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Flow Assurance Multiphase Simulations

with Wax DepositionFLOWModelR

Flow Assurance Multiphase Simulations

with Wax DepositionFLOWModelR

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Wax DepositionWax 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.

FShearing

FAdhesion,ParallelFAdhesion,Perpend.

FAdhesion

Wax Crystal

Shearing and Adhesion Forces on a Wax Crystal

shsh

sh dy

d

A

F 3

4 4 8sh

Q

R R D

3

Viscous oils have lowerwax deposition rates.

Wax Crystal Shear & Adhesion

Wax Deposition In Liquid-Filled Conduit

4

PIN, TIN

Q

To

Insulation

Insulation

T1initial T1

final

Wax Deposit

Wax Deposit

Segment 1 Segment 2 Segment 3 Segment i

L2 L3L1 Li

Ri, hi Tiinitial

Tifinal

Pipe Wall

Rinsul

Rwax

Rpipe

Ro, ho

Cooling Fluid is Water or Air

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Wax Deposition

PIN, T IN

Q

To

T1initial

T1final

Wax Deposit

Wax Deposit

Segment 1 Segment 2 Segment 3 Segment i

L2 L3L1 Li

T iinitial

T ifinal

Pipe Wall

Cooling Medium is Ground

r

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Thermal, Mechanical, and Mass Equilibrium

Bo

un

dar

y L

ayer

Wax

Dep

osi

t

FlowCo

nd

uit

Wal

lhr

Adh = Adhesion Rate of Wax Crystals

hr = Shearing Rate of Wax Crystals

hr = hrAdh - hr

The deposition rate hr = 0 at Steady State

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Thermal, Mechanical, and Mass Equilibrium

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.

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Thermal, Mechanical, and Mass Equilibrium

The equation at steady state is shown below:

rr hhadh

Bou

ndar

y L

ayer

Wax

Dep

osit

FlowCon

duit

Wal

l

hrAdh = Adhesion Rate of Waxes

hr = Shearing Rate of Waxes

hr = hrAdh - hr

The deposition rate hr = 0 at Steady State

Velocity Profile in the Boundary Layer

Diffusion of Wax Molecules from the bulk fluid throughthe Boundary Layer and instant Absorption at Wall.

Mass Flux with Adhesion (Reaction) at the Wall

for Liquid-Filled Systems

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Determine Adhesion Rate Equation

adh

rh

Need equation for the following term:

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Mass Flux with Adhesion (Reaction) at the Wall

The general equation governing wax deposition w/o shear is:

0 WaxWax

Wax Rt

cN

Where: NWax, molar flux of wax into the boundary layercWax, concentration of waxRWax, rate of adhesion of wax

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Wax Deposition Rate, Molar Flux

After the math the following equation is derived:

80.6

7.4 10Wax

o oWO

o

T MWD x

1tanaERTk WDRT WaxDeposition RateCons t k e

0r bWax WO WaxN D k c

k, is determined in the cold finger test at a given T.

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Wax Deposition Rate, Molar Flux

1 *

bulk wallat x at xk

bulk wallatCP at CP

T Tk c

T T

k, is a function of x along the pipe length. That is k1 is a function of Tbulk-Twall or T. Note that T is not constant along the pipe length because the fluid is being cooled. Tbulk 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 k1:

Where: ck and Ea are constants and CP means T at the cloud point location in pipe. The ck and Ea constants can be determined from two cold finger tests. More cold finger tests would yield a more accurate functional relationship for k.

1

aERTk k e

1tanaERTk WDRT WaxDeposition RateCons t k e

* *aEbulk wallat x at x RT

kbulk wallatCP at CP

T Tk c e

T T

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Wax Deposition Rate, Mass Flux

Convert moles to mass:

0r bWax Wax WO Waxn MW D k c

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Wax Deposit Growth Rate

Divide by wax to obtain the volumetric rate of adhesion:

0

1 1r b

adhr Wax Wax WO Wax

Wax Waxh n MW D k c

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Shearing Rate Equation

rh

Need equation for the following term:

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Wax Shearing Rate

The following limiting conditions are true for the rate of shearing wax crystals away from the wall:

• When hr, or a constant for

gravity deposition (but neglected here)

• When ∞hr∞, 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:

3 3

32 4 4 8

( 1) ( 1) ( 1) ( 1) ( 1)Q Q

m m m mm d R R Drh e e e e e

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Wax Deposit Growth Rate

Deduct the two to obtain the deposit growth rate:

adhr r rh h h

3

32

( 1)b

Qm

dWaxr WO Wax

Wax

MWh D k c e

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Wax Deposition StudyPVT & 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

Multiphase Wax Flow Assurance SimulationsFLOWModelR

1. Uses predictive portion of the EOSModelR and WAXModelR

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 FLOWModelR can simulate wax deposition in single

multi-phase pipelines and complicated pipeline networks.

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FLOWModel Simulation

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FLOWModel Simulation

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FLOWModel Simulation

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FLOWModel Simulation

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Flow Assurance Multiphase Simulations

with Wax DepositionFLOWModelR

Flow Assurance Multiphase Simulations

with Wax DepositionFLOWModelR