In a bulk production of alumina via Bayer process the product quality and process productivity both heavily depend on gibbsite precipitation step. Mathematical modelling of the precipitation process plays an important role in advancing design, optimisation, and operation of Bayer circuits.

A gibbsite precipitation model, developed in a finite element method (FEM) framework, includes gibbsite precipitation mechanisms such as nucleation, growth and agglomeration. The model couples population, mass and supersaturation balances. Different to previous precipitation models, an agglomeration model was created based on Safronov agglomeration equation and its new partial differential equation (PDE) approximation. The agglomeration model was solved using general Newton’s method-based Galerkin finite element algorithm. Automatic Gear-type time step and non-uniform adaptive mesh strategies, which support the optimal solution convergence, were used. Numerical solution for the isothermal pure agglomeration case is compared to the analytical solution of Smoluchowski equation and asymptotical solution of Safronov equation.

The new PDE agglomeration model resulted in an almost-implicit numerical algorithm with a band-diagonal sparse Jacobian matrix, which is different to the models based on original Safronov or Smoluchowski equations. For small particle sizes, the new PDE agglomeration model solution exactly reproduces the solution of Smoluchowski equation. For a high agglomeration degree, the new agglomeration model also preserves particle size distribution within the finite size interval ensuring the conservation of total particle volume.

Numerical results show that the new PDE agglomeration model based on Safronov equation is very well suited for Bayer precipitation modelling.