Wax Deposition Correlation-Application in Multiphase Wax Deposition Models
Authors: Leontaritis Kosta J. , Geroulis Efstratios 
Published: May 2011

Abstract
The two most dominant factors in wax deposition are:Brownian diffusion of wax forming molecules toward and adhesion of wax crystals at the wall. The rate of adhesion is governed by the temperature difference between wall and fluid and the wax crystal formation rate.Shearing of the wax molecules and crystals due to the hydrodynamic drag of the flowing fluid. The rate of shearing and shear force depends largely on the flow rate, viscosity, and other system parameters.
As the deposit thickness increases so is the shear rate due to the decrease in the flow area and increase in flow velocity. This increase in shear rate causes an increase in the shear stress on wax molecules and formed wax crystals which acts to diminish the wax deposition rate. This diminishing effect of shear rate on wax deposition rate has been empirically correlated with Shear Stress, t, from actual wax deposition field data and lab dynamic testing data. The correlation is being used to calculate wax deposition in conduits using mainly but not exclusively cold plate data. The overall approach consists of measuring the amount of wax deposited on a cold plate under static conditions to capture accurately the wax molecule diffusion behavior. This along with other data is used to estimate the initial 24-hour wax deposition rate in a pipeline carrying the tested oil using the new correlation that is presented in this paper. A compositional multiphase wax deposition simulator is then utilized to predict the wax deposition in a pipeline carrying the tested live or dead oil, after it has been fine-tuned to the 24-hour wax deposition rate calculated with the correlation.

Background
In a conduit, as the flowing oil is cooling down at some point its temperature arrives at the onset of wax crystallization. At this point in the pipe, where the first wax crystalls appear, the temperature difference between the conduit wall and the fluid is at its highest. Hence, the wax deposition tendency of the fluid, from the stand point of temperature difference effect, is at its highest. In general, wax deposition in tubings, flowlines, and pipelines occurs near the point where waxes begin to precipitate. The deposition rate begins then to taper off to near zero as the oil temperature approaches the conduit wall temperature. The experimental work of many investigators including that of Bott and Gudmundsson, 1977, demonstrated convincingly the above phenomena.
The temperature difference between the fluid and the wall has a marked influence on the amount of wax deposited. However, as wax begins to deposit it provides an effective insulation between the pipe wall and the fluid. Its surface temperature is higher than that of the wall. The wettability of the wall has also a significant effect on the amount of wax deposited and the phenomenon of sloughing. The more water-wet the wall is (low contact angle) the lower the deposition rate, and the more oil-wet (high contact angle) the wall is the higher the deposition rate. If water is added to the crude oil flowing within a conduit with a water-wet wall, the wax deposition rate and amount will decrease because the water will adsorb onto the wall and prevent the wax from coming into contact with the wall. The velocity of the produced fluid affects the amount of wax that stays attached on the wall. Sutton and Roberts, 1967, reported that the precipitation of wax is sometimes irreversible in that the wax, once removed from solution, is very difficult to re-dissolve in the same fluid, even after original formation temperatures are restored.