2D Unsteady heat transfer analysis of buried pipelines: the start-up case

The two-dimensional heat transfer from offshore completely buried pipelines is studied with reference to transient working conditions. In particular, the start-up case is considered, i.e. the case of a pipeline which, starting from an initial temperature equal to the initially uniform temperature Te of the soil, reaches the steady temperature Ta. Two different start-up cases are investigated: the step-rising case and the smooth-rising case; in the latter, the steady temperature Ta is reached in a finite time t0. The temperature inside the duct is considered as uniform at every instant, so that only the external heat transfer is taken into account. Moreover, the temperature of the seabed is assumed uniform, with value Te. The energy balance equation is written in a dimensionless form and is solved numerically by means of a finite element method. The dimensionless temperature field in the soil and the thermal power exchanged per unit length by the pipeline with the soil are determined. Different meshes and time resolutions are tested in order to check the reliability of the numerical solution. Moreover, different thermal diffusivities of the soil, different values of the duct radius as well as different burying depths are considered. A comparison with a simpler one-dimensional model of the phenomenon (“extra-soil layer” approximation) is performed.