Iztok Livk

Supersaturation and temperature dependency of gibbsite growth in laminar and turbulent flows

Abstract The temperature and supersaturation dependencies of gibbsite crystal growth rates in caustic aluminate solutions were experimentally investigated in both the laminar (Taylor–Couette precipitator) and turbulent (stirred tank) mixing regimes. The gibbsite precipitation experiments were conducted batchwise in a temperature range from 55°C to 90°C, but all with the same initial liquor composition and seed type. At low supersaturation it was found that gibbsite crystal growth could be described satisfactorily by a screw dislocation growth mechanism over the complete temperature range, irrespective of the flow regime. At higher supersaturation and lower temperatures, i.e. 55°C and 60°C, it is proposed that two-dimensional polynuclear growth is the dominant growth mechanism in turbulent flows. Any differences observed in the measured growth rate estimates from the laminar and turbulent systems were explained by error analysis.

An Unreacted Shrinking Core Model for Calcination and Similar Solid-to-Gas Reactions

A variation on the unreacted shrinking core model has been developed for calcination and similar non-catalytic solid-to-gas decomposition reactions in which no gaseous reactant is involved and the reaction rate decreases with increasing product gas concentration. The numerical solution of the model has been validated against an analytical solution for the isothermal case. The model parameters have been tuned using literature data for the thermal dehydration (calcination) of gibbsite to alumina over a wide range of temperatures, from 490 to 923 K. The model results for gibbsite conversion agreed well with the published experimental data. A reaction order with respect to water vapor concentration of n = −1 was found to give a good fit to the data and yield activation energies consistent with literature values. Predictions of the non-isothermal unreacted shrinking core model compare well with a more complex distributed model developed previously by the authors.

The influence of crystalliser configuration on the accuracy and precision of gibbsite crystallisation kinetics estimates

This work investigates the importance of experimental design on the accuracy and precision of estimates of the agglomeration, growth and nucleation kinetics for the gibbsite system. The work is motivated by the need to explain the differences in crystallisation kinetics parameters reported in the literature for this system. Experiments were conducted to estimate the kinetics under the same process conditions (e.g. temperature, hydrodynamics and composition) from three different crystalliser configurations, i.e. (1) batch; (2) semi-batch at constant composition with representative solids removal and (3) semi-batch at constant composition with classified solids removal. The differential method of Bramley, Hounslow, and Ryall (J. Colloid Interface Sci. 183 (1996) 155) modified for semi-batch crystallisation, was used to estimate the kinetics from each set of experimental data. Some differences in the kinetics estimates between the different configurations were observed. Dynamic simulation showed that each set of estimated kinetics was adequate for describing the experimental CSDs. The uncertainties in the agglomeration and growth rate estimates, obtained by Monte Carlo simulations, were large enough to explain the observed differences. The differences in the nucleation source term were attributed to differences in suspension density between the experiments. A sensitivity analysis found that operating conditions have a greater impact on the uncertainties in the estimated kinetics than the crystalliser configuration.

2-D Population Balance Modelling of Nucleation and Growth of Needle-shape Crystals

Abstract Population balance equation models are widely accepted for simulating various particulate processes including crystallization. In this work, a dynamic 2-D population balance equation crystallization model was solved using a finite element method-based numerical algorithm with adaptive mesh and time step for three different cases: i) constant crystal growth rate, ii) constant crystal growth and nucleation rates, and iii) nonlinear crystallization kinetics. The model results obtained for the three different cases clearly demonstrate consistency of the newly developed numerical algorithm for solving 2-D population balance models of crystallization systems that produce crystals with the variable aspect ratio.