Modelling microstructures with flexible Laguerre Mosaics

Particle-based process models offer a promising avenue towards greater predictability in geometallurgy, i.e., the ability to predict the outcomes of specific mineral processing routes from the mineralogical and microstructural ore characteristics. While the particle-based prediction of separation processes is already possible with acceptable levels of accuracy, the ability to predict the outcomes of comminution processes is currently limited to particle size distributions. Expanding comminution modelling tools to include particle microstructures would enable the full particle-based modelling of mineral processing flowsheets. As a step towards the inclusion of microstructure in comminution modelling, Laguerre tessellations are proposed to represent both the microstructure and the successive comminution steps. In contrast to the PARGEN library of simulated particles, our goal is to provide a low-parametric, dynamic, and efficient generator of parent and progeny material to inform forward and backward modelling efforts.

The idea is to follow a hierarchical decision structure in the simulation procedure. We first define an intensity field in 3D for the occurrence cell nuclei, which are then realised by a marked Poisson process. The first mark corresponds to realisations of a multinomial variable, and defines the mineral of each potential cell. Conditional on the mineral, the second mark follows a normal distribution, defining the weight of each cell, related to its size. A communition step is defined by a Voronoi mosaic, with a (t+1)-step exhibiting a higher intensity of its Poisson process than the previous t-step. To model preferential breakage, we inhibit some of the potential breakage surfaces with a probability depending on the weighted average hardness and the cleavage quality of the minerals that each surface cuts. Two consecutive comminution steps generate the corresponding parent and progeny particles, Each independently cut by a random plane to generate the equivalent of a 2D SEM-based automated mineralogy dataset.