Comparison of FEM and DPB Numerical Methodologies for Dynamic Modeling of Isothermal Batch Gibbsite Crystallization

Abstract

A population balance equation based dynamic gibbsite crystallization model, incorporating crystal growth, nucleation, and agglomeration, was solved using two different numerical techniques, namely, a fully implicit finite element method (FEM) and an explicit discretized population balance (DPB) numerical scheme. Unlike previous crystallization modeling approaches, the agglomeration model in the FEM framework was formulated based on the Safronov agglomeration equation and its partial differential equation (PDE) approximation [Bekker, A. V.; Livk, I. Agglomeration process modeling based on a PDE approximation of the Safronov agglomeration equation. Ind. Eng. Chem. Res. 2011, in press. The FEM numerical solution is implemented using a fully implicit Newton’s method Galerkin finite element algorithm, which applies automatic Gear-type time-step and nonuniform adaptive mesh strategies to help optimal solution convergence. The dynamic FEM and DPB model predictions of isothermal gibbsite crystallization, using estimated kinetic parameters, are validated against experimental crystallization data that were generated under process conditions relevant to Bayer gibbsite crystallization. Additional modeling results obtained for a modified set of kinetic parameters, prolonged crystallization times, and more complex crystal size distributions show that the novel FEM-based crystallization modeling framework offers a more accurate and computationally efficient model solution than that based on the DPB approach.

Dynamic response of a plant-scale gibbsite precipitation circuit

“…The precipitation process in the continuous precipitation tanks is modelled using a dynamic precipitation population balance equation (PBE) incorporating crystal growth, nucleation, and agglomeration kinetics (Bekker et al 2011 andBekker et al 2015) relevant to the Bayer precipitation circuit conditions. The PBE model incorporates 140 non-uniform size intervals to accurately resolve the evolution of the PSD in a particle size range from 1.4 to 307 m.…”

Agglomeration Process Modeling Based on a PDE Approximation of the Safronov Agglomeration Equation

“…The validation of the newly developed PDE agglomeration model against experimental gibbsite precipitation data is reported in a related article. 12…”

“…Gibbsite agglomeration is used as a case study to demonstrate the suitability of the new approach for an industrially important particle agglomeration system. The validation of the newly developed PDE agglomeration model against experimental gibbsite precipitation data is reported in a related article …”