Computational Workflow for the Characterization of Size, Shape, and Composition of Particles and Their Separation Behavior During Processing

Separation functions, so-called Tromp functions, are often used to quantitatively analyze the separation behavior in particle processing with respect to individual particle descriptors. However, since the separation behavior of particles is typically influenced by multiple particle descriptors, multivariate Tromp functions are required. This study focuses on methods that allow for the computation of multivariate parametric Tromp functions by means of statistical image analysis and copula-based modeling. The computations are exemplarily performed for the magnetic separation of Li-bearing minerals, including quartz, topaz, zinnwaldite, and muscovite, based on micro-computed tomography images and scanning electron microscopy with energy-dispersive X-ray spectroscopy analysis. In particular, the volume equivalent diameter, zinnwaldite fraction, flatness, and sphericity are examined as possible influencing particle descriptors. Moreover, to compute the Tromp functions, the probability distributions of these descriptors for concentrate and tailing should be used. In this study, 3D image data depicting particles in feed, concentrate, and tailings is available for the computation of Tromp functions. However, concentrate particles tend to be elongated, plate-like, and densely packed, making segmentation for extracting individual particles from image data extremely difficult. Thus, information on the concentrate could not be obtained from the available database. To remedy this, an indirect optimization approach is used to estimate the distribution of particle descriptors of the concentrate. It turned out that this approach can be successfully applied to analyze the influence of size, shape, and composition of particles on their separation behavior.