cfdoil apresentacao 2008.ppt [read-only]cfdoil.com.br/2008/pdf/presentations/18_1_1345.pdf ·...
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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)
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Topics
• Problem Description – Vacuum Tower
• Model Setup
• Modeling Approach
• Mathematical Modeling
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• Results
• Conclusion
• Acknowledgements
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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!
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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
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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
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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
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• 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.
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• Momentum Equation
– Continous Phase
– Dispersed Phase
( ) ( ) ( ) CCCTurbCCCCCCCCC rprrr
tMfTTUUU ++∇−+⋅∇=⋅∇+
∂∂
ρρ
Mathematical modeling
w w w . c f d o i l . c o m . b r
– 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
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• 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
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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.”
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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 −==
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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.
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Continuous characteristic time scale (tg)
Results
Kolmogorov time scale (tk)
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ε=
k09,0tg ε
ν= c
kt
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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+
=
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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.
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• 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)
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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
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•• 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
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•• 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
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Acknowledgements
Thank you all !!!
ESSS
w w w . c f d o i l . c o m . b r
ESSSEngineering Simulation and Scientific Software
Contact: [email protected]