Shrinking Core Approach in the Modelling and Simulation of Phosphate Ore Acidulation

Abstract

This paper deals with the modeling and simulation of the acidulation (dissolution) of phosphate ore particles in a dilute phosphoric acid solution in a batch stirred tank reactor. A shrinking core model with elimination of the products is used to describe the reaction and mass transfer phenomena involved in the three phases considered, i.e., liquid bulk, liquid film surrounding the particles and solid phase. The model is based on mass balance equations in the three phases and the corresponding equations are ODEs in the liquid bulk and in the solid phase, and PDEs in the liquid film. An estimability analysis method based on global sensitivities is used to determine the most estimable unknown parameters involved in the model equations from the available experimental data. The experiments consist of measurements over time of the conversion rate of the ore particles obtained in operating conditions similar to those used in an industrial phosphoric acid plant. The values of the least estimable parameters are fixed from the literature, while gProms environment is used to implement and solve the equations and to identify the most estimable parameters. The results obtained show a good agreement between the model predictions and the measurements with coherent values of the identified parameters.