Predicting the Long-Term Insulation Performance of District Heating Pipes
Doktorsavhandling, 2015
The aim of the studies that comprise this thesis was to predict the heat loss over time
from a range of district heating pipes insulated with closed-cells foam. The thermal
conductivity of the foam changes over time when it is not diffusion-tight encapsulated
against the environment, as diffusion alters the cell gas composition until it reaches
equilibrium with the surrounding air. Over the first thirty years of use the insulation
capacity of a straight pipe of medium size insulated with polyurethane foam decreases
by about 10%. The insulating gases cyclopentane and carbon dioxide initially present
in the foam cells diffuse out of the foam over time, while nitrogen and oxygen from
the air diffuse into it. Complete ageing increases the thermal conductivity of the
insulation by about 10 mW·m-1·K-1, but it is a slow process that takes several years.
Equilibrium is not even reached after 100 years. In this work models have been
derived that can be used to predict the long-term heat flow from the pipes and
investigate the influence of factors that have an impact.
Finite difference models for the pipes alone are presented, which consider the
variation of the cell gas composition over the foam cross section. All gases are
considered in the gas phase. But cyclopentane is also considered in dissolved state, as
well as potentially in liquid state depending on the amount and the temperature
present. In order to determine the solubility of cyclopentane in the polyurethane
matrix of the foam measurements were performed. The solubility was found to
decrease with temperature. About 50% of the cyclopentane was dissolved at room
temperature, while only about 35% was dissolved at 50ᵒC. There is a weak coupling
between the heat conduction (i.e. temperature) and the gas diffusion (i.e. cell gas
content) due to the fact that the thermal conductivity is dependent both on the
temperature and the cell gas content, which has been taken into consideration. Both
single and twin pipe geometry have been studied. Complex mathematics in the form
of a coordinate transformation is needed to perform the predictions for twin pipe
geometry.
To model installed pipes, a stationary model for annularly insulated pipes in the
ground has been developed, which also involves complicated mathematics. The
temperature is represented by series expansions; in each region with differing thermal
conductivity a separate expansion is used. The expansions are matched to each other
at the region boundaries and chosen to fulfil the boundary conditions.
Finally, the measured cell gas status of aged pipes and the results obtained by
modelling based on assumptions of their initial status and ageing conditions have been
compared. It was found that the actual aged pipes contained less oxygen and more
carbon dioxide than predicted. This is probably due to oxidation. It is interesting to
note that not only the oxygen but also the carbon dioxide content is influenced by
oxidation. By consuming oxygen and producing carbon dioxide the oxidation will
slow down the decrease of the insulation performance.
heat conduction
polyurethane foam
insulation capacity
diffusion
thermal conductivity
cyclopentane
solubility coefficient
long-term performance