1. 1 Flow Assurance Multiphase Simulations with Wax Deposition FLOWModel R

2. 2 Wax Deposition The two most dominant factors in wax deposition are: Diffusion of wax molecules toward, and crystallization and adhesion at the wall. The diffusion rate is dependent on the wax crystal formation rate (WCFR) at the wall and on the bulk wax concentration. Adhesion is governed by the temperature difference between wall and fluid. Erosion and shearing of the wax deposit due to the hydrodynamic drag of the flowing fluid. The rate of deposit shearing and shear force depends largely on the flow rate, viscosity, and other system parameters.

3. 3 Viscous oils have lower wax deposition rates. Wax Crystal Shear & Adhesion

4. Wax Deposition In Liquid-Filled Conduit 4

5. 5 Wax Deposition

6. 6 Thermal, Mechanical, and Mass Equilibrium

7. 7 As the fluid is being cooled down, at some point in the pipe, its temperature arrives at its onset of wax crystallization and wax crystals begin to form. This occurs in the Slide 4 at segment 2. At this point the temperature difference between the fluid and the wall is at its highest. As a result, the attraction of the wax crystals toward the wall is at its highest. As the wax crystal and molecule concentration of the fluid near the wall is depleted, more wax molecules diffuse through the boundary layer to replenish the concentration. The concentration of wax molecules in the bulk fluid becomes uniform or smooth primarily through convective mass transfer. As the fluid moves on downstream its temperature drops further and more wax crystals are formed. This causes the adhesion rate of wax crystals at the wall to increase that in turn causes diffusion toward the wall to increase and thus a higher level of deposit forms. 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 acts against deposition by causing an increase in the rate of wax crystals being carried away. Deposition decreases further down the pipe because the temperature of the fluid begins to approach that of the wall and, as a result, the attraction of the wax crystals diminishes. If the  T becomes zero then there is no deposition, except at extremely low flow rates at which there is non-trivial deposition due to gravity. At some time, the rate of diffusion of wax molecules and crystals toward and adhesion at the wall becomes equal to the rate of shearing wax molecules and crystals away from the wall all along the pipe length. At this time the system is said to have achieved a steady state condition.

8. 8 Thermal, Mechanical, and Mass Equilibrium The equation at steady state is shown below:

9. Boundary Layer Wax Deposit Flow Conduit Wall h r Adh = Adhesion Rate of Waxes h r  = Shearing Rate of Waxes h r = h r Adh - h r  The deposition rate h r = 0 at Steady State Velocity Profile in the Boundary Layer Diffusion of Wax Molecules from the bulk fluid through the Boundary Layer and instant Absorption at Wall. Mass Flux with Adhesion (Reaction) at the Wall for Liquid-Filled Systems

10. 10 Determine Adhesion Rate Equation Need equation for the following term:

11. 11 Mass Flux with Adhesion (Reaction) at the Wall The general equation governing wax deposition w/o shear is: Where:N Wax, molar flux of wax into the boundary layer c Wax, concentration of wax R Wax, rate of adhesion of wax

12. 12 Wax Deposition Rate, Molar Flux After the math the following equation is derived: k, is determined in the cold finger test at a given  T.

13. 13 Wax Deposition Rate, Molar Flux k, is a function of x along the pipe length. That is k 1 is a function of T bulk -T wall or  T. Note that  T is not constant along the pipe length because the fluid is being cooled. T bulk is becoming smaller and smaller as the fluid moves. Hence,  T becomes smaller and smaller as the fluid cools along the pipe. The FLOWModel assumes the following relationship for k 1 : Where: c k and E a are constants and CP means  T at the cloud point location in pipe. The c k and E a constants can be determined from two cold finger tests. More cold finger tests would yield a more accurate functional relationship for k.

14. 14 Wax Deposition Rate, Mass Flux Convert moles to mass:

15. 15 Wax Deposit Growth Rate Divide by  wax to obtain the volumetric rate of adhesion:

16. 16 Shearing Rate Equation Need equation for the following term:

17. 17 Wax Shearing Rate The following limiting conditions are true for the rate of shearing wax crystals away from the wall: When  h r  , or a constant for gravity deposition (but neglected here) When  ∞  h r   ∞, all deposit is being carried or sheared away A simple functional relation between rate of shear of deposit and shear rate meeting the above requirements is:

18. 18 Wax Deposit Growth Rate Deduct the two to obtain the deposit growth rate:

19. 19 Wax Deposition Study PVT & Wax-Tuned PARA-Type EOS Oil Characterization Wax Deposition Tests PIPEModel Tuned PIPEModel Simulate Wax Deposition in Well Tubings, Flowlines, & Pipelines Viscosity-Temperature Curve of STO Wax Deposition Test of STO: - High Shear Rate - Low Shear Rate Field wax deposition data, if available

20. Multiphase Wax Flow Assurance Simulations FLOWModel R 1.Uses predictive portion of the EOSModel R and WAXModel R to simulate the gas-liquid-wax phase behavior of the fluid along the flow conduit. 2.Utilizes AsphWax-derived compositional versions of the following multi-phase models: Beggs, H.D. and Brill, J.P.,"A Study of Two-Phase Flow in Inclined Pipes", JPT (May 1973), 607-617 Orkiszewski Vertical Correlation Flanagan-Dukler Horizontal Correlation 3.Can be used in: Steady state mode to calculate hydraulics and thermal behavior at a given flow rate Unsteady state mode to determine pressure and temperature profile against a closed valve at the host. 4.The FLOWModel R can simulate wax deposition in single multi-phase pipelines and complicated pipeline networks.

21. 21 FLOWModel Simulation

22. 22 FLOWModel Simulation

23. 23 FLOWModel Simulation

24. 24 FLOWModel Simulation

25. 25 Flow Assurance Multiphase Simulations with Wax Deposition FLOWModel R