A dynamic framework for a three phase hybrid flotation column

Abstract

A comprehensive dynamic fundamental model with Danckwerts’ boundary conditions at the pulp/froth interface has been developed for a continuous hybrid flotation column that includes a mechanically agitated section at the bottom. The model accounts for three phases, namely the water, gas, and solid particles (hydrophobic and hydrophilic), in one space dimension. The modeling framework is based on three subsystems, including a well-mixed reactor and two plug-flow reactors representing pulp (collection) and froth (cleaning) zones that are interconnected through the boundaries. The model considers the micro-scale processes taking place in the column, such as bubble-particle attachment and bubble coalescence. The resulting mathematical model is a coupled set of nonlinear heterodirectional hyperbolic partial differential equations for the pulp and the froth and a set of ordinary differential equations for the well-mixed zone. The movement between phases are given by liquid upflow, liquid downflow, and gas upflow. An important parameter in this simulation is the bubble size, which directly affects the gas holdup, and consequently the distributions of all states, including the concentration of attached minerals through the column. Qualitative validation of the model is provided by testing its predictions against experimental data from the literature for two-phase systems. Finally, the effect of some important parameters such as gas flow rate, agitation, particle size on gas holdup, distributions of value minerals, grade, recovery, and attachment/detachment rates have been studied.