COMPARISON OF DISCRETISED POPULATION BALANCE (DPB) AND FINITE ELEMENT METHOD (FEM) METHODOLOGIES FOR MODELLING BATCH GIBBSITE PRECIPITATION

摘要

A population balance equation based dynamic gibbsite precipitation model, incorporating crystalgrowth, nucleation, and agglomeration was solved using two different numerical techniques,namely, the discretised population balance (DPB) and finite element method (FEM). Different toprevious precipitation modelling approaches, the agglomeration model in the FEM framework wasformulated based on Safronov agglomeration equation and its partial differential equation (PDE)approximation. The FEM framework implemented was founded on the Newton’s method Galerkinfinite element algorithm. The applied algorithm used automatic gear, time-step and non-uniformadaptive mesh strategies, which supported optimal solution convergence. For an isothermaldynamic batch gibbsite precipitation model the numerical solutions of DPB and FEM techniquesare compared for the conditions relevant to Bayer gibbsite precipitation. Simulation results obtainedfor four different case studies suggest that the FEM-based precipitation model is in most cases moreaccurate than the DPB model.