Transfer Rate in a Reacting Flow for the Refined Sodium Bicarbonate Production Process

Transcription

1 Presented at the COMSOL Conference 2008 Hannover COMSOL Conference Hannover November, 6 th, 2008 Study of the CO 2 Transfer Rate in a Reacting Flow for the Refined Sodium Bicarbonate Production Process Christophe Wylock (F.R.S.-FNRS research fellow), Aurélie Larcy, Pierre Colinet, Thierry Cartage and Benoît Haut Chemical Engineering Department Applied Science Faculty, Free University of Brussels

2 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 2

3 Introduction Refined sodium bicarbonate (NaHCO 3 ) production (Solvay) process in bubble columns (BIR columns) Limiting step : gas-liquid CO 2 absorption Input of brine rich in Na 2 CO 3 Outlet of a gaseous mixture air residual CO 2 Study of the bubble-liquid CO 2 transfer Inlet of a gaseous mixture air CO 2 Suspension with refined NaHCO 3 (solid) Page 3

4 Introduction Main resistance : in the liquid phase, where CO 2 takes part to chemical reactions This work : modelling of the CO 2 transfer rate from a bubble to the liquid phase Rising bubble air-co 2 mixture Diffusion Liquid at rest NaHCO 3 /Na 2 CO 3 brine Gas-liquid equilibrium ( CO2) ( CO2) g l 2 reversible chemical reactions : CO +NaOH NaHCO 2 3 Na CO +H O NaHCO +NaOH Convection Page 4

5 Introduction Main resistance : in the liquid phase, where CO 2 takes part to chemical reactions This work : modelling of the CO 2 transfer rate from a bubble to the liquid phase Coupling of - Convective transport - Diffusive transport - Chemical reactions Interfacial adsorbed surfactants : change the flow field around the bubble 2 cases investigated : fully contaminated bubble (no slip) clean bubble (slip) Page 5

6 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 6

7 Modelling Incompressible Navier-Stokes mode and Convection and Diffusion mode from the C.E. module 2-D axisymmetric geometry Computational domain Semi-bubble located at the center of a semi-circular domain Inertial reference frame located at the mass center of the bubble Symmetry axis Inlet Dimensionless bubble diameter: d b = 1 Spherical inclusion Liquid flow Domain diameter: 5 d b Outlet Page 7

8 Modelling Governing equations (in vectorial dimensionless form) Navier-Stokes and continuity T ( ) 1 ( u ) u = pi+ u+ ( u) Re u = 0 Reynolds number velocity pressure Mass transport coupled with chemical reactions D Peclet number D D - D OH CO 2 HCO CO D - 3 CO2 D = 3 CO2 1 a = r1 ( u ) a CO Pe 2 concentration CO 2 CO bulk 2 i 1 st reaction rate: r 2 1 = Ha1 ( ab αc) β Hatta1 number b b = χb ( r1 r2 ) ( u ) b NaOH concentration Pe [CO 2] i [NaOH] bulk β c c = χc ( r1 r2 ) ( u ) c NaHCO 3 concentration Pe [CO 2] i [NaHCO 3] bulk β d d = χdr2 ( u ) d Na 2 CO 3 concentration Pe [CO 2] i [Na 2CO 3] bulk Hatta2 number r = Ha 2 bc d 2 nd reaction rate: ( ) 2 2 Page 8

9 Modelling Meshing Concentric circular mapped mesh Finer in the vicinity of the interface Thickness : 0.05 d b The diffusion boundary layer does not lie beyond this zone Solver : stationnary UMFPACK Page 9

10 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 10

11 Simulation results 1) Validation by comparison of the simulation results WITHOUT reactions with classical correlations from literature Drag coefficient Sherwood number Separation angle Excellent agreement validated Page 11

12 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 12

13 Simulation results 1) Validation by comparison of the simulation results without reactions with classical correlations from literature : OK 2) For operating conditions of BIR columns Bubble : 1 mm diameter and rising velocity of 0.2 m/s Re = 200 and Pe = Other parameter values 1 : α = Ha 1 = 0.19 Ha 2 = 902 β b = 4.1 β c = 0.9 β d = 0.7 χ = 64 χ = 0.03 χ = b c Study of the CO 2 transfer rate as a function of the Hatta1 number (dimensionless ratio of chemical reaction 1 rate on CO 2 diffusion rate) d 1 correlations from Vas Bhat et al. (2000) Page 13

14 Simulation results Simulations of the CO 2 concentration field No reactions : Ha 1 =0 ( and Ha 2 =0 ) Fully contaminated bubble Clean bubble Page 14

15 Simulation results Simulations of the CO 2 concentration field Slow reaction 1 : Ha 1 =0.1 Fully contaminated bubble Clean bubble Page 15

16 Simulation results Simulations of the CO 2 concentration field Moderate reaction 1 : Ha 1 =1 Fully contaminated bubble Clean bubble Page 16

17 Simulation results Simulations of the CO 2 concentration field Fast reaction 1 : Ha 1 =10 Fully contaminated bubble Clean bubble Page 17

18 Simulation results Simulations of the CO 2 concentration field Increasing CO 2 depletion for increasing reaction 1 rate Calculation of the CO 2 transfer rate : Sherwood number Enhancement factor The CO 2 consumption enhances the CO 2 transfer rate Page 18

19 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 19

20 Simulation results 3) Comparison of the 2-D axysymmetric clean bubble case and a commonly-used 1D-approach of the chemical engineering Description of the Higbie approach Liquid flow : mosaïc of liquid elements slipping on the bubble Each element stays in contact with the bubble the same time No shear stress in the liquid Diffusion is normal to the interface 2 a 1 a = 2 r 1 t Pe x 2 b βb b = + χ 2 b r r t Pe x 2 c bubble βc c = + χ 2 c r1 r2 t Pe x 2 d βd d = + χ 2 dr2 t Pe t C x ( 1 2 ) ( ) Gas-liquid interface Gas mixture Aqueous solution NaHCO 3 /Na 2 CO CO 2+OH HCO3 CO l CO 3 +H2O HCO 3+OH x=0 x ( CO2) ( 2) g Axis pointed toward the liquid phase in normal direction of the Page interface 20

21 Simulation results Comparison results Sherwood number Enhancement factor The Higbie approach provides an excellent estimation Tend to slightly underestimate the chemical reactions effect when Ha 1 >1 Page 21

22 Table of content Introduction Modelling Simulation results Validation For industrial operating conditions Comparison with a 1-D common approach Conclusions and future plan Page 22

23 Conclusion and future plans Development of a model of bubble-liquid CO 2 transfer coupled with chemical reactions (for 2 cases) : Validation without reaction : excellent agreement Estimation of the chemical enhancement on the transfer rate Excellent comparison for the transfer rate estimation between 2-D clean bubble case and 1-D Higbie approach Future plans Extension to larger bubbles (2-6 mm) 400 Re 1200 Spherical bubble ellipsoidal-shape bubble Shape coming from experimental observation Comparison with spherical shape quantification of the shape effect Page 23

24 Thanks for your attention