Discrimination of different models in the flotation of Maghara coal

Abstract

An essential requirement for the optimisation and operation of coal flotation is the availability of a mathematical model that predicts how the amount of recovery of desirable particles during a certain time period depends on the design parameters. The goal of these models is to undertake plant scale tests based on batch laboratory evaluations. The estimation of model parameters is subject to errors that can arise in different ways. Whichever the method adopted in any particular instance, knowledge of the accuracy to which the parameters may be determined is needed especially if they are used to study the effect of variables on the flotation process or to aid in the design or optimisation of a flotation circuit. The purpose of this study is to discriminate eight different competing models in the flotation of Maghara coal, as well as selection of the most appropriate model using different statistical criteria. All parameters in the different models are estimated using the experimental data. In this work, 15 data sets of time-recovery profiles are available. These results were obtained from the flotation of samples of Maghara coal below 0˙5 mm in size. These tests were executed at different conditions of collector dosages, frother dosages, and agitation speeds. Three different statistical criteria were used for comparison of different models. Two of these measures, i.e.fitting deviation (δ_f) and root mean square error (RMSE), are used for measuring the model fit. The other measure, i. e. predictive error sum of squares (PRESS) residuals, is used to measure the model stability (i.e.model robustness). Two particular models proved the best predictive power of Maghara coal flotation data – Rosin-Rammler's model (model 7) and the first-order flotation model with descritised distribution of floatabilities (model 2).