Andrey V. Bekker

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.

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.