Multidimensional modelling of particle separation processes: an approach to highly increase the number of particle properties considered

Two main approaches have been leading the latest contributions to the field of modelling particle separation processes: fundamental models that focus on the individual interactions taking place in a separation unit and empirical models that focus on the properties of individual particles (size, shape, and composition) and how they influence the separation process. Both these approaches have clear advantages and disadvantages. In this study we focus on the empirical approaches given their relevance to the raw materials field, where it is likely to encounter a large variation in particle properties, especially particle composition. Most importantly, the uniqueness of each particle in this field is expected to lead to a distinct process behaviour in a separation unit.
Tromp devised the partition curves, the first method to quantify particle behaviour in a separation process as a function of their properties. The latest developments in the field profited from the wealth of particle information provided by modern scanning electron microscope-based imaging techniques, which systematically quantifies, within a short time, a series of relevant particle properties – named here as particle data. These latest developments, however, require particles to be grouped into bins, and can only make use of up to ten particle properties. In this contribution, we present a strategy to fully benefit from the wealth of particle data, allowing to quantify the process behaviour of individual particles and to consider hundreds of particle properties. This strategy employs a regularized multinomial logistic regression, which is able to independently estimate the importance of different particle properties for the behaviour of a particle in a process and is sufficiently robust to deal with millions of particles. The relevance of the new strategy to the particle separation field is demonstrated here with a froth flotation experiment, where we highlight the effect of a particle size, shape, modal and surface composition to its overall behaviour in a flotation cell.