1 flow assurance multiphase simulations with wax deposition flowmodel r
TRANSCRIPT
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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