Analysis of the dissolution of phosphate ore particles in phosphoric acid: Influence of particle size distribution

Abstract

A first principles model is developed to describe the dissolution mechanism of phosphate ore particles in a solution of phosphoric acid. It is based on mass balance equations along with hydrodynamic and kinetic relations, combined with a shrinking core model with product removal. Furthermore, non-uniform size of ore particles is accounted for using particle size distributions (PSDs) (i.e., Rosin-Rammler-Bennett, Gamma, Gate-Gaudin-Schuhmann distributions). Moreover, a coefficient of variation (CV) is used to quantify the influence of the PSD shape on the model predictions at different temperatures, acid concentrations and stirring speeds. The resulting three-phase (i.e., solid particles, liquid film surrounding the particles and liquid bulk) involves several unknown parameters. A global estimability analysis is therefore carried out to determine the estimable parameters from the available experimental data. The most estimable parameters are then identified from measurements of the particle conversion fraction mainly collected from the literature. The optimal values of the estimable unknown parameters are very consistent with the values in the literature and the predictions show good agreement with the experimental data. Finally, the computed activation energy of the dissolution reaction is very low indicating that diffusion is the rate limiting step of the dissolution process.