The development of a wax layer on the interior wall of a circular pipe transporting heated oil: the effects of temperature-dependent wax conductivity

Sophie Mason, John Meyer, David Needham

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Abstract

In this paper we develop and significantly extend the thermal phase change model, introduced in Needham et al. (QJMAM 67:93–125, 2014), describing the process of paraffinic wax layer formation on the interior wall of a circular pipe transporting heated oil, when subject to external cooling. In particular we allow for the natural dependence of the solidifying paraffinic wax conductivity on local temperature. We are able to develop a complete theory, and provide efficient numerical computations, for this extended model. Comparison with recent experimental observations is made, and this, together with recent reviews of the physical mechanisms associated with wax layer formation, provide significant support for the thermal model considered here.
Original languageEnglish
Article number7
Number of pages30
JournalJournal of Engineering Mathematics
Volume131
DOIs
Publication statusPublished - 21 Oct 2021

Bibliographical note

Funding Information:
The authors would like to thank Ruben Schulkes (Statoil Petroleum, AS) for his helpful comments. We also thank the referees for very useful comments.

Publisher Copyright:
© 2021, The Author(s).

Keywords

  • Asymptotic limit
  • Generalised Stefan problem
  • Heated oil pipeline
  • Quasi-linear parabolic PDE
  • Wax layers

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering

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