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 toward 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.