ............................................................................................... 3
2.1 A 19th century technology with potential for the future....................................... 3
2.2 District heating and sustainable development...................................................... 5
3 INSULATION AND CASING MATERIALS IN DISTRICT HEATING PIPES ... 7
3.1 District heating pipe production........................................................................... 7
3.2 Polyurethane foam ............................................................................................... 7
3.3 High density polyethylene ................................................................................. 11
3.4 Polyethylene terephthalate ................................................................................. 11
3.5 Blowing agents – physical and environmental properties ................................. 14
3.5.1 The phase-out of chlorofluorocarbons ........................................................ 14
3.5.2 Blowing agents in PUR foam ..................................................................... 15
3.5.3 Blowing agents in PET foam ...................................................................... 18
4 INSULATION PERFORMANCE OF DISTRICT HEATING PIPES ................... 19
4.1 Introduction ........................................................................................................ 19
4.2 Heat transfer mechanisms in district heating pipes............................................ 19
4.2.1 Radiation and conduction in the polymer matrix ........................................ 21
4.2.2 Conduction in the cell gas ........................................................................... 24
4.3 Long-term thermal performance of district heating pipes ................................. 28
4.3.1 Changes in thermal conductivity over time ................................................ 28
4.3.2 Mass transport in polymeric membranes .................................................... 29
4.3.3 Mass transport in closed cell polymeric foams ........................................... 32
4.3.4 Study of mass transport in PET and PUR foam.......................................... 35
4.3.5 Study of mass transport in HDPE casing materials .................................... 42
4.3.6 Mass transport in district heating pipes ...................................................... 44
5 LIFE CYCLE PERSPECTIVE ON DISTRICT HEAT DISTRIBUTION.............. 47
5.1 District heat distribution from cradle to grave ................................................... 47
5.2 Comparison of insulation materials in district heating pipes ............................. 48
5.2.1 System description and inventory ............................................................... 48
5.2.2 LCA results ................................................................................................. 50
6 SUMMARY OF FINDINGS AND FUTURE RESEARCH ................................... 55
6.1 Comparison of cyclopentane and HFC-365mfc ................................................ 55
6.2 Comparison of PET and PUR foam ................................................................... 55
6.2 Other findings and comments ............................................................................ 56
7 ACKNOWLEDGEMENTS ..................................................................................... 57
8 REFERENCES ........................................................................................................ 59
1 INTRODUCTION
_____________________________________________________________________
1.1 Goal and scope
The aim of this thesis is to investigate the long-term thermal and environmental
performance of district heating pipes insulated with foam made of polyethylene
terephthalate (PET) and polyurethane (PUR). Two main comparisons have been
considered:
cyclopentane and 1,1,1,3,3-pentafluorobutane (HFC-365mfc) as blowing
agents in PUR foam
PET and PUR foam insulation
The insulating capacity of district heating pipes deteriorates over time due to the mass
transport of insulating gas out of and air into the foam insulation. The main part of the
work was focused on determining the thermal aging characteristics of the foams.
During the use of district heating pipes, emissions from the heat produced to
compensate for the heat losses gives rise to environmental impacts. From an
environmental perspective, the entire life-cycle of the pipes: pipe production, network
construction, network use and post-use handling (figure 1.1) is of importance,
although the use phase produces the greatest environmental impacts [Fröling 2002a,
Fröling 2004a, Fröling 2004b, Persson 2005c] and V.
District
heating pipe
production
Network
construction
Network use
Post-use
handling
Figure 1.1 The life-cycle of a district heating pipe. The shaded box indicates the
main focus of this doctoral thesis.
In paper I, the diffusion characteristics of cell gases in cyclopentane blown PUR foam
and in the high density polyethylene (HDPE) casing surrounding the foam in district
heating pipes are determined. This is a type of pipe commonly used today. In paper II,
the mass transport properties of a new blowing agent, HFC-365mfc, is studied. The
1
aging characteristics of PET foam, a possible future alternative to PUR foam, were
analysed in papers III and IV. Finally in paper V, the environmental impacts of
district heating pipes insulated with PET and PUR foam are compared by life cycle
assessment (LCA) methodology, in which all stages of the lifetime of a district
heating pipe are considered, with the exception of waste management.
1.2 Outline of the thesis
Chapter 2 provides background information about district heating. The foam (rigid
PUR and PET foam) and casing materials (LDPE and HDPE) used in or considered
for district heating pipes, are described in chapter 3. Some general characteristics of
the various blowing agents used in foam production are also described in chapter 3.
Chapter 4 covers the research results and theories concerning heat transfer
mechanisms and mass transport of cell gases in insulating foams and casing materials
in district heating pipes. In chapter 5, the environmental impacts of insulating
materials and blowing agent in the foam are discussed from a life cycle perspective.
1.3 The research group
This work was performed within the framework of a cross-disciplinary research
project between the divisions of Chemical Environmental Science and Building
Technology at Chalmers University of Technology and the Swedish National Testing
and Research Institute, and was financially supported by the Swedish District Heating
Association and the Swedish Energy Agency. The research collaboration started in
1990 with studies on CFC-free polyurethane insulated district heating pipes and
continued with studies on long-term thermal performance and life-cycle assessment in
addition to mechanical investigations of district heating pipes. Today, the focus is on
the development of new types of pipe constructions and materials.
2
2 DISTRICT HEATING
_____________________________________________________________________
2.1 A 19th century technology with potential for the future
District heating is used to heat buildings in areas with high population density and a
cold climate. Water, or steam in a few older systems, is heated in large centralized
plants and transported through a pipe network which is buried in the ground (figure
2.1). In the buildings connected to the district heating network, the heat is in general
transferred to the internal space heating system and to the tap water system by means
of heat exchangers. The cooled water is then transported back to the heat production
plant. In a modern system, with water as the energy carrier, the hot water temperature
is about 80-100 ºC and the return flow of water about 40 ºC.
1. Heat production
2. Distribution of heat (water
or steam) through the district
heating pipe network
4. Space heating
and hot tap water
systems inside
each building
3. Sub-stations
– transformation
of heat at each
building
Figure 2.1 The district heating system. The picture is taken from the homepage of the
Swedish District Heating Association [Swe DH 2005a].
3
The technology was first development in the United States in the 1870’s and then
spread to Europe where several large systems were built during the first half of the
20th century [Werner 1989]. Today, district heating supplies about 100 million people
in Europe. The amount of district heat delivered is increasing in many countries
[Euroheat & Power 2003]. District heating is most widespread in Scandinavia, Russia,
Central and Eastern Europe. In Central and Eastern Europe the market share is about
40 % while Western Europe has about 10 %. In Sweden, district heating is delivered
to almost half of all buildings [Swe DH 2005a]. In 2003, the delivered heat was 47.7
TWh and forecasts indicate that it will increase by a further 10 TWh by 2010, both
due to the planned enlargement of existing systems and the introduction of new
systems.
Despite the fact that the idea of district heating is more than a century old, it is open to
new innovations and technology. The distribution system has been developed over the
years. Very old systems used steel pipes within concrete or asbestos boxes insulated
with, for example mineral wool or cellular concrete foam [Fredriksen 1993]. Some
forty years ago pre-fabricated pipes were introduced. Today they are the most
commonly used pipes in newly constructed district heating networks. The inner pipe
is normally made of steel or copper and surrounded by PUR foam insulation and an
outer HDPE casing (figure 2.2). When the pipe is buried under ground, the casing
protects the foam against both water and mechanical pressure. The rigid PUR foam
insulation consists of closed cells initially containing an insulating gas and a small
amount of air. Today, the most commonly used blowing agents in PUR foam used in
district heating pipes are cyclopentane and carbon dioxide. Chlorofluorocarbons
(CFCs) were used until their ozone depletion effect was discovered and international
action was taken to restrict them. Sometimes a foil is placed between the outer casing
and the PUR foam in order to decrease the diffusion of cell gases and slow down the
effect of aging on the insulation capacity.
Figure 2.2 The district heating “single pipe” (top picture) and “twin pipe” (bottom
picture). These commonly used pipes have steel or copper media pipes surrounded by
polyurethane foam insulation and a high density polyethylene casing.
4
In some district heating networks, two or more media pipes are placed within the
same casing pipe (figure 2.2). In this “twin pipe” system, one media pipe is used for
transporting hot water from the heat production facility to the consumer, while the
other is used for the return flow of water. The so-called “flexible” district heating
pipes of quite small dimensions are used in the proximity of buildings. These can be
bent to some extent due to the fact that semi-flexible PUR foam and low density
polyethylene (LDPE) is used in the pipes.
Various pipe dimensions are used in different parts of the network. The outer diameter
of the pipes varies from less than 100 mm to almost 1000 mm. Large pipes are used as
main pipes close to the heat production plants where large heat flows are distributed,
while smaller pipes are installed in the vicinity of the end users.
2.2 District heating and sustainable development
In the last decades it has become very evident that human activities have an extremely
harmful impact on eco-systems, both locally and globally. Since the “World
Commission on Environment and Development” (often called “the Brundtland
commission”) in the 1980s first defined sustainable development as “…the
development that meets the needs of the present without compromising the ability of
future generations to meet their own needs”, several international initiatives have been
taken to solve some of our most serious global environmental problems [WCED
1987]. One of them is the Kyoto Protocol to the United Nations Framework
Convention on Climate Change [UNFCCC 2005], in which many of the world’s
nations agreed to reduce their emissions of greenhouse gases due to their effects on
the global climate. District heating has great potential to keep pace with the changes
in a society moving towards a higher degree of ecological sustainability. A variety of
fuels and heat sources with low net emissions of carbon dioxide can be utilised, e.g.
wood waste, natural geothermal heat sources and refuse incineration plants. Making
use of surplus heat from industry and incorporating combined heat and power (CHP)
technology can also contribute to increased energy efficiency in society. In a CHP
plant, the heat from combustion of a fuel is used to produce electricity and the
remaining heat employed in for example district heating systems. In a report
published by the International Energy Agency, it is argued that the high energy
efficiency achieved by CHP in combination with district heating systems can be of
significant value in the short term as a means of fulfilling the Kyoto agreement in
Europe [Werner 2002].
Western European district heating systems are mainly powered by fossil fuels: 34 %
coal, 31 % natural gas and 6 % oil [Euroheat & Power 2003]. Only 11 % of the heat
generated comes from renewable resources and 10 % from waste heat. The remaining
8 % is unspecified. The use of different types of heat sources and fuels varies a great
deal between different countries (figure 2.3). In Sweden, the proportion of low carbon
dioxide emitting fuels and technologies (solid biofuels, biogas, refuse incineration,
waste heat, heat pumps and CHP) increased from 60 % in 1997 to 74 % in 2003
5
[Euroheat & Power 2003, Swe DH 2005b]. The reported energy efficiency of the
district heating system was 88 % in 2003 [Swe DH 2005b]. Losses occur in the heat
production and during distribution due to pump energy and heat losses in the pipes’
insulation [Fredriksen 1993].
100%
80%
Other fuels
Renewables
Industiral waste heat
Natural gas
Oil
Coal
60%
40%
Croatia
Lithuania
Estonia
Norway
Austria
Sweden
Italy
Netherlands
Bulgaria
Finland
Denmark
Germany
0%
Czech Republic
20%
Figure 2.3 Fuels used in district heating in Europe in 2001 [Euroheat & Power
2003].
6
3 INSULATION AND CASING MATERIALS IN
DISTRICT HEATING PIPES
_____________________________________________________________________
3.1 District heating pipe production
A common production technique for PUR foam insulated district heating pipes is a
production line, where each pipe is manufactured individually. The pipes are
produced to in lengths of 6 to 16 m and the thickness of the PUR foam for each
dimension can be varied according to the intended application [Schlenter 1996]. The
HDPE casing is first produced in a continuous process where HDPE granules are
melted and extruded into a cylindrical shape and then cut to the desired length. The
media pipe is centred in the casing, after which the PUR foam formulation is injected
through a hole in the casing in the middle of the pipe or from one of the ends. The
foam is created as a result of chemical reactions of the components in the formulation.
When the PUR foam expands, it adheres to the surface of the steel pipe and the HDPE
casing. There are two types of continuous production techniques. In the “spray
process”, layers of PUR foam formulation are sprayed onto the steel pipe and the
HDPE casing is either extruded or wound around the insulation. In the continuous
moulding process, the foam formulation is laid on a PE sheet with the steel pipe
centred above it. The sheet is pulled into a pipe-shaped mould as the PUR foam
expands. The HDPE casing is then extruded onto the pipe. Finally the pipes are cut to
the desired lengths.
Production of PET foam insulated district heating pipes is still being developed. So
far, only boards of a thickness up to about 5 cm can be produced in an extrusion
process developed by the Italian company BC Foam. It is possible that the extrusion
process may be developed for the purpose of producing district heating pipes.
3.2 Polyurethane foam
Polyurethane is a widely used material. In Western Europe in 2003, PUR constituted
about 5 % or 2.7 million tonnes of the total annual consumption of plastics (figure
3.1) [APME 2004]. There has been a steady increase since 1995, when consumption
was 1.8 million tonnes [APME 1997, 2000, 2001, 2002, 2003, 2004]. The great
7
possibilities of adjusting the material properties, e.g. density, flexibility and stiffness,
opens up for a variety of different applications, such as coatings in the appliance
industry, soles for shoes, glue, mattresses, vehicle seats and insulation. In many
countries rigid PUR foam is commonly used as insulation material in the construction
industry due to its low thermal conductivity compared to other materials and the fact
to that it can be foamed on site.
8%
5%
31%
PET
11%
PUR
HDPE
LDPE
PP
PVC
17%
Others
12%
16%
Figure 3.1 Distribution of consumption of different plastics in Western Europe in
2003 [APME 2004]. “LDPE” = low density polyethylene, “PP” = polypropene,
“PVC” = polyvinyl chloride, “Others” includes for example polystyrene, polyamides
and amino polyesters.
PUR foam is formed by simultaneous polymerisation and expansion in a formulation
containing an isocyanate, a polyol and a blowing agent with a low boiling point
(figure 3.2). The polyol contains two or more hydroxyl groups.
O
O
+
R
OCN
NCO
diisocyanate
R
R'
HO
OH
polyol
R'
N
N
H
H
O
O
n
polyurethane
Figure 3.2 Polymerisation reaction of polyurethane.
The heat from the exothermic reaction vaporizes the blowing agent, thus creating the
PUR foam cell structure. Due to the fact that small amounts of water are always
present and/or added, gaseous carbon dioxide is formed in a reaction with the
isocyanate, which contributes to the formation of the cells. It is important that there is
a balance between the foam expansion and the polymerisation. A polymerisation that
is too slow can result in foam collapse. In order to control this process a catalyst
affecting the polymerisation reaction is often used.
8
Because of their high reactivity and favourable price, MDI (diphenylmethane
diisocyanate, figure 3.3) and pMDI (polymeric by-products of MDI) are the main
isocyanates used for rigid foam production today [Grünbauer 2004]. Isocyanates are
highly toxic and can cause allergic reactions in humans [Bakke 2001]. Therefore,
handling of isocyanates is problematic in the working environment. Isocyanate
molecules can also be released if the chemical links are broken due to heating of PUR
foam, e. g. when district heating pipes are welded together during the construction of
the district heating network [Bergström 2002].
OCN
NCO
Figure 3.3 MDI, diphenylmethane 4,4’-diisocyanate.
The density of the foam is determined by the hydroxyl functionality of the polyol
[Glicksman 1989]. Short chain polyols with high functionality produce a PUR foam
with more cross-links and thus a more rigid and high density product. Soft,
elastomeric foam with an open cell structure and low density is formed by using
polyols with longer chains and lower functionality. Water is also involved in reactions
that create a harder, but more fragile foam structure. For thermal insulation
applications, the heat conduction in the solid polymer must be minimized, thus the
density should be kept as low as possible without jeopardising the strength of the
foam. Normally, the density of the PUR foam in district heating pipes is about 60-70
kg·m-3.
The constituents used for rigid PUR foam production are normally derived from
fossil, non renewable resources. It is, however, possible to produce polyols from
renewable resources. Baser et al. showed that closed cell rigid PUR foam for
insulation purposes can be produced by using castor oil as the polyol [Baser 1993].
Dahlke et al. also suggest sunflower and rapseed oil produced by the German
company HOBUM Oleochemicals, as a base for polyols [Dahlke 1998]. Palm oil and
soybean oil, produce thermally stable foams with good mechanical properties [Chian
1998, Guo 1999, Javni 2000]. In order to function as a polyols, palm oil and soybean
oil has to undergo chemical processes. The hydroxyl functionality of the soybean
polyol is rather low and would consequently produce a semi-rigid foam. Guo et al.
therefore suggest the addition of hydroxyl containing crosslinkers and/or water in
order to obtain a rigid foam structure.
The price of palm oil and soybean oil, 470 and 620 US dollars per tonnes in 2004
respectively [The Hindu 2005], is lower than that of castor oil, which was 800 US
dollars per tonne in 2004 [The World Bank Group 2005]. In order to be a sustainable
polyol option, the oils must be produced in an environmentally sustainable way.
Soybean oil is the world’s most popular vegetable oil and is mainly produced in the
US (38%) and Brazil (26%) [Rainforestweb 2005, World Rainforest Movement
9
2005]. The second most popular vegetable oil is palm oil with 85 % of the total world
production in Malaysia and Indonesia. The total agricultural area for these oils
increased significantly between 1990 and 2002, 26% for soybean oil and 43 % for
palm oil. In South East Asia and Brazil, agricultural land for the production of soy
beans and oil palms has been made available by cutting down large areas of
rainforests. Besides the loss of biodiversity, a high level of pesticides and herbicides is
often used in these large monocultures.
The increased global use of PUR also results in higher amounts of waste, for which
there are several recycling methods. Flexible foams can, for example, be ground into a
powder and blended into the foam formulation for the production of new PUR
products, or granulated and joined together by means of a binder and used, for
example, as carpet underlay, athletic mats and interior vehicle parts [API 2005,
Quinlan 1994]. Polyols can be extracted from PUR foam by means of chemical
processes: glycolysis, aminolysis and hydrolysis. In glycolysis, low molecular
recycled polyols are created by dissolving PUR scrap and sometimes a catalyst in
glycol (e.g. ethylene glycol, 1,2-propylene glycol, triethylene glycol) in a reactor at
about 170-220 ºC [Borda 2000, Murai 2003]. The glycolysis reaction is believed to
occur in accordance with the reaction illustrated in figure 3.4 below (in this case with
ethylene glycol).
O
O
R
Rx
N
O
+
Ry
HO
OH
R
Ry
N
H
O
+
OH
Rx
OH
H
urethane group
glycol
glycolysis products
Figure 3.4 Glycolysis reaction of polyurethane.
Aminolysis (figure 3.5), which is performed in a similar manner to glycolysis is
assumed to follow the exchange reaction below [Kanaya 1994].
O
O
Rx
R
N
O
+
Ry
NH2
H
urethane group
amine
Ry
R
N
N
H
H
+
Rx
OH
aminolysis
glycolysisproducts
products
Figure 3.5 Aminolysis reaction of polyurethane.
Shin et al. introduced recycled polyols from glycolysis, 10-30 % by weight of the total
polyol content, in PUR foam formulation with cyclopentane and water as blowing
agents [Shin 1998]. The foams had as good or even better dimensional stability and up
to 9 % lower thermal conductivities than those prepared from virgin materials. The
low foam thermal conductivity was probably due to the small cell sizes which reduces
the contribution of radiation within the cell voids.
10
3.3 High density polyethylene
The total amount of polyethylene used in Europe (both high and low density
polyethylene) amounted to about 28 % of the total plastic consumption in 2003 (figure
3.1) [APME 2004]. Low density polyethylene, LDPE (17 %), is used for films, bags,
toys, coatings, containers and pipes, while HDPE (11 %) is used for pipes, containers,
toys, household goods, industrial wrappings and films.
The basic structure of polyethylene is the ethylene unit (-CH2CH2-). The less
branched the chain backbone, the harder the material and the higher the density. By
definition HDPE has a density of 940 kg·m-3 or more. According to the European
standard, HDPE casings of rigid PUR foam insulated district heating pipes should
have a density of at least 944 kg·m-3 [EN253:2003]. The branching and molecular
weight are the main factors that influence the physical and mechanical properties.
Polyethylene is partially crystalline, and the rate of flexibility of the material
decreases in line with increasing crystallinity. In common with most plastics, PE is
derived from crude oil.
3.4 Polyethylene terephthalate
There has been a worldwide increase in the consumption of PET during the last
decade [APME 2004, 2005]. Between 1995 and 2001 the total consumption of PET in
the world increased from about 3 million to almost 8 million tonnes. Today, the use of
PET exceeds that of PUR in Western Europe (figure 3.1). PET used for bottles and
film in Europe has increased almost threefold since 1995, while the use of the material
for textile fibres has remained more or less static (figure 3.6) [APME 1997, 2000,
2002, 2004]. PET recycling is also expected to increase due to the European
Commission’s Packaging and Packaging Waste Directive, which includes higher
targets for mechanical recycling of plastic packages all over Europe [European
Council 1994, 2005]. PET is a thermoplastic and can thus be remelted into new
products. Since production of food packages from recycled material is restricted for
hygienic reasons, new fields of application for recycled PET such as foam production,
can be developed.
millions of tonnes
3
Bottles and film
Textile fibres
2.5
2
1.5
1
0.5
0
-95
-96
-97
-98
-99
-00
-01
-02
-03
Figure 3.6 Consumption of PET in Western Europe [APME 1997, 2000, 2002, 2004].
11
PET (figure 3.7) was developed by the British Calico Printers company 1941 and was
originally used for synthetic fibers [Bousted 2002]. Films have been produced since
the mid-1960s and the PET bottle blowing technique was introduced in the 1970s.
n
O
O
O
O
Figure 3.7 Polyethylene terephthalate
Polyesters are obtained by a reaction between acid and alcohol (figure 3.8).
Terephthalic acid or di-methyl terephthalate and ethylene glycol are used in the
production of PET and the reaction takes place in the presence of a catalyst. P-xylene
derived from catalytic reforming of naphta is used to produce terephtalic acid and dimethyl terephthalate and ethylene made from cracked natural gas or the naphta
fraction from crude oil is used to produce ethylene glycol, and. [Bousted 2002]. For
both reaction routes a polycondensation reaction follows. A short liquid state
polycondensation creates an amorphous material suitable for fibres and film. Semicrystalline material for bottles and PET foam is achieved by longer period of
polycondensation [Xhanthos 2000].
HO
OH
R
+
R'
HO
OH
O
O
acid
HO
OH
R'
+
O
H
H
O
O
alcohol
O
R
ester
Figure 3.8 Principal polymerisation reaction of polyethylene terephthalate.
The production of PET foam boards is shown in figure 3.9. The polymer granules are
dried and mixed with a nucleating agent (talcum 0.5 % by mass) before entering the
extruder. The blowing agent (approx. 1 % by mass) is mixed under high pressure (7080 bar) into the polymer melt in the extruder and kept under pressure until the melt
exits through the die where the extrusion pressure is about 45-50 bar. In the
atmospheric pressure following the die lips, the blowing agent is transformed from the
liquid to the gaseous phase, creating the foam cells.
The price of virgin materials follows the fluctuations in the cost of raw oil. In 2004
the prices of PET and PUR were about the same, at around 1.8 EUR/kg [III]. The
price for recycled PET was significantly lower, around 0.5 EUR/kg. Recycled PET
has, however, been shown to be unsuitable for foam production, due to contamination
of other plastics and degradation of the material during the recycling process [Japon
2000, Xhanthos 2000]. The problem is that the viscosity of recycled PET is too low
and the melt strength inferior compared to virgin material. Foams of a very high
12
quality have been achieved in experiments where recycled PET was chemically
modified by means of multifunctional branching agents (e.g. tetraglycidyl diamino
diphenyl methane or pentaerythritol) [Japon 2000, Smith 1990, Xhanthos 2000].
Figure 3.9 Schematic illustration of a process plant used to produce PET foam sheets
[M&G Polymers 2004].
Studies show that PET undergo chemical degradation by hydrolysis if exposed to
humidity or water at high temperatures (85 and 120 ºC), which results in increased
embrittlement [Foulc 2005, Oreski 2005]. In district heating pipes, this could become
a problem for the PET foam close to the media pipe where the temperature is
elevated.
The lowest density of PET foam achieved today is about 90 kg·m-3 (average value of
a 3 cm thick board) [III]. The compressive strength of this foam was determined to
580 kPa, which is considerably higher than the required value for PUR foam in
district heating pipes, namely 300 kPa [EN253:2003]. One function of the HDPE
casing in district heating pipes is to protect the PUR foam insulation from external
mechanical pressure. Due to the high compressive strength of PET foam it may be
possible to use PET foam insulated pipes without casing or with a casing of PET.
Production techniques have not yet been developed, but the casing could, for example,
be produced by melting the outer layer of the insulation. Fewer materials in a product
makes the waste treatment of pipes taken out of use considerably easier.
13
3.5 Blowing agents – physical and environmental properties
Table 3.1 presents some technical and environmental features of previously and
currently used blowing agents in PUR and PET foam insulations. It is desirable that a
blowing agent has a fairly high vapour pressure, thus making it possible to introduce
more gas in the foam. A higher gas content leads to a slower deterioration of the
insulation capacity over time. The thermal conductivity of the blowing agent has a
major impact on the foam thermal conductivity and should be as low as possible to
ensure foam with good insulating capacity. The atmospheric lifetime is an important
environmental factor, since substances with a long life can potentially cause more
environmental damage such as ozone depletion and global warming. The ozone
depletion potential (ODP) for the blowing agents with CFC-11 as a reference
substance and the global warming potential (GWP) with carbon dioxide as reference
substance are presented in table 3.1.
The chlorofluorocarbons (CFCs) were used in the first types of PUR foam insulated
district heating pipes. Their effect on the ozone layer led to a shift towards
hydrochlorofluorocarbons (HCFCs) and carbon dioxide. Today, cyclopentane, often
in combination with carbon dioxide, is the main blowing agent in European PUR
foam insulated district heating pipes. In the United States pentafluoropropane (HFC245fa) is used as replacement for HCFCs. Pentafluorobutane (HFC-365mfc) is a gas
that has been considered for Swedish district heating pipes and was therefore
investigated in this research project. In the development of PET foam, tests with
different blowing agents have been performed in pilot plants. The gases used have
been carbon dioxide, difluoroethane (HFC-152a), (chlorodifluoroethane) HCFC-142b
and chlorodifluoromethane (HCFC-22).
3.5.1 The phase-out of chlorofluorocarbons
The 1950s marked the start of the use of CFCs in different technical applications, such
as refrigerators, air conditioners, aerosol containers, packaging materials, cleaning
solvents and insulation materials. For insulation purposes, this type of gases had some
very good technical qualities such as low thermal conductivity (7.4-8.2 mWm-1K-1
at 25 ºC for CFC-11), relatively high vapour pressure and are not inflammable [Brodt
1995, Chemnetbase 2005, Heinemann 2000, Shankland 1990a].
In the late 1970s, it was found that the CFCs and the HCFCs, had the very undesirable
effect of depleting the ozone layer in the stratosphere [The Montreal Protocol 2005].
The ozone layer is 10-50 km above the Earth’s surface and protects the Earth from the
dangerous short wave UVB radiation by absorbing the energy. The effects of higher
radiation are, for example, increased rates of skin cancer, damage to the immune
system of both humans and animals, decreased marine algae production and
diminished crop growth.
14
The first international agreement setting out a legal framework restricting the use of
ozone depleting substances in industrialised countries was the “Montreal Protocol on
Substances that Deplete the Ozone Layer” in 1987 [The Montreal Protocol 2005].
Since then, further amendments have been adopted in London (1990), Copenhagen
(1992), Montreal (1997) and Beijing (1990). By September 2002, 183 countries had
ratified the Protocol. Production and use of CFCs have been phased out in
industrialised countries, while developing countries are following phase-out
programs, culminating in a complete ban by 2010. In the case of HCFCs which have
an ozone depletion potential of about 1-11 % of that of CFC-11 [World
Meteorological Org 2002], the phase-out will be completed by 2030 in industrialised
countries and by 2040 in developing countries, although some countries have
voluntarily agreed on tighter phase-out schedules. Even though CFCs have been
phased out in Sweden, district heating pipes containing these gases are still in use.
The total amount of CFC-11, the most potent ozone depleting substance, is estimated
to 2000 tonnes in Sweden and about 8100 tonnes in all the Nordic countries
[Svanström 1996]. The gases are released to the atmosphere as they diffuse out of the
foam, which however, is a very slow process.
3.5.2 Blowing agents in PUR foam
Carbon dioxide is often used in combination with cyclopentane in PUR foam. An
advantage of carbon dioxide is that it is created during foaming by adding a small
amount of water to the PUR foam formulation. The main disadvantages of carbon
dioxide is its high thermal conductivity (16.3-16.6 mWm-1K-1 at 25 ºC) compared to
other blowing agents (table 3.1) [Albouy 1998, Brodt 1995, L'air liquide 1976,
Shankland 1990a] and its fast diffusion out of the foam leading to a rapid decrease in
insulation capacity [I]. Solely carbon dioxide blown PUR foam is normally only used
for pipes of large dimensions. Cyclopentane has lower thermal conductivity than
carbon dioxide (11.3-13.8 mWm-1K-1 at 25 ºC) [Brodt 1995, Volkert 1995] as well as
a much slower rate of diffusion [I]. The vapour pressure of cyclopentane is though
below 1 bar at room temperature (0.42 bar at 25 ºC) [Chemnetbase 2005]. In addition
to cyclopentane, iso-pentane with a vapour pressure of 0.917 bar at 25 ºC and a
thermal conductivity of 14.8 mWm-1K-1 at 25 ºC [Chemnetbase 2005, Volkert 1995]
is sometimes added into the foam formulation in order to increase the total amount of
hydrocarbons in the foam cells. Another gas sometimes used in PUR foam is npentane, which has a higher vapour pressure (0.68 bar at 25 ºC) than cyclopentane,
but somewhat higher thermal conductivity (14.8 mWm-1K-1 at 25 ºC) [Chemnetbase
2005, Volkert 1995]. From a technical point of view, a disadvantage of hydrocarbons
is their flammability, and thus extra precautions must be taken during handling and
processing operations. Although produced from fossil resources, hydrocarbons have
no ozone depletion effect and very low global warming effect. A report by Galvin et
al. summarizes the results of toxicological studied carried out on rats, mice and rabbits
since the 1940s [Galvin 1999]. From these studies it was concluded that cyclopentane
is practically non-toxic and has no significant mutagen effects.
15
Hydrofluorocarbons (HFCs) have been used as replacement options in several
technical applications including PUR foam insulation. The gases in this group are
non-ozone depleting but have rather high global warming potentials, up to 10,000
times higher than carbon dioxide [IPCC 2001a, Naik 2000]. In order to restrict the use
of HFCs, taxates have been introduced in Denmark, Norway and Austria. In Denmark
the goal is to phase out HFCs by 2006, and other European countries are expected to
follow [Danish EPA 2002]. Taxes or regulations on the use of HFCs have not yet
been introduced in Sweden [Swedish EPA 2005].
In the USA, HCFCs used for production of new insulation foams were phased out in
2003, and HFC-245fa (EnovateTM3000) is produced and marketed as a replacement
option by the American company Honeywell. As it is a non-flammable gas, it is
possible to use the same equipment as for the production of PUR foam blown with
dichlorofluoroethane (HCFC-141b) [Bogdan 2001]. The German company Bayer AG
has patents in Europe, the USA and Canada for methods to produce PUR foam with
HFCs as blowing agent [Bayer AG Leverkusen 1990, 1996]. Honeywell has acquired
a world wide licence from Bayer AG with exclusive rights for USA and Canada,
while Solvay has acquired a world licence excluding the USA and Canada. Solvay
produces a range of HFCs marketed under the name Solkane®, of which HFC365mfc is one of their main products intended for PUR foam insulation [Solvay Fluor
2005]. Due to the flammability of HFC-365mfc, the Solvay company has developed
non flammable mixtures with 7 % and 13 % heptafluoropropane (HFC-227ea). At
Solvay’s French production plant in Tavaux, all hydroflouroalkanes are manufactured
by means of hydrofluorination of a chlorinated precursor [Zipfel 1999]. At the end of
2002, a plant with an annual HFC-365mfc production capacity of 15,000 tons
commenced operation in Tavaux in France. The price of HFC-365mfc and HFC-245fa
is higher than that of cyclopentane. Since the chemicals used for the PUR formulation
differ due to the blowing agent used, the total cost must be considered.
The vapour pressure of HFC-365mfc and HFC-245ea is higher than that of
cyclopentane, which may result in a higher concentration of these gases in the foam.
The thermal conductivity of HFC-365mfc (10.6 mWm-1K-1 at 25 oC) is of about the
same as that of cyclopentane and lower than that of HFC-245fa (12.2-13.5 mWm-1K1
at 25 oC) (table 3.1). When HFC-365mfc is mixed with HFC-227ea, the thermal
conductivity of the gas mixture increases to 10.7-10.9 mWm-1K-1 at 25 oC [Zipfel
2002].
A toxicological study of HFC-365mfc showes low toxicity and no significant
mutagenicity [Zipfel 1999]. Studies on HFC-245ea show that the substance is of low
toxicity, non-mutagenic and not a teratogen [Honeywell 2005].
16
Table 3.1 Physical and environmental properties of different insulating gases used as blowing agents in PET and PUR insulation foam.
Carbon
dioxide
Cyclopentane
HFC-365mfc
F
F
F
Vapour pressure
at 25 ºC (bar)
Thermal conductivity
of gas phase at 25 ºC
(mWm-1K-1)
Flammability
limits in air (vol%)
Atmospheric
lifetime (years)
Ozone Depletion
Potential, 100 years
Global Warming
Potential, 100 years
a) [Knovel Corp 2005]
b) [Zipfel 2002]
c) [Albouy 1998]
d) [Creazzo 1995]
e) [Chemnetbase 2005]
f) [Shankland 1990a]
HFC-152a
F
F
CO2
124-38-9
44.0
C5H10
287-92-3
70.1
CF3CH2CF2CH3 CHF2CH2CF3
460-73-1
406-58-6
148.1
134.0
-78.5 a
49.3 a
40.2 b
15.3 r
c
0.42 e
0.47 (20ºC) b
16.3-16.6 c,f,g,h
11.3-13.8 i,h,v
None
HCFC-22
F
F
CFC-11
Cl
F
F
Cl
F
Cl
F
F
F
HCFC-142b
F
F
F
F
CAS registry no
Molecular weight,
gmole-1
Boiling point (ºC)
HFC-245fa
Cl
Cl
CHF2 CH3
75-37-6
66.1
CClF2CH3
75-68-3
100.5
CHClF2
75-45-6
86.5
CCl3F
75-69-4
137.4
-10 to -9.2 a,c,d,f
-40.8 a,c,d
23.7 a
1.23 (20ºC) r
-25 to
-24.1a,c,d,e,l
6.0-6.1 c,d,e
3.4-3.5 c,e
10.4 c, e
1.1 e
10.6-11.6 b,v
12.2-14.8 b,j
13.4-14.7 c,d
9.4-12.1 c,f,j
10.6-11.7 c,f,h,j
7.4-8.2 f,h,j
1.5 – 8.7 k
3.5-13.3 l,t
None b
3.7-20.2 c,m,n
9.0-14.8 c,m,n
None c
None f
<0.01 u,s
8.6-10.7 o,p,q
7.2-8.4 o,p,q,s
1.4-1.8 n,o,p,q
17.9-22.4 n,o,p,q
11.9-15.8 n,o,p,q
45-50 o,p,q
0
0
0
0
0
0.014-0.07 q
0.034-0.055 q
1
1
<10 u
782-953 o,p,q
950-1020 o,p,q
120-149 o,p,q
1957-2400 o,p,q
1700-1780 o,p,q
4600-4749 o,p,q
64.3
g) [L'air liquide 1976]
h) [Brodt 1995]
i) [Volkert 1995]
j) [Heinemann 2000]
k) [Galvin 1999]
l) [Solvay Fluor 2005]
m) [Decaire 1994]
n) [Barthélemy 1993]
o) [Naik 2000]
p) [IPCC 2001b]
q) [World Meteorological Org 2002]
r) [Honeywell 2005]
s) [Seifert 2003]
t) [Zipfel 1999]
u) [Heilig 1994]
v) [Merten 1997]
3.5.3 Blowing agents in PET foam
The production of PET foam is still on a pilot scale. HCFC-142b, HCFC-22, HFC152a, carbon dioxide and nitrogen have been used as blowing agents due to their
satisfactory performance in the production process. Other gases may be considered in
the future as the production process develops. Table 3.2 summarizes the foam
densities achieved when using the various gases. The lowest density of foam board
produced to date, about 90 kg·m-3, was achieved with a mixture of HCFC-142b and
HCFC-22 [III], which cannot be considered as a solution for the future due to the
ozone depletion potential of these gases. HFC-152a, which produces a foam with a
density of 120 kg·m-3, has a thermal conductivity in the same range as HFC-245fa and
cyclopentane as well as a somewhat lower global warming potential than HFCs (table
3.2). Inhalation experiments on rats indicate that HFC-152a has very low acute
toxicity [Keller 1996]. Carbon dioxide blown foam has been produced with densities
down to about 140 kg·m-3. Nitrogen as blowing agent produces PET foam up to
densities of 400 kg·m-3 and is not intended to be used for insulation purposes, but as
construction material.
Table 3.2 The lowest densities of the studied PET foams blown with different gases
[II, III].
PET foam blown with:
HCFC-142b/HCFC-22 *
HFC-152a
Carbon dioxide
Nitrogen
Foam density
kg·m-3
91
120
144
330
* Volume ratio HCFC-142b/HCFC-22: 60/40
18
4 INSULATION PERFORMANCE OF
DISTRICT HEATING PIPES
_____________________________________________________________________
4.1 Introduction
This chapter deals with the main factors affecting the long-term thermal performance
of district heating pipes. Chapter 4.2 contains a review of the scientific literature on
the heat transfer mechanisms in polymeric foams. The main research results on the
thermal characteristics of PET and PUR foams presented in papers I, II, III and IV
based on established theories on heat and mass transport in polymeric materials are
summarised in chapter 4.3.
4.2 Heat transfer mechanisms in district heating pipes
The temperature difference between the inside of the media pipe (T2) and the
surrounding ground (T1) is the driving force behind the heat flow through a district
heating pipe (figure 4.1). If the materials are assumed to be homogeneous and
isotropic, Fourier’s law of heat conduction describes the heat flux q (W·m-2), through
the pipe (distance r, m), with the thermal conductivity λ (W·m-1·K-1) as the
proportional coefficient:
T1
T2
r
Direction of the
heat flux, q
q
dT
dr
(4.1)
Figure 4.1 Heat flux, q (W·m-2), through a district heating pipe, T2>T1.
19
Different district heating network constructions are used, such as the three examples
shown in figure 4.2. Heat losses in a district heating network can be calculated by
using finite elements or finite differences [Jonson 2001, Persson 2005a]. Simplified
formulas for the steady-state heat flow from twin and single pipe systems has been
developed [Wallentén 1999]. Persson and Claesson have derived a similar multipole
model that can be applied to all kinds of single pipe constructions [Persson 2005b].
The low thermal conductivity of the insulating foam (20-40 mW·m-1·K-1 at 20 ºC) [II,
III, IV] compared to the surrounding ground (about 1500 mW·m-1·K-1 at 20 ºC)
reduces the heat losses from the the hot water inside of the district heating pipe.
Ground surface
λground
Tground
λfoam
λfoam
λfoam
λfoam
Tfoam
Tfoam
Tfoam
Tfoam
λfoam
Tfoam
Figure 4.2 Examples of district heating pipe constructions. Twin pipe construction
(left) and two types of single pipe constructions (middle and right).
The foam thermal conductivity of the foam can be described as the sum of the three
main mechanisms (equation 4.2). The cell gas conduction is time dependent due to the
change of cell gas composition as a result of diffusion. All mechanisms are
temperature dependent, but this dependency is more pronounced for cell gas
conduction and radiation.
foam t gas (t ) pol rad
where λfoam
λgas
λpol
λrad
(W·m-1·K-1)
(4.2)
total thermal conductivity of the foam
thermal conductivity due to gas conduction
thermal conductivity due to conduction in the polymer matrix
thermal conductivity due to radiation
Convection only occurs if the temperature is low, the temperature gradient very high
and the cell size exceeds 5 mm [Isberg 1988]. Convection is normally negligible in
the PUR foam used in district heating pipes and in the studied PET foam qualities,
due to their small cell sizes [Isberg 1988] and [IV]. If the cell gas pressure is high, the
blowing agent may partially be present as a condensed liquid in the foam cells. The
total volume of this liquid is very small and conduction in the liquid can thus be
disregarded.
20
4.2.1 Radiation and conduction in the polymer matrix
Radiation
The thermal conductivity due to radiation, λrad, in a polymeric foam takes place in all
directions from the surface of the cells, with the net energy transfer from the hot to the
cold side. The process involves several mechanisms (scattering, reflection, emission
and absorption) [Glicksman 1987, Glicksman 1997, Placido 2005]. The radiative heat
flow is strongly dependent on the temperature. Other factors that influence λrad are the
radiative properties of the cell walls and the cellular structure, such as cell shape, void
fraction, surface area to volume ratio of the cells, distribution of the cell sizes around
the mean value, fraction of the polymer material in walls between two cells and
fraction of polymer material in struts (the region of thicker walls between three cells)
[Glicksman 1997]. Generally λrad decreases with smaller cell size [Glicksman 1997,
Wu 1999b]. In a one-dimensional case, the Rosseland equation can describe the
radiative heat transfer (equation 4.3) [Siegel 2001]. The extinction coefficient, K,
describes the overall absorption ability of the material.
rad
where
16
T 3
3K
K
σ
T
extinction coefficient
Stefan Bolzman’s constant
mean foam temperature
(4.3)
(m-1)
(5.7·10-8 W·m-2·K-4)
(K)
Several models have been developed to calculate the extinction coefficient. The fact
that the cell walls in polymeric foams are transparent to infrared radiation, while the
thicker polymeric material of the struts functions as a barrier to the radiation is taken
into account in an advanced model of the extinction coefficient for cellular foams
[Glicksman 1991a, Glicksman 1997]. Experimental measurements of low density
PUR foams (about 30-50 kg·m-3), where the cell size parameters were determined by
scanning electron microscopy (SEM), show very good agreement with the model
[Eeckhaut 1996]. The coefficients describing the cell morphology and the absorption
ability of the solid polymer included in the model may differ between PET and PUR
foam.
Based on Glicksman’s theory and experimental measurements, Nielsen developed a
simplified model for the extinction coefficient of rigid PUR foams qualities used in
district heating pipes (equation 4.4) [Nielsen 1998].
1
3.76
K foam 0.0878
d foam
where
ρfoam foam density
d
cell diameter
(4.4)
(kg·m-3)
(m)
21
Olsson suggested a relationship between the extinction coefficient and foam density,
based on literature data for PUR foam of densities between 20 kg·m-3 and 60 kg·m-3,
(equation 4.5) [Olsson 1998].
K = 1700 + 70·(ρfoam-30)
(4.5)
Conduction in the polymer matrix
The contribution to the heat flow due to conduction in the foam matrix, λpol, depends
both on the thermal conductivity of the solid polymer material and the amount and
distribution of the material, such as the fraction of solid in the struts and the
distribution of cell sizes of the foam [Glicksman 1997]. Glicksman proposes a model
for closed cell foams based on the assumption of cubic cells (equations 4.6-4.8)
[Glicksman 1989].
2
3
pol
solid
pol
fs
foam
fg
fs
3
solid
1 f g pol
(4.6)
8.62
A
d 2 strut
(4.7)
solid
foam
pol
foam
1 solid
solid
pol gas
pol
(4.8)
solid
pol
fraction of solid material in the struts
void/gas fraction of the foam
thermal conductivity of the solid polymer
(-)
(-)
(W·m-1·K-1)
solid
pol
density of the solid polymer
(kg·m-3)
(ρPET = 1380 kg·m-3, ρPUR = 1200 kg·m-3)
density of the foam
density of the cell gas
mean cross-sectional area of a strut
mean foam cell diameter
(kg·m-3)
(kg·m-3)
(m2)
(m)
where fs
fg
ρfoam
ρgas
Astrut
d
Nielsen derived a model for heat conduction in PUR foam that assumes a different
distribution of heat conduction in the cell walls and struts compared to Glicksman
(equation 4.9) [Nielsen 1998]. Comparison with experimental values showed that the
model is suitable for foams with a void fraction of over 0.9 which represents PUR
foam densities below 120 kg·m-3.
λpol = (0.48·fs + 0.66·(1-fs))·(1-fg)· solid
polymer
(4.9)
The mean foam cell diameter and the area of the struts can be determined by SEM of
a two-dimensional cross-section of the foam. The characteristics of the foam are often
calculated by modelling the cells as pentagonal dodecahedrons [Glicksman 1997,
Placido 2005]. A majority of the solid polymer in PUR foam is in the struts, but the
amount varies with foam density and the blowing agent used. In studies by
22
Biedermann et al., the strut fraction of closed cell PUR foams from district heating
pipes with densities close to 60 kg·m-3 was 92-95 % [Biedermann 2001a, Biedermann
2001b].
Comparison of PET and PUR foam
The thermal conductivity of solid PUR polymer (λPUR) from district heating pipes was
determined by Nielsen et al. to 0.21 W·m-1·K-1 at 23 ºC, with a linear increase with
increased temperature of 0.2 mW·m-1·K-1·Cº between 0 ºC and 150 ºC [Nielsen 2000].
Literature values of the thermal conductivity of solid PET polymer (λPET) are similar
to λPUR. The type of PET (molecular weight and structure) and the degree of
crystallinity have been shown to affect λPET. Depending on the molecular properties,
Valcárcel et al. showed that λPET can either decrease or increase with increased degree
of crystallinity [Valcárcel 1999]. Choy et al. determined λPET for a crystallinity of 40
% to about 0.22 W·m-1·K-1 at room temperature. The carbon dioxide blown PET
foams studied in IV had a similar degree of crystallinity (35-37 %). Other reported
values of λPET at 20 ºC are 0.19 W·m-1·K-1 for both amorphous and post consumer
material [Chen 1977, Lopez 2004]. A linear relation fitted to the values reported for
the post consumer PET between 20 ºC and 100 ºC, shows a decrease with increased
temperature of 0.5 mW·m-1·K-1·ºC [Lopez 2004]. According to equations 4.6-4.8 and
given assuming that λPET and λPUR and the cell characteristics are approximately the
same, λpol for PET and PUR foam are similar.
Typically, the contribution to the thermal conductivity in PUR foam from λrad is about
four times higher than from λpol for densities normally used in district heating pipes
(about 70 kg·m3) [Smits 1991]. For PUR foam qualities used in district heating pipes,
smaller cells generally decrease λrad, while higher foam density provides a greater
contribution to λpol [Glicksman 1991a, Glicksman 1991b, Olsson 1998]. Figure 4.3
shows a tendency towards increasing values with increasing density for the PET foam
qualities studied in III and IV (cell size: 0.4-0.5 mm, densities 91-157 kg·m-3).
Assuming a typical PUR foam used in district heating pipes1, equations 4.3, 4.4 and
4.9 give a contribution to λpol + λrad of 9.8mW·m-1·K-1 at room temperature. Based on
previous measurements of foam thermal conductivities for PUR foam insulated
district heating pipes, the contribution is approximated to about 10-12mW·m-1·K-1.
The lowest value of λpol + λrad in PET foam at room temperature was 14.4mW·m-1·K-1
for a foam with the density of 120 kg (blown with HFC-152a) [III, IV].
The average cell diameter of the studied PET foams was determined to 0.4 - 0.5 mm
and no dependency on density was observed. The cells in the foam with the lowest
density (91 kg·m3) were, however, elongated in some regions. Biedermann et al.
reported cell sizes of 0.13-0.43 mm for closed cell PUR foam (densities 57-63 kg·m-3)
from district heating pipes [Biedermann 2001a]. If PET foam with lower density and
smaller cells can be developed, it would be possible to achieve λrad + λpol in the same
range as for PUR foam in the district heating pipes produced today.
1
Foam density: 70 kg·m-3, strut fraction: 92 %, cell diameter: 0.4 mm, λpol: 0.21 W·m-1·K-1 at 23 ºC
23
-1
λrad + λpol (mW · m · K )
20.0
-1
18.0
16.0
HCFC-142b/22
14.0
HFC-152a
Carbon dioxide
12.0
80
100
120
140
160
Density (kg m3)
Figure 4.3 Approximate contributions to the foam thermal conductivity due to
radiation and conduction in the solid polymer (λrad + λpol) at 25 ºC in PET foam blown
with HCFC-142b/22, HFC-152a and carbon dioxide (cell size 0.4-0.5 mm) [III,IV].
The values presented in III were recalculated using the Brokaw equation and gas
thermal conductivities from [Albouy 1998] and [L'air liquide 1976].
4.2.2 Conduction in the cell gas
The foam thermal conductivity is strongly affected by the cell gas conductivity, λgas.
In the studied PET foams (densities 91-157 kg·m-3), λgas contributed 45-60 % to the
foam thermal conductivity [III, IV]. In PUR foam (densities 35-80 kg·m-3) it can
account for up to 65-80% of the foam thermal conductivity [Olsson 1998]. In new
foam, the cells mainly contain blowing agent.
Temperature dependency
The thermal conductivity of the gases increases with increasing temperature, which is
illustrated for oxygen, nitrogen, carbon dioxide, HFC-245fa, HFC-365mfc and
cyclopentane in figure 4.4. The thermal conductivities of cyclopentane presented in
the literature show great variation. Values of between 11.3 and 13.8 m·W·m-1·K-1
have been reported at room temperature [Brodt 1995, Merten 1997]. In figure 4.4,
cyclopentane data from four different references are shown: 10 ºC from [Fleurent
1995], 25 ºC from [Volkert 1995], 50 ºC from [Takada 1999] and 62-145 ºC from
[Heinemann 2000], with a suggested polynomial formula fitted to the values.
The thermal conductivity of a gaseous compound at a certain temperature can be
calculated according to several advanced models [Laesecke 1992, Marrucho 2003,
Poling 2000]. In Reid et al. a simple model for calculating the thermal conductivity at
a certain temperature, is presented (equation 4.10) [Reid 1977]. The accuracy between
this model and literature values is higher for low temperature differences.
24
-1
-1
Gas thermal conductivity (mW · m · K )
35.0
30.0
25.0
Oxygen
20.0
Nitrogen
Carbon dioxide
15.0
HFC-245fa
HFC-365mfc
10.0
Cyclopentane
λcyclopentane = 0.0003T + 0.0595T + 10.32
2
5.0
0.0
0
50
100
150
Temperature ( ºC)
Figure 4.4 Temperature dependency of the gas thermal conductivity of nitrogen,
oxygen, carbon dioxide [L'air liquide 1976], HFC-245fa [Dohrn 1999], HFC-365mfc
[Marrucho 2002] and cyclopentane [Fleurent 1995, Heinemann 2000, Takada 1999,
Volkert 1995].
1.786
T 1 T1
T 2 T2
(4.10)
λTi
Ti
where
gas thermal conductivities at Ti
temperatures
(W·m-1·K-1)
(K)
Thermal conductivity of cell gas mixtures
Several models have been developed in order to calculate the thermal conductivity of
cell gas mixtures at low pressures [Mason 1958, 1959, Merten 1997, Nielsen 1998,
Poling 2000, Reid 1977]. Both the thermal conductivity of each gas component in the
mixture and the interactions between the molecules must be taken into account.
Difficulty in describing the thermal conductivity of the mixture occurs when one or
more of the gases involved are polar. The Wassiljewa equation from 1904 is
commonly used to calculate λgas (equation 4.11) [Reid 1977]. Equation 4.12 was
derived by Wassiljewa for binary gas mixtures [Merten 1997].
yi i
m
gas
i 1
(4.11)
m
B
j 1
ij
yj
1 si s j
Bij
2 2 si
2
Mi M j
Mj
(valid for binary gas mixtures)
(4.12)
25
where gas
i
yi
Bij
si
Mi
thermal conductivity of the gas mixture
thermal conductivity of component i
molar fractions of component i
Wassiljewa function
molecule diametre
molecular mass of component i
(W·m-1·K-1)
(W·m-1·K-1)
(-)
(-)
(m)
(g·mol-1)
Mason and Saxena proposed a modified equation where the gas viscosities also are
taken into account (equation 4.13) [Reid 1977]. Sometimes an equation for Bij based
on critical temperatures and pressures are used [Poling 2000].
1 / 2 M 1 / 4
1 i j
j M i
Bij
1/ 2
8 1 M i / M j
2
where ηi
(4.13)
gas viscosity of component i
(Pa·s)
Lindsay and Bromley’s equation also includes the boiling temperature of the
components [Reid 1977]. Brokaw suggested an empirical model (equation 4.14) [Reid
1977]. As an approximation of the cell gas mixtures in PUR insulating foams, Isberg
proposed a simplification of the Brokaw equation, where the Brokaw coefficient is set
to 0.5. This model is very accurate for mixtures of air and CFC-11 (equation 4.15)
[Isberg 1988].
λm = q · (y1· λ1 + y2· λ2) + (1-q) · (y1/ λ1 + y1/ λ1)-1
where
gas
q
(4.14)
the Brokaw koefficient
n
1
0.5 yi i n
i 1
yi
i 1 i
(4.15)
In the extended corresponding states theory (ECST), the thermal conductivity is
expressed as the sum of energy transfer due to translation effects and internal degrees
of freedom [Marrucho 2005].
Thermal conductivity properties of cyclopentane and HFC-365mfc
Merten and Rotermund compared thermal conductivities of mixtures various blowing
agents and carbon dioxide or air measured at 40 ºC with values calculated by models
from the literature (Wassiljewa, Mason and Saxena, Lindsay and Bromley and
Brokaw) [Merten 1997]. It was concluded that the models can deviate considerably
from measurements. The mean deviations from the measured values of mixtures of
cyclopentane and carbon dioxide were 0.14 to 0.50 mW·m-1·K-1. The Brokaw
26
equation gave the highest deviation. In mixtures with air the deviation was 0.73 to
0.75 mW·m-1·K-1. Marrucho et al. also found deviations between measured thermal
conductivities of mixtures of cyclopentane and nitrogen and calculated values based
on ECST [Marrucho 2005]. It is obvious that the thermal conductivities of some gas
mixtures are difficult to predict with existing models. When accurate values are
required, measured values should be used.
28
Poly. (HFC-365)
Mixtures with air
-1
-1
Gas thermal conductivity (mW·m ·K )
The measured gas thermal conductivities of HFC-365mfc and cyclopentane at 40 C
in mixtures with carbon dioxide and air are shown in figure 4.5 [Merten 1997]. The
higher vapour pressure of HFC-365mfc compared to cyclopentane makes it possible
to obtain a higher fraction for HFC-365mfc (up to 63 % at 25 ºC) than for
cyclopentane (up to 42 % at 25 ºC) [Chemnetbase 2005, Marrucho 2002].
Consequently, it is possible to achieve a lower gas thermal conductivity for the
mixture of air with HFC-365mfc than with cyclopentane (upper lines in figure 4.5).
The gas thermal conductivity of the carbon dioxide and HFC-365mfc mixture will,
however, always be approximately the same or higher than that of cyclopentane
(lower lines in figure 4.5). The concentration of carbon dioxide is high in new PUR
foam, but its rate of diffusion out of the foam is more rapid than the inward diffusion
of air and the outward diffusion of blowing agent. According to Merten and
Rotermund’s measurements new foams blown with carbon dioxide and a high amount
of HFC-365mfc could thus have the same or higher cell gas thermal conductivity as a
cyclopentane blown foam. When the carbon diode has left the foam, the cell gas
thermal conductivity of the HFC-365mfc blown foam could become lower than that
of the cyclopentane blown foam.
26
Poly. (Cyclopentane)
24
22
20
Mixtures with carbon dioxide
18
16
14
0
0.1
0.2
0.3
0.4
0.5
0.6
Volume fraction of HFC365mfc or cyclopentane
Figure 4.5 Thermal gas conductivity for HFC-365mfc and cyclopentane in mixtures
with air and carbon dioxide at 40 ºC (mixtures prepared at 25 ºC) The figure is based
on tables 2,6 and 7 and figures 5, 12 and 14 in [Merten 1997].
27
4.3 Long-term thermal performance of district heating pipes
24
Foam thermal conductivity
-1
mW·m ·K
-1
4.3.1 Changes in thermal conductivity over time
The increase in λfoam over time in a closed cell polymer foam is caused by the change
in the cell gas mixture due to diffusion, which is exemplified for PUR foam in figure
4.6 [I-IV]. In both PET and PUR foam, carbon dioxide leaves the foam faster than air
(oxygen and nitrogen) enters it [I,III,IV]. The diffusion of physical blowing agents
(e.g. cyclopentane or HFCs) out of the foam is comparatively slow [I-III]. The
thermal conductivity of air at 25 ºC is about 26 mWm-1K-1, which is considerably
higher than that of the blowing agents (carbon dioxide: 16.4, cyclopentane: 12.1-13.8,
HFC-365mfc: 10.6 mWm-1K-1). The diffusion process thus lead to an increase in
λfoam until the whole foam is completely filled with air and devoid of blowing agent.
The time required to complete the process depends on the initial cell gas composition
as well as on the characteristics of the foam, e.g. density and degree of crystallinity [IIV]. The HDPE casing of PUR foam insulated district heating pipes has been found to
affect the diffusion rate of some gases, by acting as a barrier [I,II]. Thus, in order to
determine the thermal aging of a district heating pipe, the transport of cell gases both
in the insulating foam and the casing material must be taken into account.
22
20
Partial pressure (kPa)
0
150
Total pressure
100
Nitrogen
50
Cyclopentane
Oxygen
Carbon dioxide
0
0
Time
Figure 4.6 The partial pressure changes of cell gases in a PUR foam slab due to
diffusion (lower graph) and its effect on λfoam (upper graph) at room temperature.
28
A fraction of the cell gases are present dissolved in the polymer matrix and as liquid
in the cells if the vapour pressure of the gas is exceeded. The fraction of blowing
agent starts to decrease after excess liquid has evaporated and diffused out of the
foam. Liquid blowing agent can act as a buffer, slowing down the process of
deterioration of the insulating capacity of the foam. The cell gas content in newly
produced PUR foam insulated district heating pipes from various producers was
analysed in a study initiated by the Swedish district heating association. Up to 45 %
by weight of the cyclopentane content in the foam cells was present as liquid in the
foam cells.
4.3.2 Mass transport in polymeric membranes
Mass transport in polymeric materials is a complex process, where the materials
and/or the penetrating molecules can interact in different ways, causing disturbances
that complicates a description of the process by means of theoretical models [Rogers
1986]. Experimentally determined parameters describing diffusion of a gas are only
valid for a specific polymer with its unique molecular characteristics (degree of
crystallinity, polymer chain length and branching etc.) and the amount of additives
that may be present. The situation becomes even more complicated when the polymer
has a closed cell structure, but several models have been developed to experimentally
determine and theoretically describe such cases [Brodt 1995, du Cauzé de Nazelle
1995].
At a microscopic level, the diffusion process in insulating foam takes place from cell
to cell through the thin membrane surrounding each cell. The casing material
surrounding district heating pipes can also be considered as a membrane. The driving
force behind the mass transport of a gas through a membrane is the partial pressure
gradient of the gas over the membrane, with net mass transfer in the direction from
the side with the highest partial pressure to the side with the lowest (figure 4.7). The
total mass flow at a certain time of gas component i through an isotropic membrane,
can be described by Fick’s first law of diffusion (equation 4.16).
J i Ppol ,i
where Ji
Ppol,i
1
pi
x
(4.16)
mass flow
polymer permeability coefficient
(mole·m-2·s-1)
(mole·m-1·s-1·Pa-
partial pressure
distance in the direction of the diffusion
(Pa)
(m)
)
pi
x
29
Polymer
membrane
1. Gas molecules
dissolve (Spol,i)
2. Diffusion (Dpol,i)
3. Gas molecules
desorb (Spol,i)
Pressure gradient
Pi,1
pi,1 > pi,2
pi,2
Permeation (Ppol,i)
- the sum of processes 1-3
Distance (x)
Figure 4.7 Permeation of gas component i through a polymer membrane.
Permeation can be divided into a three-stage process [Rogers 1986]. At first the gas is
dissolved at the surface of the membrane, a process that is characterized by the
polymer solubility coefficient (Spol,i). The dissolved gas diffuses through the
membrane, described by the polymer diffusion coefficient (Dpol,i). The diffusion step
can be considered as a sequence of small jumps, each involving a potential barrier.
The surrounding polymer chain segments are rearranged in each step, which involves
a number of van der Waal interactions. Finally, the gas molecules desorb from the
other side of the membrane surface. Under ideal conditions, the dissolved gas at the
boundary of the membrane is in equilibrium with the gas outside the membrane, as
described by Henry’s law (equation 4.17). The permeability coefficient is the product
of the solubility and the diffusion coefficients (equation 4.18). Fick’s first law of
diffusion can thus be rearranged into equation 4.19. All coefficients are specific for
every penetrant in a given polymer.
c pol ,i S pol ,i pi
(4.17)
Ppol,i = Spol,i · Dpol,i
(4.18)
J i D pol ,i
c pol ,i
x
(4.19)
where
cpol,i concentration of gas in the polymer (at the membrane surface) (mole·m-3)
pi
partial pressure (outside the membrane surface)
(Pa)
Spol,i polymer solubility coefficient
(mole·m-3·Pa-1)
Dpol.i polymer diffusion coefficient
(m2·s-1)
30
The change in the concentration of a penetrant at any point within the membrane is
given by Fick’s second law of diffusion (equation 4.20). In this differential equation
the diffusion coefficient is a constant and thus independent of time, distance and
concentration of the sorbed pentetrant.
2 p
pi
D pol ,i 2 i
t
x
(4.20)
These mathematical descriptions of the diffusion process assume homogeneous
materials and do not take into account the normal variations in the structures of a
polymeric material. Often the diffusion coefficient is not constant. A common case is
that Dpol,i is dependent on the concentration of the sorbed penetrant in the polymer,
(equation 4.21) [Rogers 1986].
pi
p
D pol ,i c pol ,i i
t x
x
(4.21)
The equation can be rewritten as equation 4.22. By performing experiments within
small intervals of cpol,i, the second term in the equation can be omitted [Rogers 1986].
The concentration dependency can then be obtained from several mean diffusion
coefficients determined over each interval.
pi
2 p D pol ,i (c pol ,i ) pi
D pol ,i (c pol ,i ) 2
x
x
x
t
(4.22)
Another approach often used to describe diffusion in polymers is the free-volume
theory, originally presented by Cohen and Turnbull in 1959 and developed by several
researchers since then [Duda 1996]. In these models, the polymer volume can be
divided into an occupied and a free part that is created by thermal fluctuations,
through which molecules can penetrate. Generally, an increase in temperature
provides energy for enhanced movement of the polymer segments, which can also be
described as an enlargement of the total free-volume [Rogers 1986].
If the diffusion is assumed to follow Fick’s and Henry’s laws, the temperature
dependency of Ppol,i, Spol,i and Dpol,i can be can be described by Arrhenius types of
relationships (equations 4.23-4.25), where EP, ES and ED are the activation energies
[Rogers 1986].
31
EP
Ppol ,i P0 exp
R T
(4.23)
ES
S pol ,i S 0 exp
R T
(4.24)
ED
D pol ,i D0 exp
R T
(4.25)
where
P0, S0, D0,
EP, ES, ED
R
T
pre-exponential factors
activation energy for each process
the gas constant
temperature
(J·mole-1)
(J·K-1·mole-1)
(K)
Deviations occur when other factors affect the mobility of the polymer chains, such as
interactions between the penetrant and the polymer or between penetrants, increased
mobility at the glass transition or melting temperature and defective structures such as
voids and microcracks [Lewis 2003, Rogers 1986].
4.3.3 Mass transport in closed cell polymeric foams
Mass transport in a closed cell foam involves permeation through the cell walls as
well as transport within the cell voids and is dependent both on the properties of the
gas and on the structural characteristics of the foam e.g. foam density, cell size
distribution, cell elongation, cell orientation and the thickness of the cell walls [Brodt
1995, du Cauzé de Nazelle 1995]. The overall mass transfer of gas component i in the
foam can be characterized by the effective diffusion coefficient (Deff,i) and the
effective permeability coefficient (Peff,i) are used if the foam is assumed to be a
homogeneous material. Models of diffusion in closed cell foams can be divided into
two categories: continuous and discrete [Alsoy 1999]. The models presented below
are one dimensional, but can easily be extended to more dimensions. The temperature
dependency of Peff,i and Deff,i can be assumed to follow the Arrhenius relationships in
the same way as Ppol,i and Dpol,i (equations 4.23 and 4.25).
In the continuum approach, which was first developed by Francis J. Norton in 1967,
the foam is considered as a homogeneous, continuous medium [du Cauzé de Nazelle
1995, Fröling 2002a, Norton 1967, Olsson 2001a]. The model is based on the
following assumptions:
32
1. The effective diffusion coefficient of each gas in the polymer (Dpol,i) is
independent of its respective concentrations in the polymer. Thus a linear
concentration gradient across the cell walls is assumed and both Fick’s law
and Henry’s are valid.
2. The diffusion processes of the different gases are independent of each other.
3. No pores exist in the cell walls
4. The mass storage capacity of the gas in the foam is represented exclusively by
the storage capacity of the cell voids, i.e. no gas is considered to be dissolved
in the polymer.
Fick’s first and second laws with the effective diffusion and permeability coefficients
(equations 4.26 and 4.27) can then describe the mass transport of a gas in the foam,
analogous with the theory for mass transport through a membrane described in
chapter 4.4.1. The relationship between the coefficients is described by equation 4.28.
J i Deff ,i
p
ci
Peff ,i i
x
x
2 p
pi
Deff ,i 2 i
t
x
(4.27)
Peff,i = Svoid,i · Deff,i
(4.28)
where Deff,i
Peff,,i
1
(4.26)
effective diffusion coefficient
effective permeability coefficient
(m2·s-1)
(mole·m-1·s-1·Pa-
cell gas concentration of component i
cell gas pressure of component i
“solubility” in the cell voids, =1/(R·T)
(mole·m-3)
(Pa)
(mole·m-3·Pa-1)
)
ci
pi
Svoid,i
The membrane permeation model describes the diffusion as a cell to cell process that
follows Fick’s law [Brodt 1995, du Cauzé de Nazelle 1995, Norton 1982]. Different
models of the foam structure can be used, from simple cubic cell structures to
modelled networks of polyhedrons with imperfections [du Cauzé de Nazelle 1995].
33
Equation 4.29, which is derived from the mass balance of one cell, may be used to
calculate Deff, where a geometrical factor Fgeo, summarizes the structural properties of
the foam [Bart 1993, Brodt 1995]. A minimum of Fgeo is obtained by assuming that
the polymer material is distributed as plane sheets, which gives equation 4.30 [Brodt
1995]. More advanced Fgeo can be calculated by modelling the cells as spheres, cubes
or truncated octahedrons [Brodt 1995, du Cauzé de Nazelle 1995]. Equation 4.31
displaces the case of truncated octahedrons [Brodt 1995] .
Deff ,i
f g / RT (1 f g ) S pol ,i
Fgeo ,min
Fgeo
D pol ,i S pol ,i Fgeo
d
1
1 f g m
3.69
1 fw f g
where Deff,i
Dpol,i
Spol,i
Fgeo
R
T
fg
fw
d
m
(4.29)
(4.30)
(4.31)
effective diffusion coefficient in the foam
diffusion coefficient in the polymer
solubility coefficient in the polymer
geometrical factor
gas constant = 8.314
temperature
void/gas fraction of the foam
fraction of polymer in the struts
cell diameter
membrane thickness
(m-2·s-1)
(m-2·s-1)
(molem-3Pa-1)
(-)
(Pam-3mole-1K-1)
(K)
(-)
(-)
(m)
(m)
The membrane permeation model and the continuum model can be combined. If the
cell gases are considered ideal, the relationship between the effective diffusion
coefficient and the effective permeability coefficient can be written according to
equation 4.32. In the case of insulating foams, the void fraction is often close to 1,
since the volume of the polymer is very small. Equation 4.29 can then be reduced to
equation 4.33. Combining equations 4.32 and 4.33 yields an approximate expression
for calculating Peff from the polymer diffusion and solubility coefficients as well as
the geometrical coefficient (equation 4.34).
34
Deff ,i Peff ,i R T
(4.32)
Deff ,i D pol ,i S pol ,i Fgeo R T
(4.33)
Peff = Dpol · Spol,i · Fgeo
(4.34)
Applying equation 4.34 to equation 4.29 eliminates Fgeo. Rearrangement of the
equation produces an equation for Peff, where the first product originates from the gas
in the voids and the second from the gas dissolved in the polymer matrix (equation
4.37).
fg
Peff ,i Deff ,i
S pol ,i (1 f g )
R T
(4.35)
There are controversies about the type of models that should be used to determine
effective diffusion coefficients in closed cell polymer foams. Attempts have been
made to compare the discrete models with experimental data from the literature, in
order to determine their validity [Alsoy 1999, Pilon 2000]. Discrepancies have been
revealed, but it should be borne in mind that the diffusion coefficients are very much
dependent on the characteristics of the polymer [Pilon 2000]. In the case of PUR
foam, many different polyols and isocyanates can be used, but the types of precursors
used are rarely specified in the literature. It is argued that the discrete models fail to
correctly describe the diffusion process for the heavier blowing agents due to their
deviations from Henry’s law. Therefore a discrete unsteady-state model taking the
concentration dependency into account was suggested by [Alsoy 1999].
4.3.4 Study of mass transport in PET and PUR foam
The effective diffusion coefficients of the cell gases in insulating foams can be
determined by measuring the change in partial pressures over time and applying the
commonly used diffusion theories [Svanström 1997b]. This method (described below)
was used in I-IV to determine Deff for air and blowing agents in PET and PUR foams.
Other methods for the determination of Deff are measurements of the changes in foam
thermal conductivity [Booth 1996]; indirect sorption experiments where the pressure
change in the atmosphere surrounding a sample is recorded [Brodt 1995, Brodt 1993,
Mitalis 1991, Page 1992]; determination of the gas flow in a foam sample due to an
imposed pressure gradient [Shankland 1990b]; and gravimetric studies [Booth 1996,
Booth 1993, Cuddihy 1967]. The time needed to determine the diffusion process can
be speeded up by reducing the size of the foam samples or increasing the temperature
[Isberg 1988, Svanström 1997b].
35
Experimental procedures
The effective diffusion coefficients of the cell gases (carbon dioxide, oxygen, nitrogen
and physical blowing agents) in PET and PUR foam were determined by means of
aging experiments on foam cylinders (diameter 20.8 mm, length 40-65 mm), taken
from foam slabs or district heating pipes [I-IV]. The cylinder ends were sealed by
gluing aluminium plates with epoxy or by applying a mixture of beeswax and paraffin
in order to prevent longitudinal diffusion. The cylinders were stored at different
temperatures (23 ºC, 40 ºC, 60 ºC and 90 ºC) and the cell gas content was determined
after different lengths of time using the experimental set up illustrated in figure 4.8
[Svanström 1997b].
Dinitrogen oxide was flushed through the system in order to remove all oxygen after
which nitrogen and then the foam cylinders were ground and the released cell gases
collected in a glass syringe. The composition of the gas was analysed by gas
chromatography. Since the volume of the foam cylinder and the volume of the
released cell gases at ambient pressure are determined, it is possible to calculate the
partial pressure of all the cell gases in the foam. The experimental procedure on the
PUR foam samples took place at the same temperature as that at which the sample
was stored, so that the equilibrium between the gas dissolved in the polymer matrix
and the gas in the cells would not be changed. Friction during grinding caused the
PET foam samples to melt if the temperature during grinding was too high. All PET
foam samples were therefore analysed at room temperature. This is not expected to
have a significant influence on the results, since the solubility of cell gases in PET is
low (table 4.2) [III].
The solution of Fick’s second law for a foam cylinder (equation 4.27 for cylindrical
coordinates) was used to calculate the change in mean partial pressure of the cell
gases in a PUR cylinder (equation 4.36) [Svanström 1997b]. The effective diffusion
coefficient for each gas and sample was determined by fitting a calculated curve to the
experimentally determined partial pressure change.
p i p0i
4 exp β 0j2 Deff ,i t
j 1
where
36
β
a
(4.36)
2
0j
pi
mean partial pressure of component i
(Pa)
p0i
a
β0j a
t
initial partial pressure of component i
cylinder radius
roots of the zero order Bessel function
time
(Pa)
(m)
(-)
(s)
The concentration of blowing agent in the polymer was determined by placing a
quantity of PUR and of PET foam powder from a previous cell gas analysis into steel
containers and expose them to a high temperature (280 ºC) [Holmgren 2004]. After
cooling, the gas mixture in the container was analysed by gas chromatography. Spol,i
was calculated according to Henry’s law (equation 4.17) using the calculated
concentration of the cell gas in the polymer and the partial pressure determined from
the previous cell gas analysis. The solubility coefficient of cyclopentane in PET,
which is not used as a blowing agent in PET foam today, was determined by exposing
ground PET foam to a known partial pressure of cyclopentane in a vessel until
equilibrium was reached. Thereafter the procedure described above was applied in
order to determine the concentration of the cell gas in the polymer [III].
Figure 4.8 Experimental set up to determine the partial pressure of cell gases in
PET and PUR foam.
37
Summary of results
The experimentally determined effective diffusion coefficients and activation energies
based on the Arrhenius relationship in PUR and PET foams of different densities are
shown in table 4.1 [I-IV]. Polymer solubility coefficients from experiments and the
literature are presented in table 4.2. A review of literature values of effective diffusion
coefficients in PUR foam for some blowing agents is presented in table 4.3.
All diffusion coefficients were determined for the first 100-3500 hours, depending on
the diffusion rate. The shorter times were used for fast diffusing gases at high
temperatures. Diffusion of oxygen, nitrogen and carbon dioxide in both PUR and PET
foam and HCFCs in PET foam closely followed the theoretical diffusion model.
Initially, a more rapid rate of diffusion than predicted by the theoretical model was
obtained for cyclopentane and HFC-365mfc in PUR foam, possibly due to the
interference of mechanisms other than diffusion. One explanation is the effects of the
surface damage caused when the cylinders are taken from the foam slabs or district
heating pipes.
Table 4.1 Experimentally determined effective diffusion coefficients (Deff) and
activation energies (ED) for different cell gases in PUR and PET foam.
Foam density
Deff
EDeff
PET foam
PUR foam
kg·m-3
Carbon
dioxide
Oxygen
Nitrogen
Cyclopentane
HFC-365mfc
Carbon
dioxide
Oxygen
Nitrogen
HCFC-22
HCFC-142b
·103 J·mole-1
·10-13 m2·s-1
58-71
[I]
58-71
58-71
58-71
34-52
157
[I]
157
157
91
91
[IV]
[I]
[I]
[II]
[IV]
[IV]
[III]
[III]
23ºC 40ºC 60ºC 90 ºC
500
1300 14000a)
150
25
0.6
1.0
45
15
1.5
1.7c)
0.5c)
40b)
4
650
220
7
4500a)
2000a)
10a)
40b)
55b)
35b)
85
150
1000
25d)
20
3.5
40
7.0
290
70
25d)
35d)
a)
New measurements from foam taken from a district heating pipe (foam density 58 kg·m-3).
b)
Calculated between 23 ˚C and 90 ˚C.
c)
Recalculated from [III], by taking a damaged outer layer of 0.4 mm into account.
d)
Calculated between 23 ˚C and 60 ˚C.
Long-term measurements of the partial pressure change of cyclopentane and HFC365mfc in PUR foam cylinders (up to 16000 hours) showed deviations from the ideal
diffusion model. Over time the diffusion seems to become increasingly slower. Lower
diffusion coefficients would thus be obtained for a curve fitted to the values
determined after long time compared to those presented in table 4.1. This may be
caused by concentration or time dependency. Generally, the concentration
dependency of diffusion coefficients in polymers increases with the size of the
diffusing molecule [Duda 1996]. According to measurements by Hong et al., there are
indications of lower diffusion and permeability coefficients in solid polyurethane with
38
decreasing concentration of blowing agent [Hong 2001]. In a study by Holmgren no
relationship between the solubility coefficients of cyclopentane and the partial
pressures of the gas in PUR foam cells was found [Holmgren 2004]. This was also the
case in a small-scale study of HFC-365mfc in PUR foam [Mangs 2002].
Table 4.2 Solubility coefficients (10-3 mole·m-3·Pa-1) at 23-25 ºC in PUR and PET
polymers.
PUR
PET
a)
Carbon dioxide
0.82-0.90
1.33 g)
a)
Oxygen
0.062
0.058 g); 0.041 h)
Nitrogen
0.041 a)
0.076 g)
b)
a)
c)
d)
d)
2.4 [III]
Cyclopentane
8.8 ; 11.4 ; 12.3 ; 18.5 ; 23.6
[II]
e)
e)
HFC-365mfc
6.0 ; 9.3 ; 9.7
HCFC-22
1.8 f); 4.2 e)
0.4 [III]
HCFC-142b
4.0 e); 5.4 e)
0.5 [III]
d)
d)
HCFC-152a
3.8 ; 4.0
0.3 [III]
a)
e)
b)
f)
[du Cauzé de Nazelle 1995]
[Holmgren 2004]
c)
[Mangs 2002]
d)
[Hong 2001]
[Hong 1998]
[du Cauzé de Nazelle 1995]
g)
[Lewis 2003] Amorphous PET
h)
[Liu 2004a] Amorphous PET
A literature review reveals great variations in the effective diffusion coefficients of
carbon dioxide (70-420·10-13 m2·s-1), oxygen (40-700·10-13 m2·s-1) and nitrogen (5.530·10-13 m2·s-1) in different types of PUR foams at 20-25 ºC [Svanström 1997a]. The
results of the present study are thus within this range (see table 4.1). The variations in
the literature data may be due to the experimental method used as well as to the foam
formulation and morphologies of each of the studied foams. The type of polyol in the
PUR formulation has been shown to have a significant effect on both the diffusion
and the solubility coefficient [Kaplan 1994].
Table 4.3 Effective diffusion coefficients of blowing agents at 20-25 ºC in PUR foam
published in the literature.
Foam density Deff
Reference
·10-13 m2·s-1
kg·m-3
[Thijs 1994]
Cyclopentane
n.g.
0.5
[Svanström 1997b]
43-49
1-5
[Capella 1996]
30.5
6.2
[Bazzo 1994]
n.g.
8.3
[Zipfel 1998]
HFC-365mfc
n.g.
0.5
[Modesti 2005]
32-36
0.52
[Wu 1999a]
n.g.
3.1
[Wu 1999a]
HFC-245fa
n.g.
0.39
[Modesti 2005, Modesti 2004]
33-36
0.69-0.91
[Bazzo 1994]
HCFC-22
n.g.
12
[du Cauzé de Nazelle 1995]
35
18
[Bhattacharjee 1995]
n.g.
6.6-45
[Bart 1993]
n.g.
60
[Bazzo 1994]
HCFC-142b
n.g.
2.2
n.g. = not given
39
Comparison of cyclopentane and HFC-365mfc in PUR foam
At room temperature, the determined effective diffusion coefficient of HFC-365mfc
(1.0 m·s-1) is about twice as high as that of cyclopentane (0.6 m·s-1). It should be
borne in mind that Deff increases with decreasing foam density, since less material
gives lower resistance to gas transport [Brodt 1995], and that the density of the
studied HFC-365mfc blown foams (34-52 kg·m-3) is lower than that of the
cyclopentane blown foams (58-71 kg·m-3).
Effective diffusion coefficients for cyclopentane in PUR foam found in the literature
vary between 0.5 and 8.3·10-13 m2·s-1 (table 4.3). The densities were though not given
for all foams. The value of HFC-365mfc is similar to those reported by Zipfel et al.
and Modesti et al., (0.5-0.52 m·s-1) while the value given by Wu et al. is slightly
higher (3.1 m·s-1) [Modesti 2005, Wu 1999a, Zipfel 1998]. The diffusion coefficients
of HFC-245fa presented in table 4.3 are similar to the HFC-365mfc values. Studies of
the long-term thermal performance of HFC-245fa blown PUR foam report a slower or
similar aging performance compared to that of cyclopentane blown PUR foam
[Doerge 2001, Seifert 2003].
Despite the fact there are large discrepancies in the literature between the solubility
coefficients for cyclopentane in PUR, these coefficients are all higher than those
determined for HFC-365mfc (table 4.2). The value reported by Holmgren, which was
achieved using the same procedure as for HFC-365mfc, is however similar. In one
study, Dpol of HFC-365mfc in PUR polymer at 24 ºC were determined to 3.2 and
4.4·10-16 m2·s-1 [Hong 2001]. In the same study, the cyclopentane values were: 4.6
and 5.1·10-16 m2·s-1. Two gases with similar Spol, and Dpol, such as HFC-365mfc and
cyclopentane will have about the same value of Deff in foams with the same cellular
structure (equation 429 and 4.33).
Comparison of PET and PUR foam
The determined effective diffusion coefficients of carbon dioxide, oxygen and
nitrogen are about 10-30 times lower in PET foam than in PUR foam for all
temperatures studied (table 4.1). The largest difference between the foams is obtained
for nitrogen. In IV the changes in gas thermal conductivity over time for 35 mm thick
carbon dioxide blown PET and PUR foam boards at different temperatures were
calculated according to the determined diffusion coefficients. The calculated aging of
the PET foam board was approximately 10 times slower than that of the PUR foam
board. The density of the carbon dioxide blown PET foam for which Deff were
determined was high (157 kg·m-3), which gives slower diffusion of gases and an
unfavourably high contribution to λfoam from conduction in the polymer matrix.
In order to predict the performance of carbon dioxide blown PET foam of lower
density, a new study of the density dependency of the effective diffusion coefficients
of carbon dioxide at 60ºC was performed. Foam cylinders with a density of 123kg·m-3
(HFC-152a blown) and 95kg·m-3 (HCFC-142b/22 blown) were placed in a steel
vessel with a constant slow flow of carbon dioxide. The cell gas composition of the
40
cylinders was determined after different lengths of time with the method described
above, and a curve for the inward diffusion was fitted to the values. In figure 4.9 the
determined effective diffusion coefficients for carbon dioxide are shown together with
those determined for foam with a density of 157 kg·m-3 in IV. The oxygen and
nitrogen values for foam densities of 120 and 157 kg·m-3 are are from III and IV. The
equations in the figure are approximations of the density dependency of the effective
diffusion coefficients. Calculating an approximate value of Deff for carbon dioxide in
PET foam of a density of 60 kg·m-3 result in 1000·10-13 m2·s-1, which is very similar
to the experimentally determined value (1300·10-13 m2·s-1) of PUR foam with a
density of 58-71 kg·m-3 [I]. The calculated values for oxygen and nitrogen in PET
foam (240 and 30·10-13 m2·s-1) are lower than those in PUR foam (650 and 220·10-13
m2·s-1), although the former figures are more uncertain.
The effective diffusion coefficients of HCFC-22 (1.7·10-13 m2·s-1) and HCFC-142b
(0.5·10-13 m2·s-1) were also determined for PET foam with a density of 91 kg·m-3. The
literature values for these gases in PUR foam are 12 to 60·10-13 m2·s-1 for HCFC-22
and 2.2·10-13 m2·s-1 for HCFC-142b (table 4.3).
The solubility coefficients in table 4.2, which is a summary of both experimental
studies and literature values, show a tendency towards lower values for the heavier
blowing agents in PET compared to PUR, contributing to lowering the permeability of
PET foam in accordance with diffusion theories (equations 4.33 and 4.34). The values
of carbon dioxide and air are similar in PET and PUR. Dissolved blowing agent may
act as a buffer, thus maintaining the concentration of blowing agent in the foam cells.
However, high amounts of blowing agents in PUR foam lead to decreased
compression strength of the foam according to [Singh 1998].
200
Deff (10
2 -1
-15 2
300
-13
m ·s )
400
-12
-10
D eff,CO2 = 6·10 ρ - 2· ρ + 2·10
-13
-11
-14
-12
Carbon dioxide
Oxygen
Nitrogen
D eff,O2 = -1·10 ρ + 3·10
100
D eff,N2 = -2·10 ρ + 4·10
0
80
100
120
140
160
180
-3
Foam density (kg·m )
Figure 4.9 The effective diffusion coefficients of carbon dioxide, oxygen and nitrogen
in PET foams of different densities (ρ) at 60 ºC. The values of carbon dioxide at 95
kg·m-3 and 123 kg·m-3 are from a new study while the other values are from III and
IV.
41
The carbon dioxide blown PET foam of a density of 157 kg·m-3 had a degree of
crystallinity of 35 % [II]. Studies on mass transport of oxygen in PET show that the
diffusion, permeability and to some extent solubility coefficients decrease with
increasing crystallinity [Hedenqvist 1996, Lin 2002, Liu 2004b, Natu 2005, Qureshi
2000, Sekelik 1999]. Including copolymers in PET can also reduce the gas transport
in the polymer [Hibbs 2004, Polyakova 2001a, Polyakova 2001b, Sekelik 1999].
About 0.5 % talcum by mass is added to the foam formulation during PET foam
production. Sekelik et al. has showed that Ppol, Dpol and Spol of oxygen in PET with
isophthalate copolymer is reduced when the amount of talcum in the polymer is
increased [Sekelik 1999]. The mass transport properties of carbon dioxide and oxygen
in PET are impaired if the polymer is oriented, as for example is the case in drawn or
blown PET bottles [Lewis 2003, Liu 2004a, Liu 2004b, McGonigle 2001, Qureshi
2000].
Activation energies in PET and PUR foam
The activation energies of the diffusion coefficients of carbon dioxide, oxygen and
nitrogen in PUR foam calculated in accordance with the Arrhenius relationship are
higher in PUR than in PET foam (table 4.1). The diffusion coefficients at different
temperatures and the curves calculated in accordance with the Arrhenius relationship
are also shown in figure 4.10. The diffusion coefficients above the polymer glass
transition temperatures (Tg), determined to 78 ºC in the PET foam [I], were excluded
from the calculations, since the apparent activation energy normally increases above
Tg [Duda 1996]. In one study of the diffusion of carbon dioxide, oxygen and nitrogen
in PET (35-46 % crystallinity), higher activation energies were obtained above than
below Tg [Michaels 1963], similar to the PET foam presented in figure 4.10. Other
studies of diffusion characteristics of carbon dioxide and air in PET and other
polymers show similar results [Koros 1978, Yasuda 1977]. McBride et al. have
studied the diffusion of carbon dioxide, oxygen and nitrogen in polyurethane block
polymers and found discontinuities from the Arrhenius relationship around Tg
[McBride 1979]. The glass transition temperature in PUR foam used for district
heating pipes is probably above the studied interval [Bergström 1996].
4.3.5 Study of mass transport in HDPE casing materials
The diffusion coefficient of HFC-365mfc in HDPE was determined by storing a
sample of HDPE casing in an atmosphere saturated with HFC-365mfc at 23C and
atmospheric pressure [II]. A calculated curve obtained by solving Fick’s second law
for an infinite slab was fitted to the measured weight increase, which gives a polymer
diffusion coefficient of 0.23·10-13 m2·s-1. The calculated curve asymptotically
approaches a value of approximately 0.7 % by weight, and the solubility coefficient of
HFC-365mfc in HDPE was calculated to 0.81·10-3 mole·m-3·Pa-1 based on this value.
42
2
-1
Effective diffusion coefficient (m · s )
1.0E-08
PUR: carbon dioxide
PUR: oxygen
PUR: nitrogen
PUR: cyclopentane
PUR: calculated
PET: carbon dioxide
PET: oxygen
PET: nitrogen
PET: calculated
1.0E-09
1.0E-10
1.0E-11
1.0E-12
1.0E-13
Tg, PET: 78 ºC
1.0E-14
0.0027
0.0029
0.0031
0.0033
0.0035
-1
1/T (K )
Figure 4.10 Effective diffusion coefficients of cell gases in PUR foam (density 58-71
kg·m-3) and PET foam (density 157 kg·m-3) at different temperatures. The lines were
calculated assuming an Arrhenius relationship between 23 ºC and 60 ºC [I,III,IV].
The glass transition temperature (Tg) for the PET foam (78 ºC) is indicated.
The procedure for determination of the diffusion and solubility coefficients of
cyclopentane in HDPE was analogous with that of HFC-365mfc, although in this case
the sample was removed from the saturated atmosphere, and the weight decrease due
to desorption was measured [I]. The diffusion coefficient of cyclopentane in HDPE
was also shown to increase with increasing cyclopentane content in the polymer.
Therefore Deff was determined for different contents of cyclopentane. For a
cyclopentane content representative of a district heating pipe at 23 ºC, Deff was
determined to 1·10-13 m2·s-1. The solubility coefficient was determined to 2.3·10-3
mole·m-3·Pa-1 by measuring the weight increase of HDPE samples stored for about
one month in autoclaves containing a certain amount of cyclopentane.
A steady-state transmission method described in [Olsson 2001b], was used to
determine the permeabilities of oxygen, nitrogen and carbon dioxide in HDPE at
different temperatures (5-40 ºC) [I].
43
4.3.6 Mass transport in district heating pipes
In order to evaluate the diffusion characteristics of different gases in district heating
pipes insulated with PUR or PET foam, the influence of both the foam and the casing
must be considered. The mass transfer resistance is a combination of the permeability
coefficient of the gas component i in each material and the thickness of the material.
The Biot number can be used to determine in which of the materials the dominating
mass transfer resistance occurs, for a homogeneous foam slab and a polymer
membrane [Brodt 1995]. If the Biot number for a gas component (equation 4.37), is
equal to 1, it means that the resistance of that gas is the same in both materials. Bii <
1 means that the dominant resistance is found in the casing material, and Bii > 1 that
the dominant resistance is in the polymer foam.
Bii
case
Ppol
L foam
,i
foam
Lcase Peff ,i
where Bii
case
Ppol
,i
1
the Biot number for gas component i
(-)
permeability coefficient in casing material (mole·m-1·s-1·Pa-
)
permeability coefficient in the foam
Pefffoam
,i
1
(4.37)
(mole·m-1·s-1·Pa-
)
Lcase
Lfoam
casing thickness
foam thickness
(m)
(m)
Table 4.4 shows the permeability coefficients used to calculate the Biot numbers for
different material combinations. The permeability coefficients in the table refer to a
temperature of 20-25 ºC. The temperature at the surface of a district heating pipe will
be lower (about 15 ºC) and there will be a temperature gradient across the foam (about
40-100 ºC at the media pipe). For a district heating pipe in use, the Ppol values are thus
lower and Peff values higher than those in table 4.4. Higher Peff value reduces the Biot
number. A casing thickness of 3 mm and a foam thickness of 40 mm were assumed.
The main barrier to mass transport of carbon dioxide, oxygen and possibly nitrogen in
a district heating pipe insulated with PUR foam is in the HDPE casing material, while
the foam has the highest resistance to cyclopentane and HFC-365mfc. In another
study by Olsson et al., the determined permeabilities of gases in HDPE and PUR foam
from district heating pipes show that the main resistance to carbon dioxide is in the
casing, while for oxygen and nitrogen it is in the foam [Olsson 1999]. For PET foam
insulated pipes with PET casing, the main resistance to all gases is in the foam. The
values of the low density PET foam are, however uncertain. The results are dependent
on the pipe dimension. If the thickness of the insulations was doubled for all
combinations of materials, the main resistance to all gases would be in the foam for
both PET and PUR foam insulation.
Today it is common to put a diffusion barrier between the PUR foam insulation and
the LDPE casing in flexible pipes. In these pipes, fast axial transport of cell gases out
44
of the foam has been observed, which may be caused by poor fastening between the
material layers [Reidhav 2005].
The purpose of the casing material is to protect the PUR foam from water uptake and
mechanical pressure. In III, the compressive strength of PET foams of different
densities was determined. A foam with a density of 84 kg·m-3 had a compressive
strength of 580 kPa. The required value for PUR foam in district heating pipes is 300
kPa [EN253:2003]. PET foam insulated district heating pipes may not require casing
for mechanical reasons. A casing could, however retard the long-term aging of the
insulation properties. Studies show that surface modifications of PET can reduce the
permeation of gases. Plasma-ion implementation of PET films significantly reduced
the permeabilities of carbon dioxide and oxygen compared to untreated polymer
[Sakudo 2005]. By applying a silica-like layer, a low permeability of oxygen was
achieved [Zhu 2005].
Table 4.4 Permeabilities (10-16 mole·m-1·s-1·Pa-1) and calculated Biot numbers at 2025 ºC for a foam thickness of 40 mm and a casing material thickness of 3 mm.
Pipe material
PUR foam
(ρfoam = 58-71 kg·m-3)
HDPE casing
PET foam
(ρfoam = 157 kg·m-3)
PET casing
PET foam
(ρfoam = 60 kg·m-3)
PET casing
Cell gas
Carbon dioxide
Oxygen
Nitrogen
Cyclopentane
HFC-365mfc
Carbon dioxide
Oxygen
Nitrogen
Carbon dioxide
Oxygen
Nitrogen
Ppol casing
8.6 a)
1.9 a)
0.65 a)
23 [I]
0.19 [II]
1.1 b)
0.28 b)
0.052 b)
1.1 b)
0.28 b)
0.052 b)
Peff foam
290 c)
49 c)
10 c)
0.5 d)
0.6 [II]
7.2 e)
0.11 e)
0.014 e)
8.6 f)
0.15 f)
0.001 f)
Biot number
0.4
0.5
0.9
600
4
2
30
50
1.7
25
69
a)
[Olsson 2001b] and [I]
Ppol calculated from equation 4.18 with Dpol and Spol from [Lewis 2003]
c)
[Olsson 1999]
d)
Peff calculated from equation 4.35, Deff from [I], Spol from [Holmgren 2004], fg= 0.95
e)
Peff calculated from equation 4.35, Deff from [IV], Spol from [Lewis 2003], fg= 0.88
f)
Peff calculated from equation 4.35, Deff calculated with equations in figure 4.9 and activation energies
from [IV], Spol from [Lewis 2003], fg= 0.96
b)
45
46
5 LIFE CYCLE PERSPECTIVE ON DISTRICT
HEAT DISTRIBUTION
_____________________________________________________________________
5.1 District heat distribution from cradle to grave
The life cycle of a district heating distribution system from the extraction of raw
materials from the nature (cradle) to the waste treatment at the end of the product
lifecycle (grave) can be divided into four main phases (figure 1.1): production of
district heating pipes, construction of district heating pipe network, distribution of
heat, and waste management of pipes taken out of use (post-use handling). This
division was used in V, where PET foam and PUR foam insulated pipes were
compared by means of life cycle assessment (LCA) and in previous studies on district
heat distribution [Fröling 2002a, Fröling 2004a, Fröling 2004b, Persson 2005c].
Waste management was not considered in any of these studies, since to date, pipes
have not been taken out of use in a large scale.
Th LCA methodology is outlined in the ISO 14040 international standard. The
objective of LCA is to quantify the environmental impacts of emissions, resource use
and waste from all processes and transports involved during the whole life cycle of a
product or service on ecological systems and human health [Baumann 2004,
Hauschild 1998, Nord 1995]. The identified emissions are classified and characterised
into different impact categories such as global warming potential (GWP), photo
oxidant creation potential (POCP), acidification potential (AP) and depletion of finite
resources (RD) based on scientific criteria. Sometimes different weighting methods,
e.g. EcoIndicator99 or Ecoscarcity, which summarises the different impacts into one
figure, are used. This step is not always performed, as it is rather subjective.
LCA can be used to identify the processes, components and systems of a product or
service that are the major contributors to environmental impacts or resource depletion.
Different products/processes can be compared in order to choose the best alternative.
LCA can provide guidance for long-term strategic planning and policy decisions both
in the private and public sector. It should be noted that LCA only takes technical
aspects into account and does not include studies on economic and social effects. An
LCA study always involves simplifications and assumptions.
47
5.2 Comparison of insulation materials in district heating pipes
5.2.1 System description and inventory
An LCA of district heating pipes with different insulation and casing materials was
performed [V]. The different types of pipes included in the study are shown in table
5.1. The objective was to investigate whether PET foam insulated district heating
pipes have the potential to compete with traditional cyclopentane blown PUR foam
insulated pipes from an environmental perspective. The study of PET foam insulated
pipes is hypothetical, since it is not yet possible to produce these pipes. The high
density carbon dioxide blown PET foam was considered due to the fact that its longterm thermal performance has been extensively investigated. Low density foam was
included, since it is a possible development alternative. Foam made from recycled
PET represents an interesting possibility for the future. A comparison was made with
pipes insulated with carbon dioxide blown PUR foam, despite the fact that this is not
commonly used today. The study is also included pipes insulated with HFC-365mfc
blown PUR foam.
Table 5.1 Types of district heating pipes included in the LCA study.
Pipe alternative Foam type
Casing material
PUR (cp)
HDPE
PUR (365)
PUR (CO2)
PET (HD, vir)
PET (HD, rec)
PET (LD, vir)
PET (LD, rec)
Foam density Blowing agent
(kg·m-3)
PUR
86
Cyclopentane/
carbon dioxide
PUR
86
HFC-365mfc/
carbon dioxide
PUR
77
Carbon dioxide
Virgin PET
157
Carbon dioxide
Recycled PET 157
Carbon dioxide
Virgin PET
86
Carbon dioxide
Recycled PET 86
Carbon dioxide
HDPE
HDPE
Virgin PET
Recycled PET
Virgin PET
Recycled PET
The functional unit was 1 meter of pipe construction, which includes 1 meter of flow
pipe and 1 meter of return pipe over a period of 30 years. Pipes of the DN100/225
dimension were studied (steel tube outer diameter/thickness: 114/3.6 mm, casing pipe
outer diameter/thickness: 225/3.4). Three impact categories were considered: GWP
(kg CO2-equivalents), AP (kg SO2-equivalents) and RD (kg·year-1). Pipe production,
network construction and network use were included in the study.
Pipe production inventory data were taken from a previous study on PUR foam
insulated district heating pipes [Fröling 2004a]. The production was assumed to be the
same for pipes insulated with PET foam, with the exception of the PET foam
production itself, which was approximated with foam board production [V].
Production of virgin PET granules for foam and casing pipe was taken from an APME
report [Bousted 2002] while the PET recycling process was approximated with a
study on polyethylene packages recycling in Sweden [Carlsson 2002]. Only the main
materials (steel pipe, insulating foam, pipe casing and copper wire) and energy use
were included in the study of the pipe production, since a previous study of PUR foam
48
insulated pipes shows that they contribute with 90 % or more to the environmental
impacts. A study on PUR foam boards blown with HFC-365mfc showed that, during
foam manufacture, the contribution of the blowing agent is higher in terms of GWP
and similar in terms of AP when compared to n-pentane blown boards [Krähling
2000]. The GWP per mass of HFC-134a was about the same as cyclopentane in
another LCA study [Katz 2003]. Due to lack of inventory data for production HFC365mfc, these data were, however, assumed to be the same as those used in this study
for cyclopentane. Network construction data for urban and green areas were taken
from [Fröling 2004b] and assumed to be the same for all pipe alternatives.
Heat generated by the average Swedish district heat mix in the year 2000 and use of
natural gas combustion (heat only boilers) were considered during the use phase. The
Swedish district heat mix consists of 32 % renewable fuel, 29 % waste incineration,
15 % heat pumps, 6 % oil, 5 % peat, 5 % natural gas, 4 % coal and 4 % electricity
[Swe DH 2005a]. Natural gas combustion was chosen because it was the major
primary energy source for district heat in several European countries in 2001
[Euroheat & Power 2003]. The average thermal conductivities of the foams and the
total heat losses from the DH networks over the 30 year period were calculated
according to a method described in [Persson 2005a]. The following temperatures were
used: 80 ºC for the media flow pipe, 40 ºC for the media return pipe and 15 ºC in the
soil surrounding the casing pipe (mean annual value). Explicit finite differences were
used for the gas transport through the foam, and the casing was considered as surface
resistance. A stationary temperature profile was used for each time step in which the
diffusion was calculated, The initial partial pressures of the cell gases for each type of
foam used in the pipes are presented in table 5.2.
Table 5.2. Initial partial pressures of cell gases at 20-25 ºC of the studied foam types
(cp = cyclopentane, 365 = HFC-365mfc).
Foam quality
PUR foam (25 ºC)
[Swe DH 2004]
PUR foam (25 ºC)
[Marrucho 2002, Swe
DH 2004]
PUR foam (20 ºC)
[Svanström 1999]
PET foam (20 ºC)
[IV]
*
#
cp/carbon
dioxide
blown
365/carbon
dioxide
blown
Carbon
dioxide
blown
Carbon
dioxide
blown#
cp or
365
42*
57*
Initial partial pressures (kPa)
Carbon
Oxygen Nitrogen
dioxide
67
0.4
0.7
52
0.4
0.7
122
0.2
0.7
80
2.5
2.5
20 % by mass of the total cyclopentane or HFC-365mfc content (gas + liquid) in the cells as liquid.
The same initial partial pressures are assumed for all PET foam types.
49
The transport coefficients used to calculate the change in the cell gas mixture over
time in the foam cells are presented in table 5.3. For all foams, λgas was calculated
using Wassiljeva’s equation with modification by Mason and Saxena [Reid 1977]. For
the PUR foams, and the low density PET foam, λpol was calculated by means of a
matrix conduction model [Nielsen 1998] and λrad according to the Rosseland equation
[Siegel 2001]. In the case of high density PET foam, an equation taken from [IV] was
used.
Table 5.3. Coefficients used to calculate cell gas transport in the insulation and
casing materials based on Arrhenius relationships. Two temperature intervals are
given for PET because of the change in diffusion characteristics at or close to the
glass transition temperature [IV]. (cp = cyclopentane)
PUR foam1
D0 (10-6 m2·s-1)
ED (103 J·mole-1)
PET foam2
D0
HD foam (10-9 m2·s-1)
LD foam (10-8 m2·s-1)
ED (103 J·mole-1)
PE3
Ppol
(10-16 mole·m-1·s-1·Pa-1)
EP (103 J·mole-1)
PET4
Ppol
(10-16 mole·m-1·s-1·Pa-1)
EP (103 J·mole-1)
Temp.
(ºC)
cp
HFC365
Carbon
dioxide Oxyg.
Nitrog.
15-80
15-80
0.170
35.3
0.0444
32
480
39.9
341
41.7
10300
54.3
231
0.140
52.8
0.324
26.7
63.6
9.83
0.103
5.62
0.558
21.8
66.4
161
0.881
50.9
2.83
34.1
77.1
15-60
60-80
15-60
60-80
15-60
60-80
23
23.0
0.19
8.60
1.90
0.650
15-60
9.94
9.94
27.0
34.8
39.2
25
1.23
0.311
0.0579
15-60
33.6
33.6
33.6
1)
HFC-365mfc: Deff at room temperature is from [II] ED is calculated from [Zipfel 1998].
LD foam: the density dependency of the diffusion coefficients was calculated according to the
equations in figure 4.9. ED was assumed to be the same as for HD foam.
3)
Calculated from I, II and [Brodt 1995]. EP of HFC-365mfc was approximated.
4)
Ppol is based on diffusion and solubility coefficients from [Lewis 2003]. EP of all gases were
approximated based on a value for oxygen calculated from [Liu 2004a].
2)
5.2.2 LCA results
The characterised environmental impacts for all the pipe systems are reported in table
5.4. The dominating environmental impact during the studied parts of the life cycle is
caused by the heat losses for all studied impact categories. The average heat losses
during 30 years of use are shown in figure 5.1. PET foam insulated pipes have the
same environmental impact irrespective of whether virgin or recycled material is
used. The performance of pipes insulated with high-density PET is about the same as
those insulated with carbon dioxide blown PUR foam. If the foam density is lowered,
50
PET foam can compete with cyclopentane blown PUR foam. These results illustrate
the fact that gases generally diffuse more slowly in PET foam compared to PUR foam
[III, IV]. Carbon dioxide is the fastest diffusing of all the blowing agents used today
in insulating foam [I-IV]. It is likely that other gases can be utilized in PET foam in
the future, thus further reducing the heat losses of PET foam insulated pipes.
Compared to cyclopentane blown foam pipe insulation, HFC-365mfc blown PUR
foam may perform better, mainly due to the higher vapour pressure of HFC-365mfc
which allows more gas in the foam cells.
Table 5.4. Characterised environmental impacts of a 1 m DN100/225 pipe network
(1m flow pipe and 1 m return pipe) over 30 years with regard to global warming
potential (GWP, kg CO2-equivalents), acidification potential (AP, kg SO2-equivalents)
and resource depletion (RD, kg·year-1).
Pipe production
Pipe alternative
PUR (cp)
PUR (365)
PUR (CO2)
PET (HD, vir)
PET (HD, rec)
PET (LD, vir)
PET (LD, rec)
*
GWP
63
63
62
81
41
67
41
AP
0.31
0.21
0.30
0.52
0.11
0.38
0.10
RD
0.65
0.65
0.64
0.69
0.32
0.56
0.32
Network construction*
(green area/urban area)
GWP
22/39
22/39
22/39
22/39
22/39
22/39
22/39
AP
0.20/0.37
0.20/0.37
0.20/0.37
0.20/0.37
0.20/0.37
0.20/0.37
0.20/0.37
RD
0.20/0.34
0.20/0.34
0.20/0.34
0.20/0.34
0.20/0.34
0.20/0.34
0.20/0.34
Network use, 30 years
(Swedish fuel mix/natural
gas)
GWP
AP
RD
500/1500 2.7/1.1 1.7/8.4
450/1400 2.4/1.0 1.6/7.7
620/1900 3.3/1.3 2.2/10.6
650/2000 3.5/1.4 2.3/11.0
650/2000 3.5/1.4 2.3/11.0
500/1500 2.7/1.1 1.8/8.5
500/1500 2.7/1.1 1.8/8.5
PET (HD)
PET (LD)
Values from [Fröling 2004b].
Heat losses
Normalised values
1.0
0.8
0.6
0.4
0.2
0.0
PUR (CP)
PUR (365)
PUR (CO2)
Figure 5.1. Heat losses of a 1 m DN100/225 pipe network (1m flow pipe and 1 m
return pipe) over 30 years: Normalised values, PET(HD) = 1. The results are similar
for both low and high-density PET foam, regardless of whether recycled material is
used in the production.
51
Figure 5.2 a-c shows the environmental impacts characterised as GWP (a), AP (b) and
RD (c) during the use phase for the Swedish heat mix and natural gas boilers as heat
source. Due to the high amount of renewable fuels used for Swedish district heat
production (32 %), the carbon dioxide emissions are about one third of those of the
natural gas boiler system. The acidifying effect is, however higher in the Swedish
case, since the heat mix contains small proportions of coal and peat (4 and 5 %
respectively). A system based exclusively on fossil fuels result in a resource depletion
that is almost five times higher than the Swedish heat mix.
The high global warming potential of HFC-365mfc makes its use questionable. If the
total amount of HFC-365mfc (0.22 kg) in the PUR foam of the studied system (2 m
DN100/225 pipes) were to be emitted to the atmosphere after 30 years, it would result
in 220 kg CO2-equivalents (GWP100years = 1000) [IPCC 2001b, Naik 2000, World
Meteorological Org 2002]. In the system heated with the Swedish fuel mix, foam
blown with HFC-365mfc makes a 50 kg lower contribution to global warming in
terms of CO2-equivalents compared to cyclopentane blown foam. In the case of the
system heated with the natural gas boiler, the emissions of CO2-equivalents are 100
kg lower for the HFC-365mfc blown foam. With regard to the global warming and in
comparison with cyclopentane blown PUR foam, this study cannot justify the use of
HFC-365mfc in PUR foam insulated district heating pipes.
Pipe production and network construction constitute a small part of the environmental
effects of the studied life cycle. Their relative contribution increases with higher
proportions of renewable resources in the heat mix. Figure 5.3 shows the normalised
values of the environmental impacts during production of the pipes studied. The
difference between the pipes is mainly due to the type and amount of insulation
material used, since the impact from the steel pipe, copper wire, casing material,
blowing agent and energy used for pipe assembly are more or less identical. The high
density PET foam results in the highest impacts, while low-density PET foam
performs in a similar fashion to PUR foam. Utilisation of recycled PET has the
potential to significantly reduce the impact compared to PUR foam.
Network construction is assumed to be similar for all pipe systems, although PET pipe
installation techniques could differ. A large part of the environmental impacts are
accounted for by the excavation work (up to 40 %) [Fröling 2004b]. In urban areas,
deeper trenches and asphalt restoration are necessary, resulting in higher impacts
compared to green areas. Research is performed in order to determine the minimum
depth for pipe trenches without jeopardising the strength of roads and pipes [Nilsson
2005].
52
a) GWP - Network use
Swedish heat mix
Natural gas
kg CO 2 -equivalents
2000
1500
1000
500
0
PUR (CP)
PUR (365) PUR (CO2)
PET (HD)
PET (LD)
b) AP - Network use
Swedish heat mix
kg SO2-equivalents
4.0
Natural gas
3.0
2.0
1.0
0.0
PUR (CP)
PUR (365)
PUR (CO2)
PET (HD)
PET (LD)
c) RD - Network use
Swedish heat mix
12.0
Natural gas
kg·year
-1
10.0
8.0
6.0
4.0
2.0
0.0
PUR (CP)
PUR (365) PUR (CO2)
PET (HD)
PET (LD)
Figure 5.2. Characterised environmental impacts of a 1 m DN100/225 pipe network
(1m flow pipe and 1 m return pipe) over a 30-year period with regard to a) global
warming potential (GWP), b) acidification potential (AP) and c) resource depletion
(RD).
53
Pipe production
Global warming
Acidification
Resource depletion
1
Normalised values
0.8
0.6
0.4
0.2
0
PUR
PET (HD, vir) PET (HD, rec) PET (LD, vir) PET (LD, rec)
Figure 5.3. Characterised environmental impacts for pipe production: normalised
values, PET(HD) = 1, for global warming potential, acidification potential, and
resource depletion. The PUR foam insulated pipes gives a similar result for all
studied blowing agents.
It has been shown that the total environmental impact from the first three phases of
the life cycle of district heating pipes is very much dependent on how the heat is
produced. In this thesis, pipes of the DN100/225 dimension were studied, and
previous research shows similar results for other pipe dimensions [Fröling 2004a,
Fröling 2002b, Fröling 2004b, Persson 2005c]. The relative contribution of each
phase varies according to the dimension. Large pipes have a higher contribution
related to the production while the use phase results in a lower one. Twin pipe
systems generally gives rise to lower contributions related to pipe production (less
material use), network construction (less excavation) and heat losses compared to
single pipe systems. The results are, however dependent on the amount of insulation
material used in the respective steel pipe dimension.
In one study different space heating alternatives (district heating, heat pump and
pellet, oil and electricity furnaces) were compared [Bengtsson 2005]. The results were
dependent on the heat mix in the district heating network and the delivered effect per
metre of pipe, i.e. the population density of the residential area. Use of large amounts
of bio-fuels makes district heating a good alternative in terms of GWP and RD,
especially in densely populated areas. Only pellet furnaces and heat pumps (using the
Swedish electricity mix) result in lower environmental impacts in these categories.
Compared to electricity furnaces (Swedish electricity mix), district heating with
natural gas boilers will result in lower impacts. In low density areas, oil furnaces may
also perform better than district heating with natural gas boilers.
54
6 SUMMARY OF FINDINGS AND FUTURE
RESEARCH
_____________________________________________________________________
6.1 Comparison of cyclopentane and HFC-365mfc
Based on the experimentally determined coefficients and literature values it can be
concluded that the diffusion characteristics of cyclopentane and HFC-365mfc in PUR
foam are similar [I,II]. Additional studies of HFC-365mfc diffusion characteristics at
high temperatures are recommended.
The LCA study reveals that, when the first three phases of the life cycle (pipe
production, network construction and network use) are considered, pipe insulation
consisting of HFC-365mfc blown PUR foam may reduce environmental impacts from
global warming (GWP), acidification (AP) and depletion of resources (RD) compared
to cyclopentane blown foam. This is mainly due to the higher vapor pressure of HFC365mfc, which allows more insulating gas in the foam cells [Chemnetbase 2005,
Zipfel 2002]. In comparison with cyclopentane, HFC-365mfc blown PUR foam as
district heating pipe insulation only can not be justified, on account of the high
contribution to global warming that would occur if all the HFC-365mfc in the pipes
were to be released into the atmosphere.
6.2 Comparison of PET and PUR foam
The determined effective diffusion coefficients of carbon dioxide, oxygen and
nitrogen are lower in PET foam than in PUR foam at 23-90 ºC [IV]. According to the
the Arrhenius relationship, the activation energies of these gases are lower in PET
foam compared to PUR foam [I, IV]. The determined solubility coefficients of
blowing agents show a tendency towards lower values in PET than in PUR foam [IIII]. These experimental results gives that the decrease of insulating capacity of PET
foam over time compared to PUR foam, due to the diffusion of cell gases, is slower.
The contribution to foam thermal conductivity due to radiation in the cells and
conduction in the polymer matrix in the type of PET foam available today is higher
than in the PUR foam used for district heating pipes [III, IV]. If PET foam with a
55
lower density and smaller cells could be developed, it might be possible to achieve the
same values as those of for PUR foam.
The environmental performance (in terms of GWP, AP, RD) of pipes insulated with
high-density PET foam is similar to pipes insulated with carbon dioxide blown PUR
foam [V]. PET foam with a lower density has been shown to be a possible competitor
to cyclopentane blown PUR foam for pipe insulation. Recycled PET has the potential
to significantly reduce the impacts caused by pipe production compared to PUR foam.
A future trend towards increased recycling of PET can be expected in Europe,
possibly as a result of increased PET consumption and current regulations (the
Packaging and Packaging waste directive). Recycled PET has also the advantage of a
lower price than virgin PET and PUR. Problems due to degradation and
contamination of other plastics can be solved by means of chemical modifications
[Japon 2000, Smith 1990, Xhanthos 2000].
Due to its high compressive strength, pipes insulated PET may not require a casing
[III]. Less different types of material would simplify the waste treatment of pipes
taken out of use.
The literature reports that PET is subject to chemical degradation due to hydrolysis
and becomes brittle when exposed to water at high temperatures [Foulc 2005, Oreski
2005]. The extent of these effects on foam used in district heating pipes and possible
solutions to the problem should be investigated.
6.2 Other findings and comments
Differences between diffusion theories and the result of long-term experiments were
noted in the case of HFC-365mfc. Such differences have been reported in the
literature for heavy and slow diffusing blowing agents with relatively high polymer
solubility coefficients [Duda 1996, Hong 2001]. Further studies of possible
concentration dependencies are necessary in order to understand and simulate these
mechanisms.
When calculating the long-term thermal performance of insulating foams, accurate
cell gas thermal conductivity values are important. In the literature, gas thermal
conductivity values for blowing agents are often inconsistent. The literature also
makes it clear that the thermal conductivity of some gas mixtures is difficult to predict
with existing models [Marrucho 2005, Merten 1997]. Further studies of the thermal
conductivity of blowing agents and mixtures of gases would be a desirable
contribution to this field.
56
7 ACKNOWLEDGEMENTS
_____________________________________________________________________
There are many who, in various ways, have contributed to the realisation of this
work:
The financial support from “Svensk Fjärrvärme” (the Swedish District Heating
Association) and “Energimyndigheten” (the Swedish Energy Agency) is greatly
appreciated, as is as the guidance obtained as a result of the meetings with the
reference group.
It has been wonderful to be a part of the successful and creative research team led by
my vice supervisor Prof. Ulf Jarfelt (Building Technology) and my supervisor Ass.
Prof. Olle Ramnäs (Chemical Environmental Science). Thanks to everybody who
participated in the group during my time as a PhD-student: Dr. Gunnar Bergström, Dr.
Morgan Fröling, Dr. Maria E. Olsson, Lic. Eng. Camilla Persson and Lic. Eng.
Charlotte Reidhav.
Assistance from industry was necessary to complete the work. Göran Johansson at
Powerpipe Systems AB, Alberto Bruschieri and Renato Crana at BC Foam, Tor-Ivar
Pettersen and Stein Dietrichson at Fagerdala Hicore and Tonino Severini and Emilio
Villa at M&G Polymers, thank you for your cooperation, your supporting in providing
materials for experiments and for sharing your knowledge.
Special thanks to Prof. Göran Petersson, Ass. Prof. Magdalena Svanström and Lic.
Eng. Maria Olsson at Chemical Environmental Science, who were always ready to
give advice and happy to cooperate in all matters pertaining to our work and common
goals: general environmental issues, teaching and scientific work.
I would also like to thank everybody who has inspired, encouraged and guided me in
the course of my work: my colleagues at Chalmers, my students, all my friends and
family.
57
58
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