A Method to Detect Abnormal Gas Dispersion Conditions in Flotation Machines

: This short communication presents a methodology to detect abnormal gas dispersion conditions in ﬂotation machines. These abnormal conditions are characterized by the signiﬁcant presence of cap-shaped bubbles. The approach considers the use of a bubble size analyzer to measure gas dispersion at industrial scale. The detection of abnormal conditions is critical when estimating bubble size by automated software. Otherwise, the estimates are signiﬁcantly biased, since irregular bubbles are typically removed from the analysis. From the recorded images and the respective black and white representation, the variability of the shadow percentage caused by the bubbles in the vision ﬁeld, abruptly increases in the presence of cap-shaped bubbles. Experimental conditions with coefﬁcients of variation lower than 60–70% in the shadow percentage represent spherical and spherical-ellipsoidal regimes. In the former, automated bubble sizing software has proved to be sufﬁciently effective in obtaining reliable results. In the latter, different segmentation techniques have been proposed to obtain satisfactory results. Abnormal conditions are detected under coefﬁcients of variation greater than 80% in the shadow percentage. The presence of cap-shaped bubbles causes inefﬁciencies in the collection of hydrophobic minerals in the pulp zone as well as disturbances in the separation stage (froth zone). Therefore, the detection of these irregular bubbles is suitable to provide feedback to ﬂotation processes, allowing gas dispersion to be driven towards normal operating conditions.


Introduction
Since the introduction of bubble size analyzers to characterize gas dispersion in flotation, several applications have been proposed to better understand and improve the process performance. For example, the relationship between gas dispersion and flotation kinetics [1][2][3], frother characterizations [4,5], collection and froth response relationships [6][7][8], among others. Most of these characterizations have been conducted at laboratory scale, in which flotation machines are typically operated in regimes dominated by spherical bubbles. Thus, the use of bubble samplers along with visual techniques for bubble size quantification has been successful in bubble size determination, due to the efficiency of software tools for circular detection [9,10]. However, industrial practice has shown deviations regarding spherical regimes, leading to bubble populations including ellipsoidal and cap-shaped bubbles (transitions to ellipsoidal and churn-turbulent regimes, respectively). The characterization of bubbles in the ellipsoidal regime has been subject to significant improvements due to the use of ellipse fitting by regression [9,11] or solidity together with moment-based axis quantifications [12,13]. However, these estimations are only successful when the percentage of bubbles observed in clusters is low or moderate-low. Cap-shaped bubbles are identified by their low circularities or solidities in 2D representation, and 2 of 7 automated software typically removes them from the image processing, biasing the bubble size estimation. However, complex clusters also present low circularities, which hinders the automated identification of irregular bubbles by image processing.
Large cap-shaped bubbles lead to detrimental performances in flotation due to a decrease in the available bubble surface and lower froth stability. Cap-shaped bubbles imply a higher Sauter mean diameter D 32 = Σd i 3 /Σd i 2 and, therefore, a lower bubble surface area flux S B , which has proved to be correlated with the collection rate constant [1][2][3]. In addition, these bubbles present higher terminal velocities [14,15], increasing the disturbances at the pulp-froth interface [16]. These disturbances increase entrainment and bubble coalescence throughout the froth, affecting the concentrate grades [16]. Although large cap-shaped bubbles result in negative effects on metallurgical performance, their detection has not received sufficient attention even though these conditions have been observed at industrial scale in flotation machines [9,17].
This short communication presents a methodology to detect significant presences of cap-shaped bubbles in flotation. The technique employs images acquired from the McGill bubble size analyzer (MBSA) [18] in their black and white representation. The variability of the shadow percentage obtained from the binary images is used as an indicator of abnormal gas dispersion conditions. The technique is tested with industrial data from mechanical flotation cells and columns.

Materials and Methods
Gas dispersion measurements were conducted in mechanical flotation cells (selfaerated and forced air) and flotation columns from different industrial concentrators. One hundred and two datasets were analyzed, with six of them corresponding to columns. Bubble populations were measured using the McGill bubble size analyzer shown in Figure 1a. The sampling tube was immersed about 15-30 cm below the pulp-froth interface to capture bubbles entering the froth. The chamber was fully filled with process water, which was displaced by the rising bubbles. A deflecting glass is installed in the MBSA to observe the bubbles in a 2D plane. A digital video camera (Canon GL2, Canon U.S.A. Inc., Lake Success, NY, USA) was used for image acquisition at a sampling rate of 30 frames per second. The image processing was carried out at time intervals of 1 s to avoid autocorrelation between the analyzed images. The visual field was set at 3.5 cm × 4.67 cm, leading to a resolution of 0.0729 mm/pxl. The MBSA was adapted to determine the local superficial gas rate J G , which can be estimated by water volume displacement over time. The MBSA was completely sealed to avoid possible leaks in the industrial measurements, which is critical for reliable gas dispersion results.
A semi-automated image analysis tool based on the Image Processing Toolbox of Matlab (The MathWorks Inc., Natick, MA, USA) was used to obtain the bubble size distributions (BSD) and the statistical parameters from the bubble population, e.g., Sauter mean diameter. All images were analyzed based on their black and white representation. A hierarchical algorithm was implemented, which firstly allowed single bubble diameters to be estimated as equivalent ellipsoid diameter (volumetric). Simple clusters were automatically and sequentially segmented using Watershed and Hough transforms [10,19]. Complex clusters and irregular bubbles were manually estimated to reduce biases in the BSD estimations. Figure 1b illustrates the image processing procedure, in which bubbles highlighted by crosses were manually analyzed.
The shadow percentage σ B was related to the D 32 values to detect churn-turbulent conditions. This parameter corresponds to the number of black pixels divided by the total pixels in the processed images [20], as described by Equation (1). In the example of Figure 1b, σ B is approximately 22%. The variability of σ B showed an abrupt increase as gas dispersion transitioned to churn-turbulent regimes.   [20]) and (b) example of the image processing procedure (modified from [9]).  Figure 2b) conditions presented stable shadow percentages with moderate variability with respect to the average. Conditions transitioning to churn-turbulent regimes presented peaks in the shadow percentage due to the random appearance of large cap-shaped bubbles, as shown in Figure 2c. Figure 3 presents the normalized shadow percentages for the three conditions shown in Figure 2. This normalized parameter represents instantaneous σ B values divided by the average σ B. The presence of cap-shaped bubbles increases the relative variability of σ B in experimental conditions that transitioned to churn-turbulent regimes. Spherical and spherical-ellipsoidal conditions resulted in significantly lower relative variability, with normalized σ B values oscillating around 1. Results from Figures 2 and 3 show that the presence of cap-shaped bubbles caused high instantaneous σ B values, similar to spherical-ellipsoidal regimes with high gas hold-up. However, transitions to churn-turbulent regimes showed abrupt variations from low to high σ B values. These variations were indirectly used to detect problems in gas dispersion. Normal conditions can be associated with a wide range of σ B values, which were consistently steadier in all measurements.  [20]) and (b) example of the image processing procedure (modified from [9]).  Figure 2b) conditions presented stable shadow percentages with moderate variability with respect to the average. Conditions transitioning to churn-turbulent regimes presented peaks in the shadow percentage due to the random appearance of large capshaped bubbles, as shown in Figure 2c. Figure 3 presents the normalized shadow percentages for the three conditions shown in Figure 2. This normalized parameter represents instantaneous σ B values divided by the average σ B . The presence of cap-shaped bubbles increases the relative variability of σ B in experimental conditions that transitioned to churnturbulent regimes. Spherical and spherical-ellipsoidal conditions resulted in significantly lower relative variability, with normalized σ B values oscillating around 1. Results from Figures 2 and 3 show that the presence of cap-shaped bubbles caused high instantaneous σ B values, similar to spherical-ellipsoidal regimes with high gas hold-up. However, transitions to churn-turbulent regimes showed abrupt variations from low to high σ B values. These variations were indirectly used to detect problems in gas dispersion. Normal conditions can be associated with a wide range of σ B values, which were consistently steadier in all measurements. Figure 4 shows the relationship between the Sauter mean diameters of the BSDs and coefficients of variation of the shadow percentage cv σB . The coefficient of variation (or relative standard deviation) corresponds to the standard deviation divided by the mean value. Although noisy, the relative variability of σ B explains part of the variability of D 32 , which is observed as an increase in bubble size at higher cv σB . Spherical (D 32 2.0 mm) and spherical-ellipsoidal (2.0 mm D 32 5.0 mm) regimes are observed with cv σB lower than 70%. These experimental datasets correspond to typical operations in flotation, including flotation machines with D 32 > 3.0 mm that are commonly associated with moderate-high superficial gas rates [21]. Five experimental conditions presented transitions from ellipsoidal to churn-turbulent regimes. These datasets presented binary images as those shown in Figure 2c. As a result, the cv σB values were consistently greater than 80%. Thus, high relative variability in the shadow percentage can be used as an indicator of transitions towards churn-turbulent regimes.   images should be split into several sub-images to conduct the image analysis. For f of view much bigger than the cap-shaped bubbles, the average σ B can also be in the r of normal conditions. In this work, the field of view was chosen to characterize BSD the spherical and spherical-ellipsoidal regimes, which also allowed the gas dispersio stability to be observed, given random sampling in the image processing. Results from Figure 4 indicate that abnormal conditions are observed when D mm. However, these results were obtained by a semi-automated approach, in whic regular and cap-shaped bubbles were manually processed. The identification of thes normal conditions from D32 estimates is then a time-consuming procedure. As mo BSD characterizations involve automated image processing, biased bubble size est tions may be significant in industrial practice. Irregular objects can also be detecte shape factors such as circularity or solidity; however, complex clusters also presen shape factors, hindering the detection of cap-shaped bubbles. The use of the relative iability of the shadow percentage is then a practical tool to detect abnormal condi It should be noted that the relative variability of σ B was used as an indirect indication of the presence of cap-shaped bubbles. This variability was estimated from time series as those shown in Figure 3, for sampling intervals that reduced the chances of autocorrelation. However, the relative variability in σ B is only detected when the field of view is sufficiently small to observe the time instability (and spatial non-uniformity). Otherwise, the images should be split into several sub-images to conduct the image analysis. For fields of view much bigger than the cap-shaped bubbles, the average σ B can also be in the range of normal conditions. In this work, the field of view was chosen to characterize BSDs in the spherical and spherical-ellipsoidal regimes, which also allowed the gas dispersion instability to be observed, given random sampling in the image processing.

Results and Discussions
Results from Figure 4 indicate that abnormal conditions are observed when D 32 > 6 mm. However, these results were obtained by a semi-automated approach, in which irregular and cap-shaped bubbles were manually processed. The identification of these abnormal conditions from D 32 estimates is then a time-consuming procedure. As most of BSD characterizations involve automated image processing, biased bubble size estimations may be significant in industrial practice. Irregular objects can also be detected by shape factors such as circularity or solidity; however, complex clusters also present low shape factors, hindering the detection of cap-shaped bubbles. The use of the relative variability of the shadow percentage is then a practical tool to detect abnormal conditions and to provide feedback to flotation operations. The technique implementation is straightforward, with low computational cost.
The abnormal conditions highlighted in Figure 4 correspond to BSDs measured in three first cells of rougher flotation banks and in two flotation columns. Insufficient frother conditioning time, damaged sparger, and lack of maintenance in the bubble generation systems were the main possible causes for the significant presence of cap-shaped bubbles in these flotation machines.

Conclusions
A straightforward image processing technique was proposed to detect abnormal gas dispersion conditions in flotation. This technique was based on the relative variability of the shadow percentage of binary images of bubble populations. The methodology was applied to industrial data from flotation cells and columns. The results showed that:

•
The presence of cap-shaped bubbles caused peaks in the instantaneous shadow percentage, increasing its variability. This variability was significantly lower under spherical and spherical-ellipsoidal regimes.

•
The relative variability of the shadow percentage justified part of the variability of the Sauter mean diameter. Under spherical and spherical-ellipsoidal regimes, a noisy increasing trend between the cv σB and the D 32 was observed. • An abrupt increase in the coefficient of variation of the shadow percentage was observed in abnormal gas dispersion operations. • A threshold of cv σB ≈ 80% was determined as suitable to detect a significant presence of cap-shaped bubbles in flotation machines. From this threshold, D 32 > 6 mm were observed.
The detection of cap-shaped bubbles from the relative variability of the shadow percentage is proposed to provide feedback to flotation processes. Thus, normal carrying capacities with nonsignificant disturbances at the pulp-interface can be monitored.