A new statistical view to modeling of particle residence time distribution in full-scale overflow ball mill operating in closed-circuit

In the present study, residence time distribution (RTD) of an industrial ball mill operating in closed-circuit with hydrocyclones was measured. Several probability distribution functions (PDFs) constituting exponential, Weibull, Gamma, logistic, normal, and lognormal were applied to obtained RTD results and evaluated based on Anderson-Darling statistic (AD) and associated p-value indices. In addition, three most common empirical RTD models (i.e., perfect mixer, N-Mixer and Weller) were fitted to the given practical data. Aside from assessment of coefficient determination (R-2) for each model, a factor of incorporating the number of model parameters was considered using Bayesian information criterion, low of iterated logarithm criterion and Akaike information criterion. It was revealed that Weibull PDF is fitted reasonably well to the measured experimental data compared with the other PDFs. Despite the relative variance (sigma(2)) of N-Mixer model was slightly less than the corresponded value of Weller model, the goodness of fit criterion (R-2) and all four information criteria (IC) showed better results for Weller model. Therefore, one large with two small tanks in series along with a dead time was selected as the best model from the statistical point of view. Finally, it was concluded that the RTD models must be evaluated not only on the basis of goodness of fit but also the number of model parameters should be taken into account.