Numerical investigation of the influence of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank

Abstract

The effect of kinetics and shape factor on barium sulfate precipitation in a continuous stirred tank has been investigated numerically through solving the standard momentum and mass transport equations in combination with the moment equations for crystal population balance. The numerical method was validated with the literature data. The simulated results include the distribution of the local supersaturation ratio in the reactor, the mean crystal size, and the coefficient of variation. The simulation results show that the value of shape factor used in the model affected greatly the mean crystal size and the moments of the crystal size distribution. The influence of the kinetic expressions on the simulation is also analyzed. It is important to investigate the relationship of the shape factor with the precipitator type and other operation conditions to obtain reliable simulation results and suitable kinetic equations of crystal nucleation and growth rates.

Keywords

stirred tank / numerical simulation / precipitation / shape factor / crystal kinetics

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Acknowledgements

Financial support from the National Natural Science Foundation of China (Grant Nos. 20236050, 50404009 and 50134020), the National Basic Research Priorities Program (No. 2004CB217604) and the National High Technology Research and Development Program of China (Grant No. 2007AA060904) is gratefully acknowledged.

Nomenclature

b	width of baffle, m
B	nucleation rate, #·m-3·s-1
C	clearance of impeller to tank bottom, m
C.V.	coefficient of variation defined by Eq. (9)
c	concentration, kmol·m-3
d	diameter of impeller, m
d32	mean particle size, m
G	growth rate, m·s-1
H	height of the tank, m
Ksp	solubility product, kmol2·m-6
k	turbulent kinetic energy m2·s-2
kv	The volumetric crystal shape factor
L43	mean particle size, m
Mc	mole mass of the crystal, kg·kmol-1
Mt	mass concentration of crystal, kg·m-3
mj	jth moment of crystal size distribution, mj·m-3
N	impeller speed, r·min-1
r	radial coordinate, m
Sa	supersaturation ratio
Sc	turbulent Schmidt number
Sg	specific crystal growth rate
T	tank diameter, m
u, v, w	velocity of liquid phase in r, θ, z direction, m·s-1
Xj	conversion ratio of ion j
z	axial coordinate, m
μeff	effective viscosity, m2·s-1
Γeff	diffusion coefficient, m2·s-1
ϕ	general variable
θ	tangential coordinate, rad
ρ	solution density, kg·m-3
ρcrystal	density, kg·m-3
τ	mean residence time, s
ϵ	turbulent energy dissipation rate, W·kg-1
Δc	Supersaturation, kmol·m-3

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