Robust Phenomenological Model for Simulation of Transient Wax Gelation in Submarine Pipelines
Authors: Villazon Guillermo German Michel , Civan Faruk 
Published: May 2011

Abstract
A two-phase modeling approach to wax gelation in shut-in submarine pipelines is presented and validated with experimental data. Accurate correlation of pressure dependence of the Wax Appearance Temperature is developed. Relevant mechanisms of wax gelation without forced convection are described in detail. Initial temperature profile of oil flowing through a pipeline under steady-state conditions is estimated based on an analytical solution obtained for turbulent flow of a single-phase system undergoing heat transfer. The natural convection phenomenon is represented by assigning a proper value to thermal conductivity of the liquid phase. Phenomenological models for transient cooling in a circular pipe cross-section and along vertical pipelines are derived. Typical simulation results indicate that prevailing pressure conditions of vertical submarine pipelines greatly affects the wax precipitation phenomenon and the relaxation of wax precipitation can be avoided by adequate insulation.

Introduction
A proper model for describing the waxy-oil gelation can be instrumental for effective management of the shut-in submarine pipelines because wax gelation can affect the restarting conditions significantly (Ekweribe et al, 2009).
Shut-in pipelines are often scheduled for maintenance or emergency reasons. Prolonged exposure to cold surroundings may result in complete loss of production facility (Gluyas and Underhill, 2003). Therefore, appropriate modeling of wax precipitation and gelation is essential for ensuring flow assurance in submarine pipelines subject to cold sea-water temperatures. Wax precipitation and gelation is mainly driven by the thermodynamics and phase behavior induced by heat transfer occurring between the pipeline fluid and the surrounding sea-water environment. Cooling of oil due to heat loss causes the separation of heavy components, wax in particular, in the form of a crystalline structure saturated with oil.
Precipitates of wax crystals may aggregate and interlock, and thus the wax/oil mixture behaves as a highly viscous gel. A solid-like state is attained when the waxy-oil is allowed to cool down over prolonged periods of time by heat loss towards the sea-water environment. Wax deposition reduces the cross-sectional area of pipeline available for flow when production is resumed or even worse if the deposited wax has effectively plugged the pipe, thus choking the pipeline to cease the flow completely. Obviously, coolest sections of pipes have the greatest potential of plugging.
A submarine pipeline that has been shut-in is susceptible to complete gelation because the sea-water temperature is generally below the phase-transition temperature. A shut-in submarine pipe is a system left without the benefit of the heat supplied by the oil produced from a reservoir. Even though proper insulation may deter wax precipitation and gelation for some time, extended exposure to the low sea-water temperature conditions without such heating source may eventually induce complete wax precipitation and subsequent gelation problems. The heat loss towards the surroundings is determined by the difference in temperature between the sea-water and the pipe wall. This outward heat flow occurring at the pipe wall sets the wall temperature to be lowest in the radial direction over the cross-sectional area of the pipe. Consequently, the first wax crystals precipitate at the pipe-wall around its perimeter over any given cross-sectional area. This induces a layered aggregation of wax crystals and an inward laminar growth of the gelled wax region.
The local heat capacity and thermal conductivity vary as more wax separates from the liquid oil near the wall. The wax crystals form a resistance to heat transfer once the local temperature drops to below the WAT. Consequently, the greater resistance near the pipe-wall acts as insulation for the liquid in the pipe center which is relatively warmer. Moreover, the heat loss outward to the surroundings induces more separation of wax that provides greater insulation to the center region and the crystalline growth starts to build up. This leads to a higher concentration of wax observed near the pipe-wall.