8 th world congress of chemical engineering process design symposium

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

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

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


Introduction

Schematic view of a BIR column


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

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)


Introduction

The Cholette & Cloutier model for a CSTR

deadzone

bypassbypass

deadzone

Real CSTR Model

perfectly mixed zone

perfectly mixed zone

diffusion


Presentation plan




Modeling

Compartmental modeling at steady-state• Schematic view


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)


Modeling

All equations and jump conditions: see «Compartmental modeling of an industrial bubble column» in the special issue of Chemical Product and Process Modeling



Presentation plan




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



Presentation plan




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

-



Presentation plan




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)


( ) expJ L

c LG G

3NaHCO

LS

QT

MM

3

3 3

NaHCO

6 V crkJG

MM


Presentation plan




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


Chemical conversion rates


Presentation plan




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


Simulation

Simulation results


Gas flow rates with height CO2 transfer rate with height

Concentration evolution with height Concentration evolution following compartment


Presentation plan




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%)


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%)



Presentation plan




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,...)


Thanks for your attention.

Appendix : Modeling

Gas-gas exchange (between small and large bubbles)• Bubble population gas hold-up

• Net exchange

• Exchange superimposed (break-up - coalescence)

• Pressure


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

, 1 2

1 ( ) ( )( )

1 ( ) ( )

l cr

l cr cr

l i

dpg z z

dz

dpg z z

dz

Appendix : Modeling

Gas-gas exchange (between small and large bubbles)• Molar gas flow rate

• CO2 molar flow rate


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

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


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

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:


( ) 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

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

8 th world congress of chemical engineering process design symposium

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