Compartmental modeling of an industrial bubble column Christophe
Compartmental modeling of an industrial bubble column Christophe Wylock, Aurélie Larcy, Thierry Cartage, Benoît Haut ULB – Transfers, Interfaces and Processes August, 27 th, 2009 8 th World Congress of Chemical Engineering Process Design Symposium Canada - Québec - Montréal 2009
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 2
Introduction § Refined sodium bicarbonate (Na. HCO 3) • 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-CO 2 mixture under the form of bubbles in an aqueous solution of Na 2 CO 3 and Na. HCO 3 – CO 2 is absorbed and chemical reactions occur in liquid phase (CO 2)g (CO 2)l CO 2 + OH- HCO 3= + H 2 O HCO 3 - + OH– Create a supersaturation of Na. HCO 3 precipitation of Na. HCO 3 crystals: Na+ + HCO 3 - (Na. HCO 3)s Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 3
Introduction § Schematic view of a BIR column Liquid inlet Gas outlet (air –residual CO 2 ) z Htot Htr, n Htr, i Trays Htr, 2 Cylindrical core of the column Htr, 1 Hcr Degassing loops Hl Circulation loops Suspension Gas inlet (air – CO 2) 0 Suspension outlet (liquid – refined Na. HCO 3) Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 4
Introduction § Limiting step : CO 2 absorption rate (only 50%) § Moreover, new applications of Na. HCO 3 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 Processes Applied Science Faculty, Université Libre de Bruxelles Page 5
Introduction § The Cholette & Cloutier model for a CSTR Real CSTR Model bypass perfectly mixed zone diffusion dead zone
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 7
Modeling § Compartmental modeling at steady-state • Schematic view Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 8
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 rate o Global and back-mixing liquid flow rates – Inside each compartment o o Gas-liquid (CO 2 absorption) Gas-gas (between the 2 bubble populations) Liquid-solid (Na. HCO 3 precipitation) Chemical reactions (in the liquid phase) Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 9
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 Processes Applied Science Faculty, Université Libre de Bruxelles Page 10
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 11
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 CO 2 transfer only from the small bubble population • Exchange between the 2 populations by the break-up and coalescence phenomena proportional to the gas hold-up • Equations function of the liquid and solid characteristics Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 12
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 13
Modeling § Gas-liquid exchange (CO 2 absorption) • Small bubble-liquid mass transfer modeled using Higbie approach (depending on concentrations and liquid flow) • Coupling with chemical reactions: only 1 pseudo 1 st order reversible reaction: CO 2+OH- HCO 3 - Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 14
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 15
Modeling § Liquid-solid exchange (Na. HCO 3 precipitation) • Solid phase: modeled by Population Balance Equation (PBE) Crystal Size Distribution (CSD) : • Solid mass fraction and liquid-solid Na. HCO 3 transfer rate can be deduced from the CSD (function of concentrations and liquid flow rate) Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 16
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 17
Modeling § Chemical reactions in liquid phase • Species concentrations in a compartment are affected by: – flow rates from and to neighbor compartments – gas-liquid CO 2 transfer – liquid-solid Na. HCO 3 transfer Chemical conversions to reach back the equilibrium • Set of equations come from mass balances and chemical equilibria Chemical conversion rates Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 18
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 19
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 Processes Applied Science Faculty, Université Libre de Bruxelles Page 20
Simulation § Simulation results Gas flow rates with height Concentration evolution with height CO 2 transfer rate with height Concentration evolution following compartment Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 21
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 22
Results and discussion § Simulation results comparison with experimental measurements • For the initial set of estimated modeling parameters fsim =0. 18 (fmeas ~ 0. 2) Global simulated CO 2 absorption: 50% (measured ~ 50%) Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 23
Results and discussion § Simulation results comparison with experimental measurements • With another set of modeling parameter values fsim =0. 19 (fmeas ~ 0. 2) Global simulated CO 2 absorption: 55% (measured ~ 50%) Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 24
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 25
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 Processes Applied Science Faculty, Université Libre de Bruxelles Page 26
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 Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 28
Appendix : Modeling § Gas-gas exchange (between small and large bubbles) • Molar gas flow rate • CO 2 molar flow rate Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 29
Appendix : Modeling § Gas-liquid exchange (CO 2 absorption) • Bubble-liquid CO 2 mean flux density • Gas-liquid CO 2 transfer function • Transferred CO 2 amount inside the ith compartment Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 30
Appendix : Modeling § Liquid-solid exchange (Na. HCO 3 precipitation) • Solid phase: modeled by Population Balance Equation (PBE) • Mean slurry residence time : with • Solid mass fraction: • Liquid-solid Na. HCO 3 transfer rate: Transfers, Interfaces and Processes Applied Science Faculty, Université Libre de Bruxelles Page 31
Appendix : Modeling § Chemical reactions in liquid phase
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