Characteristic Time Scales for an

Eulerian-Lagrangian Multiphase Flow

Model in Vacuum Towers

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Model in Vacuum Towers

Antonio V. S. Castro (PETROBRAS)

Karolline Ropelato (ESSS) Speaker

Milton Mori (UNICAMP)

Washington Geraldelli (PETROBRAS)

Topics

• Problem Description – Vacuum Tower

• Model Setup

• Modeling Approach

• Mathematical Modeling

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• Results

• Conclusion

• Acknowledgements

Problem Description

Vacuum Tower

HGO

LGO

Region ofStudy

Objective

To analyze the liquid and

vapor behavior, since it can

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Slop Wax

LVGO = Light Vacuum Gas Oil

HVGO = Heavy Vacuum Gas oil

affect directly the operational

performance!

Spray section:

• Prescribed mass flow

• 41 sprays

Demister: subdomain condition

• Outlet condition

• Isotropic Loss Model

Model Setup

Geometry and Computational grid

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Vapor Inlet:

• Prescribed mass flow

LVGO

Draw-off Pan

Model Setup

Geometry and Computational grid

• Computational grid

Number of nodes ≅ 1.110.274Prisms layers = 10

Mesh refinament for spray discretization

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Detailed numerical discretization

Modeling Approach

• The Phases approach

– Continuous phase: vapor (Eulerian)

– Dispersed phase: liquid droplets distribution

(Lagrangian)

• Lagrangian tracking for the liquid droplets

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• Lagrangian tracking for the liquid droplets

used to predict spray distribution

• Simulations on steady-state

• k-ε turbulence model was applied on

continuous phase

• Present work:

– Eulerian-Lagrangian approach

– Takes into account the influence of the liquid flow within

the vapor phase flow

• Allows to predict the spray distributor arrangement and geometry

improvement

Modeling Approach

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improvement

– Important assumptions

• Constant droplet average diameter

– dp=0,7 mm

– The model can predict the diameter variation along the tracking

• Droplets wall restitution was desconsidered.

• Momentum Equation

– Continous Phase

– Dispersed Phase

( ) ( ) ( ) CCCTurbCCCCCCCCC rprrr

tMfTTUUU ++∇−+⋅∇=⋅∇+

∂∂

ρρ

Mathematical modeling

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– Dispersed Phase

( )

−++−−=dt

dU

dt

dUd

dt

dUdUUUUCd

dt

d DCD

CCDcDCD

D ρπρππρ 332

12

1

6

1

8

1M

Applied in momentm equation for

continous phase (two-way

coupling)

DRAG Pressure gradient Virtual Mass

( ) allDcDCD

D

D FUUUUCdmdt

dU+−−= 2

8

1πρ

• Energy Equation

– Continous Phase

( ) ( ) ccLmccccccccccc SQhTrhUrhrt

++Γ=∇−•∇+∂∂

λρρ

Mathematical modeling

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– Dispersed Phase

( ) ( )421

4

1pppL

DCPD nTdh

dt

dmTT�ud

dt

dTcm σπελπ −++−= ∑∑

Convection Mass Transfer Radiation

ε=

k09,0tg

– Continuous characteristic time scale (tg)

“Average time of the large eddies in the

continuous phase considering the k-ε turbulence

model.”

where:

Mathematical modeling

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ε= 09,0tg

εν

= ckt

where:

k ≡ turbulent kinetic energy [m2/s2]

ε ≡ rate of dissipation of “k” [m2/s3]

ν ≡ cinematic viscosity [m2/s]

– Kolmogorov time scale (tk)

“Characteristic time scale of the smallest

scales – Kolmogorov Scales.”

rDc

dp

dVC3

D4t

ρ

ρ=

– Lagrangian relaxation time (td) “Represents the entrainment of the

particles by the continuous phase.” where:

k ≡ turbulent kinetic energy [m2/s2]

Dp ≡ Droplet diameter [m]

CD ≡ Drag coefficient (Schiller Naumann)

Mathematical modeling

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k

V

2

3C1

tt

2

r

g

dg

β+

=45,0C =β

– Vapor-droplet turbulent correlation (tdg)

“The time of interaction between particle

motion and continuous phase”

CD ≡ Drag coefficient (Schiller Naumann)

Vr ≡ Slip velocity [m/s]dcslipr uuVV −==

k

dk

t

t

edissipativ scale Kolmogorov

timerelaxation LagrangianSt ==

• Stokes in Kolmogorov scales (Stk)

Mathematical modeling

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Stokes 0: droplets velocity approaches the carrier phase velocity;

Stokes ∞: droplets velocities is unaffected by the fluid;

Stokes = 1: droplets cluster, coalescence risk.

Continuous characteristic time scale (tg)

Results

Kolmogorov time scale (tk)

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ε=

k09,0tg ε

ν= c

kt

Lagrangian relaxation time (td) Vapor-droplet turbulent correlation (tdg)

Results

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rDc

dp

dVC3

D4t

ρ

ρ=

k

V

2

3C1

tt

2

r

g

dc

β+

=

Stokes na escala de Kolmogorov

Results

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Stokes 0: droplets velocity approaches the

carrier phase velocity;

Stokes ∞: droplets velocities is unaffected by

the fluid;

Stokes = 1: droplets cluster, coalescence risk.

• Heat TransferF

E

D

C

B

A

Heat transfer

regions

Results

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≅≅≅≅ 78%

≅≅≅≅ 22%

A

0.0E+00

1.0E+06

2.0E+06

3.0E+06

4.0E+06

5.0E+06

6.0E+06

A B C D E F

Regiões

Tro

ca T

érm

ica (W

)

Dp=0,7 mm

Dp=0,34 mm

Heat exchanger

(W)

Conclusions

• The model has been proved to be useful in

determining the vacuum tower behavior;

•• CFDCFD methodologymethodology providesprovides::

–– dropletsdroplets liquidliquid distributiondistribution characterizationcharacterization

–– thethe influenceinfluence ofof vaporvapor inletinlet inin continuouscontinuous andand

w w w . c f d o i l . c o m . b r

–– thethe influenceinfluence ofof vaporvapor inletinlet inin continuouscontinuous andand

disperseddispersed phasephase behaviorbehavior..

•• TheThe resultsresults ofof thisthis studystudy pointedpointed thethe importanceimportance ofof

anan engineeringengineering analysisanalysis forfor vaporvapor inlet,inlet, consideringconsidering

generalgeneral operationoperation conditioncondition

•• TheThe modelmodel hashas beenbeen provedproved toto bebe usefuluseful inin

determiningdetermining thethe vacuumvacuum towertower behaviorbehavior;;

• CFD methodology provides:

– droplets liquid distribution characterization

– the influence of vapor inlet in continuous and

Conclusions

w w w . c f d o i l . c o m . b r

– the influence of vapor inlet in continuous and

dispersed phase behavior.

•• TheThe resultsresults ofof thisthis studystudy pointedpointed thethe importanceimportance ofof

anan engineeringengineering analysisanalysis forfor vaporvapor inlet,inlet, consideringconsidering

generalgeneral operationoperation conditioncondition

•• TheThe modelmodel hashas beenbeen provedproved toto bebe usefuluseful inin

determiningdetermining thethe vacuumvacuum towertower behaviorbehavior;;

•• CFDCFD methodologymethodology providesprovides::

–– dropletsdroplets liquidliquid distributiondistribution characterizationcharacterization

–– thethe influenceinfluence ofof vaporvapor inletinlet inin continuouscontinuous andand

Conclusions

w w w . c f d o i l . c o m . b r

–– thethe influenceinfluence ofof vaporvapor inletinlet inin continuouscontinuous andand

disperseddispersed phasephase behaviorbehavior..

• The results of this study pointed the importance of

an engineering analysis for vapor inlet, considering

general operation condition

Acknowledgements

Thank you all !!!

ESSS

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ESSSEngineering Simulation and Scientific Software

Contact: ropelato@esss.com.br