Estimating Residence Time Distributions in Industrial Closed-Circuit Ball Mills

Abstract

This paper compares two deconvolution methodologies used to estimate residence time distributions (RTD) in industrial closed-circuit ball mills. Parametric and non-parametric deconvolution techniques were evaluated. Both techniques allowed for direct RTD estimates from inlet and outlet tracer measurements in the mills, with no need for mass balances nor assumptions to correct the effect of the tracer recirculation in the grinding circuits. Measurements of inlet and outlet concentrations were conducted by radioactive solid tracers and on-stream detectors. The parametric deconvolution was applied assuming the N-perfectly-mixed-reactors-in-series model, whereas the non-parametric deconvolution consisted of a constrained least squares estimation subject to non-negativity. The shapes of the estimated RTDs were consistent between these methodologies, showing mound-shaped distributions in all cases. From the parametric approach, mixing regimes described by 2–4 perfect mixers in series were observed, which indicated significant differences regarding perfect mixing. The mean (τmean) and median (τ50) residence times were more consistent with the RTD shapes when applying the parametric deconvolution. The non-parametric approach was more sensitive to noise, a disadvantage leading to mean residence times significantly higher than the median, and less consistent with the RTD locations. From the comparisons, the estimation strategies proved to be applicable in industrial closed-circuit ball mills. The parametric deconvolution led to better overall performances for τ50 = 1.7–8.3 min, given a suitable model structure for the RTDs.

Keywords

• residence time distribution
• closed-circuit ball mills
• parametric RTD estimation
• constrained least-squares estimation
• industrial tracer tests