Modeling an industrial sodium bicarbonate bubble column reactor

Abstract

This paper deals with the study of the gas-liquid mass transfer, coupled with chemical reactions, the gas-liquid-solid mass transfer, and crystallization. Sodium bicarbonate is produced in a bubble column reactor which contains a solution of carbonate and bicarbonate and carbon dioxide gas injected into this column. In this mathematical modeling, a mole balance has been instituted on flows and components through the bubble column. A population balance is utilized to obtain the nucleation and growth formula for the solid phase. Danckwerts theory is utilized for mass transfer between gas and liquid phases. This model can predict the effects of several parameters on the production and size distribution of sodium bicarbonate crystals and also conversion of carbon dioxide. The mathematic simulator model results are compared with the experimental results to valid this model. Effects of different parameters on the production and size distribution of sodium bicarbonate crystals and also absorbent of carbon dioxide are investigated. Keywords Sodium bicarbonate Á Bubble column Á Triple phase mass transfer Á Crystallization Á Modeling List of symbols a Growth rate coefficient b Growth order (g) B 0 Nucleation (#/s kg solution) C CO 2 e Carbon dioxide concentration in liquid bulk (mol/m 3) c Nucleation rate coefficient C CO 2 i Carbon dioxide concentration in gas-liquid interface (mol/m 3) d Magma density order d B Average of bubbles diameter (m) D CO 2 Carbon dioxide molecular diffusion coefficient (m 2 /s) D g Gas phase radial dispersion coefficient (m 2 /s) D l Liquid phase radial dispersion coefficient (m 2 /s) d R Column diameter (m) E Enhancement factor e Nucleation order g Gravity (m/s 2) G Molar velocity of gas (mol/m 2 s) G 0 Growth rate (lm/s) G FR Gas flow rate (m 3 /s) h Column height (m) H Henry constant (Kmol/atm m 3) I Ionic content of solution (kg ion/m 3) I 0 Height of column that sodium bicarbonate reachs to saturation concentration k Constant rate of first order reaction (1/s) K l Liquid phase mass transfer coefficient (m/s) L Molar velocity of liquid (mol/m 2 s) L FR Liquid mass flow rate (kg/s) L nu Size of crystals (lm) M T Magma density (g crystal/kg solution) N Flux of mass transfer (mol/m 2 s) n Population density (no./lm kg solution) n Dis Flux of mass transfer by dispersion (mol/m 2 s) no Number of nucleons that born at dz P 0 Gas pressure at bottom of column (atm) P CO 2 Carbon dioxide partial pressure at gas phase (atm) P CO 2 e Carbon dioxide partial pressure at liquid bulk (atm) P CO 2 i Carbon dioxide partial pressure at gas-liquid interface (atm) Q Liquid flow rate (m 3 /s) r Rise of nucleons from dz to bottom of the column (m 3) R Gases constant (J/g mol K) S Molar velocity of solid (mol/m 2 s) T Liquid temperature (K) t Time U g Gas phase velocity (m/s) U l Liquid phase velocity (m/s) V Volume of element (m 3) w Weight fraction of component in liquid phase Dw Supersaturation (g NaHCO 3 /kg solution) x Mole fraction of components in liquid phase x à NaHCO 3 Mole fraction of sodium bicarbonate at supersaturation y Mole fraction of components in gas phase z Height of column (m) Greek symbols a g Gas-liquid interface (m 2 /m 3) a s Solid-liquid interface (m 2 /m 3) d Liquid surface tension (N/m) e g Gas holdup e l Liquid holdup l j jth moment of population density l l Liquid dynamic viscosity (N s/m 2) q H 2 O Water density (kg/m 3) q l Liquid density (kg/m 3) t l Liquid kinematic viscosity (m 2 /s)