Predicting the Long-Term Insulation Performance of District Heating Pipes

Doctoral thesis, 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.