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This paper deals with the counting and measuring of overlapping circular objects in binary images, a problem that arises in the mineral processing industry when estimating the distribution of bubble diameters in flotation cells in order to predict the geometallurgical performance of the flotation process. By viewing the images as realizations of a stationary planar Boolean model with circular grains and by using two-point set statistics, it is possible to jointly estimate the average number of objects per unit area and their diameter distribution. When applied to real and simulated images, this method is shown to give accurate estimates, to be robust to the presence of noise contaminating the images and of moderate drifts in the number of objects per unit area, and to speed up the processing time with respect to currently used methods. Combined, these properties serve to make the method suitable for an on-line monitoring of the flotation process. [ABSTRACT FROM AUTHOR]

Ore hardness plays a critical role in comminution circuits. Ore hardness is usually characterized at sample support in order to populate geometallurgical block models. However, the required attributes are not always available and suffer for lack of temporal resolution. We propose an operational relative-hardness definition and the use of real-time operational data to train a Long Short-Term Memory, a deep neural network architecture, to forecast the upcoming operational relative-hardness. We applied the proposed methodology on two SAG mill datasets, of one year period each. Results show accuracies above 80% on both SAG mills at a short upcoming period of times and around 1% of misclassifications between soft and hard characterization. The proposed application can be extended to any crushing and grinding equipment to forecast categorical attributes that are relevant to downstream processes. [ABSTRACT FROM AUTHOR]

Abstract Flotation tests at laboratory scale describe the metallurgical behavior of the minerals that will be processed in the operational plant. This material is generally composed of ore and gangue minerals. These tests are usually scarce, expensive and sampled in large supports. This research proposes a methodology for the geostatistical modelling of metallurgical recovery, covering the change of support problems through additive auxiliary variables. The methodology consists of simulating these auxiliary variables using a Gibbs Sampler in order to infer the behavior of samples with smaller supports. This allows downscaling a large sample measurement into smaller ones, reproducing the variability at different scales considering the physical restrictions of additivity balance of the metallurgical recovery process. As a consequence, it is possible to apply conventional multivariate geostatistical tools to data at different supports, such as multivariable exploratory analysis, calculation of cross-variograms, multivariate estimations, among others. The methodology was tested using a drillhole database from an ore deposit, modelling recovery at a smaller support than that of the metallurgical tests. The support allowed for the use of the geochemical database, to consistently model the metal content in the feed and in the concentrate, in order to obtain a valid recovery model. Results show that downscaling the composite size reduces smoothing in the final model. Highlights • A downscaling approach to integrate metallurgical and geochemical data is presented. • Metallurgical recovery is simulated using auxiliary additive variables. • A Gibbs Sampler is used to impose constraint on total mass of metal among composites. • A synthetic and a real case study demonstrate the proposed methodology. [ABSTRACT FROM AUTHOR]