A framework for polydisperse pulp phase modelling in flotation

Abstract

Froth flotation is one of the most widely-used mineral processing operations. The pulp zone in flotation tanks is polydisperse in general and serves as a medium for the interaction between the solid particles and the gas bubbles in a liquid continuum, leading to particle–bubble attachment/detachment and bubble coalescence/breakage phenomena. To better predict the hydrodynamics and inform the design of e cient flotation equipment, it is therefore important to accurately model and simulate the evolution of the size distribution of the dispersed phases. This has created an urgent need for a framework that can model the pulp phase in an e cient manner, which is not currently available in the literature. The available software products are not e cient enough to allow for a tractable modelling of industrial-scale flotation cells and in some cases they cannot model the polydispersity of the dispersed phase at all. This work presents an e cient numerical framework for the macroscale simulation of the polydisperse pulp phase in froth flotation in an open-source finite element computational fluid dynamics (CFD) code that provides an e cient solution method using mesh adaptivity and code parallelisation. A (hybrid finite element–control volume) finite element framework for modelling the pulp phase has been presented for the first time in this work. An Eulerian–Eulerian turbulent flow model was implemented in this work including a transport equation for attached and free solid particles. Special care was taken to model the settling velocity of the free solids and the modification of the liquid viscosity due to the presence of these particles. Bubble polydispersity was modelled using the population balance equation (PBE), which was solved using the direct quadrature method of moments (DQMOM). Appropriate functions for bubble coalescence and breakage were chosen in the PBE. Mesh adaptivity was applied to the current problem to produce fully-unstructured anisotropic meshes, which improved the solution e ciency, while all simulations were executed on a multicore architecture. The model was validated for 2D simulations of a bubble column against experimental results available in the literature. After successful validation, the model was applied to the simulation of the pulp phase in a flotation column for monodisperse and polydisperse solids. Polydispersity of the solids was modelled for the first time in this work using three separate solid size classes. A clear dependence of the flotation rate on the particle size was noticed and the monodisperse solids simulations were shown to over-predict the flotation rate. Other than flotation, this open-source framework can be used for the simulation of a variety of polydisperse multiphase flow problems in the process industry.