Transient Wax Gel Formation Model for Shut-In Subsea Pipelines

Physics of wax gel formation during shut-in is analyzed and described over a cross-section of a typical subsea pipeline. Two regions are identified during this process: the liquid and gel regions. Phase transition is assumed to occur at the liquid-gel interface. Unsteady-state heat and mass transfer models are proposed for each region. Two diffusion streams are evaluated: the dissolved wax molecules moving from the pipe center towards the wall due to temperature gradient and subsequently concentration gradient and the wax molecules diffusing from the liquid-gel interface into the gel deposit. This model is essentially the modification of the model given by Bhat et al [1] which considered transient heat transfer and neglected mass transfer of wax molecules through the gel deposit and the model by Singh et al [2] which considered transient mass transfer of molecules with carbon numbers higher than the critical carbon number (CCN) necessary for wax diffusion into gel deposit but did not consider transient heat transfer effects during the cooling process. This paper presents a transient-state formulation circumventing the limitations of these previous models and better represents the true cooling and gelation process occurring in a shut-in subsea pipeline filled with waxy crude.