A dynamic flotation model for predictive control incorporating froth physics. Part II: Model calibration and validation

Abstract

Modelling for flotation control purposes is the key stage of the implementation of model-based predicted controllers. In Part I of this paper, we introduced a dynamic model of the flotation process, suitable for control purposes, along with sensitivity analysis of the fitting parameters and simulations of important control variables. Our proposed model is the first of its kind as it includes key froth physics aspects. The importance of including froth physics is that it improves the estimation of the amount of material (valuables and entrained gangue) in the concentrate, which can be used in control strategies as a proxy to estimate grade and recovery.

In Part II of this series, experimental data were used to estimate the fitting parameters and validate the model. The model calibration was performed to estimate a set of model parameters that provide a good description of the process behaviour. The model calibration was conducted by comparing model predictions with actual measurements of variables of interest. Model validation was then performed to ensure that the calibrated model properly evaluates all the variables and conditions that can affect model results. The validation also allowed further assessing the model’s predictive capabilities.

For model calibration and validation purposes, experiments were carried out in an 87-litre laboratory scale flotation tank. The experiments were designed as a randomised full factorial design, manipulating the superficial gas velocity and tailings valve position. All experiments were conducted in a 3-phase system (solid-liquid–gas) to ensure that the results obtained, as well as the behaviour of the flotation operation, are as similar as possible to those found in industrial flotation cells.

In total, six fitting parameters from the model were calibrated: two terms from the equation for overflowing bubble size; three parameters from the bursting rate equation; and the number of pulp bubble size classes. After the model calibration, simulations were performed to validate the predictions of the model against experimental data. The validation results revealed good agreement between experimental data and model predictions of important flotation variables, such as pulp level, air recovery, and overflowing froth velocity. The high accuracy of the predictions suggests that the model can be successfully implemented in predictive control strategies.