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Compartmental modeling of an industrial bubble columnChristophe Wylock, Aurélie Larcy, Thierry Cartage, Benoît HautULB – Transfers, Interfaces and ProcessesAugust, 27th,2009
8th World Congress of Chemical Engineering Process Design SymposiumCanada - Québec - Montréal 2009
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 2
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Introduction
Refined sodium bicarbonate (NaHCO3)
• One of the oldest production process of the Solvay group• Has numerous applications• Produced in bubble columns, called the BIR columns
– Dispersion of an air-CO2 mixture under the form of bubbles in an aqueous solution of Na2CO3 and NaHCO3
– CO2 is absorbed and chemical reactions occur in liquid phase
(CO2)g (CO2)lCO2 + OH- HCO3
-
CO3= + H2O HCO3
- + OH-
– Create a supersaturation of NaHCO3 precipitation of NaHCO3 crystals:
Na+ + HCO3- (NaHCO3)s
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 3
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Introduction
Schematic view of a BIR column
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 4
Gas inlet (air – CO2)
Gas outlet(air –residual CO2 )
Suspension outlet(liquid – refined NaHCO3)
Liquid inlet
Trays
Cylindrical core of the column
Degassing loops
Circulation loops
z
0
Htot
Htr,n
Htr,1
Htr,
2
Htr,i
Hc
rHl
Suspension
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Introduction
Limiting step : CO2 absorption rate (only 50%)
Moreover, new applications of NaHCO3 require more control on precipitation process
Past optimizations: empirical approach, that has reached its limit more fundamental approach is needed, but complex• 3 phases system• Many phenomena, on different space and time scale• Coupling of the phenomena
Goal of this work: development of an operational model of BIR column, using compartmental modeling approach (Cholette&Cloutier)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 5
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Introduction
The Cholette & Cloutier model for a CSTR
deadzone
bypassbypass
deadzone
Real CSTR Model
perfectly mixed zone
perfectly mixed zone
diffusion
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
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Modeling
Compartmental modeling at steady-state• Schematic view
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 8
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Modeling
Compartmental modeling at steady-state• The column is divided into a set of compartments• Each compartment contains:
– Perfectly mixed liquid phase
– Gaseous phase 2 bubble populations, modeled by plug flow
– In the lowest: perfectly mixed solid phase, modeled by PBE
• Mass transfers occur:– Between compartments
o Global gaseous flow rateo Global and back-mixing liquid flow rates
– Inside each compartmento Gas-liquid (CO2 absorption)
o Gas-gas (between the 2 bubble populations)
o Liquid-solid (NaHCO3 precipitation)
o Chemical reactions (in the liquid phase)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 9
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Modeling
All equations and jump conditions: see «Compartmental modeling of an industrial bubble column» in the special issue of Chemical Product and Process Modeling
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 10
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 11
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Modeling
Gas-gas exchange (between small and large bubbles)• 2 bubble populations
– large bubbles : 5 - 8 cm– small bubbles : 2 - 5 mm
• Flow modeled by a plug flow
• Gas-liquid CO2 transfer only
from the small bubble population• Exchange between the 2
populations by the break-upand coalescence phenomenaproportional to the gas hold-up
• Equations function of the liquid and solid characteristics
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 12
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 13
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Modeling
Gas-liquid exchange (CO2 absorption)
• Small bubble-liquid mass transfer modeled using Higbie approach (depending on concentrations and liquid flow)
• Coupling with chemical reactions: only 1 pseudo 1st order reversible reaction: CO2+OH- HCO3
-
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 14
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 15
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Modeling
Liquid-solid exchange (NaHCO3 precipitation)
• Solid phase: modeled by Population Balance Equation (PBE)
Crystal Size Distribution (CSD) :
• Solid mass fraction and liquid-solid NaHCO3 transfer rate can be deduced from the CSD (function of concentrations and liquid flow rate)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 16
( ) expJ L
c LG G
3NaHCO
LS
QT
MM
3
3 3
NaHCO
6 V crkJG
MM
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 17
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Modeling
Chemical reactions in liquid phase• Species concentrations in a compartment are
affected by:– flow rates from and to
neighbor compartments
– gas-liquid CO2 transfer
– liquid-solid NaHCO3 transfer
Chemical conversions to reach back the equilibrium
• Set of equations come from mass balances and chemical equilibria
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 18
Chemical conversion rates
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 19
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Simulation
All modeling parameters can be estimated (at least roughly) :• Experimental measurements• Literature review of theoretical and experimental
work• Theoretical analysis• Computational Fluid Dynamics simulation
The model can be simulated
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 20
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Simulation
Simulation results
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 21
Gas flow rates with height CO2 transfer rate with height
Concentration evolution with height Concentration evolution following compartment
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 22
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Results and discussion
Simulation results comparison with experimental measurements• For the initial set of estimated modeling parameters
sim=0.18 (meas~ 0.2)
Global simulated CO2 absorption: 50% (measured~ 50%)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 23
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Results and discussion
Simulation results comparison with experimental measurements• With another set of modeling parameter values
sim=0.19 (meas~ 0.2)
Global simulated CO2 absorption: 55% (measured~ 50%)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 24
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Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles
Presentation plan
Introduction Modeling
• Division into a set of compartments• Gas-gas exchange• Gas-liquid exchange• Liquid-solid exchange• Chemical reactions
Simulation Results and discussion Conclusion
Page 25
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Conclusions
An "operational" BIR column model is developed Reasonable agreement with experimental measurement
(despite the roughly determination of some parameters) Important differences with observed results remain Further studies has to be performed
• Development of accurate correlation to estimate or adjust modeling parameters
• Experimental validation
Already a tool to develop new design of BIR bubble column reactors (number of trays/compartment, height, liquid or gas flow rates, diameter of core or loops,...)
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 26
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Thanks for your attention.
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Appendix : Modeling
Gas-gas exchange (between small and large bubbles)• Bubble population gas hold-up
• Net exchange
• Exchange superimposed (break-up - coalescence)
• Pressure
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 28
2 1
1
,1,2 1
,
( ) 1 ( )
11( ) 1 ( ) 1
1
d
l crd s
d s cr
z z
z z
2, ,
( )( ) ( ) ( ) ( )GL G ls G sl
dN zF z T z T z T z
dz
, 1 2
, 1 2
( ) 0
( )
( ) ( )
G ls
G sl
F z
T z B z z
T z F z B z z
, 1 2
, 1 2
( ) 0
( ) ( )
( )
G ls
G sl
F z
T z B z z F z
T z B z z
,11 2
,1
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1 ( ) ( )( )
1 ( ) ( )
l cr
l cr cr
l i
dpg z z
dz
dpg z z
dz
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Appendix : Modeling
Gas-gas exchange (between small and large bubbles)• Molar gas flow rate
• CO2 molar flow rate
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 29
1 1 11 2
2 2 21 2
( )( )( ) ( )
1 ( ) ( )
( )( )( ) ( )
1 ( ) ( )
l
l
U zp zN z z G
RT z z
U zp zN z z G
RT z z
1 1 2 , 1 ,
2 2 2 , 1 ,
( ) ( ) ( ) ( )
( ) ( ) ( ) ( )
G sl G ls
GL G sl G ls
dN z y z y z T z y z T z
dzd
N z y z T z y z T z y z T zdz
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Appendix : Modeling
Gas-liquid exchange (CO2 absorption)
• Bubble-liquid CO2 mean flux density
• Gas-liquid CO2 transfer function
• Transferred CO2 amount inside the ith compartment
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 30
2
2
CO - -2CO , 2 11 , 11 ,
-11 ,
( ) ( ) 1( ) CO OH erf OH
2OH
l i l i l i Ci i iCl i i
Dp z y zN z h k k t
RT tk
2CO -11 , exp OHl i Ci
C
Dk t
t
2CO2 2( ) ( ) ( )GLT z a z N z
1
, ( )i
iGL i GLT T z dz
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Appendix : Modeling
Liquid-solid exchange (NaHCO3 precipitation)
• Solid phase: modeled by Population Balance Equation (PBE)
• Mean slurry residence time :with
• Solid mass fraction:
• Liquid-solid NaHCO3 transfer rate:
Transfers, Interfaces and ProcessesApplied Science Faculty, Université Libre de Bruxelles Page 31
( ) expJ L
c LG G
3NaHCO
LS
QT
MM
3
3 3
NaHCO
6 V crkJG
MM
1, 2,1cr suspcr cr
H
Q
, 0
1( )
crH
i cr icr
z dzH
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Appendix : Modeling
Chemical reactions in liquid phase
,1 ,1 , 2 , 2 ,1 2 , 1,1 1
- - -,1 ,1 , , ,1 1, 2,1 1
-,1 ,1 , 3
1 2 CO 1 CO 1 CO
1 2 OH 1 OH 1 OH
1 2 HCO 1
i r i i n r i n r i GL i ii i i
i r i i n r i n r i i ii i i
i r i i n ri
Q Q Q Q Q T
Q Q Q Q Q
Q Q Q Q
- -, 3 ,1 3 1, 2, ,11 1
= = =,1 ,1 , 3 , 3 ,1 3 2,1 1
-3 1
1 , 1-
21 1
=3 1
2 , 1-
HCO 1 HCO
1 2 CO 1 CO 1 CO
HCO
OH CO
CO
OH
i n r i i i i LSi i
i r i i n r i n r i ii i i
il i
i i
il i
Q T
Q Q Q Q Q
K
K
-31 1
HCOi i