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.
Highlights
In oil field operation, it is generally required that oil is transported in long sea bed pipelines
We have developed and analysed in detail the simple thermal model for the development of a wax layer on the interior wall of a circular pipe transporting heated oil containing dissolved paraffinic wax, which was introduced in [1]
This approach is gaining considerable traction compared to the traditional mechanical and material diffusion theories; it is able to describe features associated with wax layer formation which have been absent from, or even contrary to, the outcomes from the mechanical and material diffusion theories
Summary
It is generally required that oil is transported in long sea bed pipelines. The extensive review by Mehrotra et al [9] has given a thorough consideration of experimental evidence, which provides significant and substantial support for the thermal phase change mechanism introduced in [1], as the principal and key mechanism in the process of wax deposition on the interior wall of pipes transporting heated oil. It indicates that we may expect wax layer local conductivity to decrease as local temperature decreases, with as much as a 30% variation within a given wax layer With this inclusion in the mathematical model developed in [1], the significant change is that the associated free boundary problem [IBVP] becomes non-linear.
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