The concentrate ash content analysis of coal flotation based on froth images

Minerals Engineering 92 (2016) 9–20

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The concentrate ash content analysis of coal flotation based on froth images Jiakun Tan a, Long Liang a, Yaoli Peng a,b, Guangyuan Xie a,b,⇑ a b

School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, China National Engineering Research Center of Coal Preparation and Purification, China University of Mining and Technology, Xuzhou 221116, China

a r t i c l e

i n f o

Article history: Received 26 November 2015 Revised 16 February 2016 Accepted 17 February 2016

Keywords: Coal flotation Ash content Concentrate Froth Images

a b s t r a c t Ash content is a vital indicator for coal flotation performance. Froth plays an important role in determining flotation concentrate grade and there are strong correlations between the concentrate froth and the ash content. Therefore, the research in the correlations is of great importance for further flotation prediction and control. In this paper, flotation experiments were conducted at different frother dosages and froth depths using a flotation column. It was found that there were relations between the ash content, yield and water recovery of the concentrates. Variables of froth property such as the average gray value, the homogeneity, the burst bubble parameters and the height over weir were extracted from video images and were analyzed to explain the flotation results. The connections between the variables and the concentrate ash content were analyzed. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Ash content is a significant indicator of coal industry as coal products must satisfy the requirements for various applications. In coal preparation, the performance of the gravity separation of bulk particles is usually better than that of the flotation of fine particles, so the ash content of flotation concentrate must be strictly controlled to maximize the financial profitability. Traditionally, operators of flotation could only adjust parameters timely according to their experience (Moolman et al., 1996; Hätönen, 1999; Holtham and Nguyen, 2002; Aldrich et al., 2010; Shean and Cilliers, 2011). The exact results of coal flotation performance could only be tested after the long-time processing of sampling, filtrating, drying, sample preparing and burning to ash. It is too late to adjust the flotation parameters after obtaining the result of concentrate ash content. Once the disturbances of flotation input appear, amounts of concentrate could not meet the requirement of ash content by the delayed adjustment. While in base metal applications, X-ray fluorescence (XRF) analyzers are used for on-line assaying the elemental contents in the flotation streams which is important to effective flotation control (Wills and Napier-Munn, 2006; Shean and Cilliers, 2011). However, the relevant research can be scarcely found in coal flotation area. The

timely, accurate and applicable measurement of the concentrate ash content is rather challenging. Among the methods to detect or predict the ash content of coal, the prediction by froth features is the most applicable one for timely and repeatable requirements. High temperature ashing method is used as the standard method due to the accuracy and stability, but it is time-consuming. Other methods such as double c-ray transmission method (Tang et al., 1998; Yazdia and Esmaeilnia, 2003; Zhu and Zhang, 2004) and neutron analysis method (Cheng, 2005; Sibiya et al., 2014) are relatively accurate and quick, but they are costly and very harmful to the environment. As a result, these methods are not widely used. Recently, image processing of flotation froth is used to predict and analyze the flotation concentrate grade and satisfactory results can be obtained (Shean and Cilliers, 2011). Some froth variables can be obtained with the help of froth images and used to analyze the relation with concentrate grade, such as air recovery (Moys, 1984; Barbian et al., 2005, 2006, 2007; Zheng et al., 2006a; Hadler and Cilliers, 2009; Hadler et al., 2010) and bubble burst rate (Morar et al., 2012a, 2012b). Air recovery represents the fraction of the air that overflows the cell as unbroken bubbles.

a¼ ⇑ Corresponding author at: School of Chemical Engineering and Technology, China University of Mining and Technology, Xuzhou 221116, China. E-mail address: [email protected] (G. Xie). http://dx.doi.org/10.1016/j.mineng.2016.02.006 0892-6875/Ó 2016 Elsevier Ltd. All rights reserved.

Q out f  v f  hw  w ¼ Q Q

ð1Þ

where Qout is the volumetric flowrate of air leaving the top surface of the froth as unbroken bubbles, Q is the volumetric flowrate of air introduced in the column, f is the fraction of air in the overflowing

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froth, vf is the velocity of the bubbles on top of the froth, hw is the height of the froth overflowing at the weir and w is the weir lip length. The higher a refers to the lower the loss of air by bubble breakage and the higher the froth stability. (1  a) represents the fraction of bubbles bursting on the froth surface. Its correlations with concentrate grade were found in copper and platinum flotation. Bubble burst rate could also characterize the froth stability which also relates to the concentrate grade in copper and platinum flotation (Morar et al., 2012a, 2012b). The bubble burst rate was extracted by comparing two consecutive frames after segmentation and aligning the images. It was supposed to burst if the ratio of the bubble size from the first frame to the average area of the intersecting bubbles is greater than a threshold (Morar et al., 2012a). In coal flotation, Qu et al. (2013) investigated the links between air recovery, froth stability and coal flotation performance. It was found that there is a strong correlation between the air recovery and the dynamic froth stability which was determined by measuring the maximum froth height in a non-overflowing froth column. At a fixed aeration rate (hydrodynamic condition) and various MIBC concentrations, a strong correlation between air recovery and coal flotation performance was also observed. Some other froth variables relating to the concentrate grade are extracted and directly applied to establish or train models such as regression model, neural network or support vector machine. These froth features are mainly bubble size, froth velocity, froth color and froth stability. Jahedsaravani et al. (2014) extracted froth features by image processing in the batch flotation of a copper sulfide ore. The relationships between the froth features and concentrate grade were successfully modeled using the neural networks. Marais and Aldrich (2011) estimated the platinum flotation grades and recoveries from froth image data. It was shown that grades and recoveries can be reliably estimated from a number of different features by use of linear and nonlinear models. The similar research was also conducted in other fields, such as iron flotation (Mehrabi et al., 2014), zinc flotation (Kaartinen et al., 2006) and bauxite flotation (Cao et al., 2013). In coal flotation area, Hargrave et al. (1996) found that the gray level has correlations with flotation performance. Wang et al. (2001) developed the relationship between the features of froth image and indicators of coal flotation concentrate. Citir et al. (2004) calculated the average bubble diameter in each image for coal flotation by image processing off-line. The relationship between the mean bubble diameter and the cumulative grade was described by the linear fitting functions. The reason why concentrate grade can be predicted by froth property is not very clear at current stage. But it can be interpreted to a certain extent by the interaction between particles and bubbles (Ventura-Medina and Cilliers, 2002; Barbian et al., 2007). Hydrophobic particles that attach on the bubbles enter the froth phase. They may detach from the bubble lamellae when bubble burst or coalesce occur. The detached particles then enter the Plateau border, where three lamellae meet. The liquid of the froth is mainly in the Plateau borders, as well as the entrained hydrophilic particles. The liquid, hydrophilic particles and detached hydrophobic particles in the Plateau border may drain back to the pulp. Drainage could reduce the entrainment and it also causes the bubble coalescence or burst. Hence, froth features could reflect the concentrate grade. In addition, particle properties have significant influence on froth property (Johansson and Pugh, 1992; VenturaMedina et al., 2004; Barbian et al., 2007; Aktas et al., 2008; Cole et al., 2010; Tang et al., 2010; Farrokhpay, 2011; Wang et al., 2014, 2015). Particle size and hydrophobicity affect the froth stability and water recovery very much in coal flotation (Liang et al., 2015). In return, froth properties such as stability, mobility, water content under different conditions can also affect the particles that are loaded on the bubble lamellae or entrained in the plateau borders (Ventura-Medina and Cilliers, 2002; Shi and Zheng, 2003;

Zheng et al., 2006b; Barbian et al., 2007; Farrokhpay, 2011; Wang and Peng, 2014; Haffner et al., 2015; Razavi et al., 2015; Wang et al., 2015). It can be summarized that there are complex interactions between the particles that determines the concentrate grade and the bubbles that determines the froth properties. However, the understanding of the complex three-phase froths is far from unambiguous (Morar et al., 2012a) at current stage. There is little research concerned concentrate ash content analysis by froth images in coal flotation. In this research, the concentrate ash content was analyzed at different frother dosages and froth depths. Froth property variables relating to the concentrate ash content were proposed to explain the flotation results. The average gray value of flotation froth at different flotation time was used to analyze the concentrate ash content and the froth overflowing speed. The homogeneity was proposed to characterize the bubble size in coal flotation froth, the images of which were difficult to segment under small error. The texture homogeneity was analyzed as a function of offset to estimate the froth bubble size at different frother dosages and flotation time. The height over weir was studied individually as a function of time. The fluctuation range and frequency features were interpreted by the burst bubble size and overflow velocity. Bubble burst parameters were also investigated to analyze its correlations with ash content. 2. Experimental 2.1. Materials Coal sample was obtained from a flotation feed stream in a coal preparation plant in Linhuan, China. The size analysis of the flotation feed was shown in Table 1. Table 1 shows that the fraction of the particles finer than 74 lm is the dominant fraction which constitutes nearly half the total sample. The ash content increases with the size decreases. This could be explained by the fact that the gangue minerals are easily to degrade and much secondary slime is produced during the separation process. 2.2. Flotation experiments A pneumatic flotation column of 1 L was designed to conduct the flotation experiments. No agitation is applied in the flotation column, so relative peaceful froths which are favorable for the extraction of froth properties could be obtained. 60 g of coal were used in each batch flotation with 1 L of tap water. Kerosene and 2-octanol were used as the collector and the frother. The dosage of the collector was 330 g/t consistently, while the frother dosage increased from 27 g/t to 206 g/t. The slurry was first conditioned in a 1.5 L XFD flotation cell for 2 min. Then the collector was added and another 2 min of conditioning was kept before adding the frother. The slurry conditioning was stopped 30 s after the frother was added. Then the slurry was poured into the flotation column. One camera (Canon PC1331) was set on an iron shelf above the flotation column and another camera (Nikon D7100) was set on the camera tripod on the side of the flotation column. The frame rates of the cameras above and on the side are 30 and 29 frames per second Table 1 Sieving results of the coal sample finer than 500 lm. Size (lm)

Fraction (%)

Ash content (%)

500–250 250–125 125–74 74 Total

20.68 18.59 14.39 46.34 100.00

12.92 22.84 29.97 36.82 28.29

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respectively. There were two LED lights above the column on the shelf for illumination. One large piece of white paper was set on the back of column for better image processing condition. The cameras started to record the video before the aeration valve was opened. The column aeration rate was fixed to 0.1 m3/h and the flotation time was 50 s. The total number of images captured for a given frother dosage is 1500 (30 ⁄ 50) images of the top froth surface and 1450 (29 ⁄ 50) images of the column side. During the flotation, no adding water or wash water were applied. The concentrates with water were weighed to calculate water recovery. All the concentrates and tailings were filtered and then were dried in an oven for 8 h at 70 °C. The flotation system was shown in Fig. 1. 2.3. Froth property measurements 2.3.1. Gray value Gray value measurement was once used to predict coal flotation performance, including ash content and froth mass flows rates by Hargrave et al. (1996). The gray level of an image is between 0 (black) and 255 (white). Hargrave et al. (1996) used the gray levels of 75 to 175 to discard the areas of light reflections and shadows. It was found that the gray level of the froth was significantly influenced by the amount of 63 lm clay present in the froth. However, in this research, gray values of all pixels with full range gray levels were used for statistical results. This is because the light reflections and shadows are actually related to the froth properties. Images of flotation froths were first cropped and then the average gray value was calculated using Matlab. When the average gray value was analyzed as a function of flotation time, frames obtained every second during the overflow time at each frother dosage were used. Then every 5 average gray values were averaged again to plot the figures to reduce the fluctuations. 2.3.2. Homogeneity for bubble size estimation Image processing methods are usually used to extract the bubble size on the top of froth by programming or using software (Aldrich et al., 1997; Forbes, 2007). Watershed segmentation (Sadr-kazemi and Cilliers, 1997) and valley edge detection method (Yang et al., 2009; Wang et al., 2013) are commonly used algorithms to segment the images. Softwares such as VisioFroth (Bailey et al., 2005; Runge et al., 2007; Zanin et al., 2009; Kurniawan et al., 2011; Wang and Peng, 2013) and SmartFroth (Morar et al., 2012b) are also widely applied. In addition, other methods such as electro-resistivity or conductivity method (Xie et al., 2004; Bhondayi and Moys, 2014) have also been tried to detect the bubble size in the froth. Normally, images should be pretreated and segmented by image processing methods before the bubble size distribution are

obtained. The light spots on the top of the bubbles with a large gray value and the shadows between the bubbles with a small gray value are usually used to segment the froth image. However, the practical images of coal flotation were difficult to segment even contrast enhancement and filtering were applied to pretreat the images. Examples of practical images are shown in Fig. 2. Actually, irregular shapes of both dark and light colors could be seen on the surface of bubbles in most of the froth images. Some part of the bubble surface was even transparent and the bubbles below could be seen as shown in Fig. 2. Therefore, the texture features were chosen to represent the bubble size in this research as a statistical method. Texture is the correlation of gray level of adjacent pixels. Froth texture features are often extracted by Gray Level Co-occurrence Matrix, Neighbouring Grey Level Dependence Matrix, Wavelet Transform Analysis, Fast Fourier Transforms and so on (Haralick et al., 1973; Moolman et al., 1994, 1995a, 1995b; Liu et al., 2002a, 2002b, 2005; Bartolacci et al., 2006; Marais and Aldrich, 2011). In this research, homogeneity was used to estimate the bubble size. Homogeneity is one of the properties of the gray-level cooccurrence matrix (GLCM). The gray-level co-occurrence matrix is also known as the gray-level spatial dependence matrix and obtained by calculating how often a pixel with the intensity (gray-level) value i occurs in a specific spatial relationship to a pixel with the value j. The probability can be represented as P(i, j, d, h), where d and h are the distance and angle between the two pixels. If an image has g gray levels, then the density functions can be represented as g  g matrices. Each element (i, j) in GLCM specifies the number of times that the pixel with value i occurred with a certain d and h to a pixel with value j. One simple example is shown in Fig. 3 to illustrate the corresponding relations when the GLCM is created. The 3  3 matrix is the gray levels from an image. The angle is 0 and the distance is 1. The values in the matrix are scaled into 8 gray levels, defined as 1–8. The gray levels pair of 7 and 8 occurs twice, so the element in the GLCM on the right is 2 where i = 7 and j = 8. The empty boxes in the 8  8 matrix are zeros. Then the GLCM could be normalized as follows so that the sum of its elements is equal to 1:

2

0 0 0 0

60 6 6 60 6 60 6 6 60 6 60 6 6 40 0

0

0

0

0

7 7 7 7 7 0 0 0 0:1667 0 7 7 7 0 0:1667 0 0 0 7 7 0 0:1667 0 0:1667 0 7 7 7 0 0 0 0 0:3333 5 0 0 0 0 0

0 0 0

0

0

0

0

0 0 0

0

0

0

0

0 0 0 0 0 0 0 0 0 0

3

Homogeneity is one of the statistics derived from GLCM and measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal. The formula of homogeneity is:

Homogeneity ¼

X i;j

pði; jÞ 1 þ ji  jj

ð2Þ

The homogeneity of the example can be calculated as follows:

Homogeneity ¼

0:1667 0:1667 0:1667 þ þ 1 þ j4  7j 1 þ j5  5j 1 þ j6  5j 0:1667 0:3333 þ þ 1 þ j6  7j 1 þ j7  8j

¼ 0:54 Fig. 1. Flotation experiments system (1 – XFD flotation cell; 2 – flotation column; 3 – camera on the side; 4 – camera above; 5 – LED lights; 6 – background paper; 7 – iron shelf; 8 – flowmeter and valve; 9 – air pump).

ð3Þ

The range of homogeneity is from 0 to 1. Homogeneity is 1 for a diagonal GLMC, which indicates that the image is extremely homogeneous. Homogeneity should increase with the bubble size.

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Fig. 2. Practical images of coal flotation froths.

Fig. 3. The corresponding relations when the GLCM is created.

In this research, the homogeneity was obtained by Matlab. The homogeneity at different flotation time was calculated as the average homogeneity from three frames every second during the time period, while the homogeneity at different frother dosages was averaged by the 20 frames obtained every second during the first 20 s after overflow. 2.3.3. Bubble burst parameters The images were displayed frame by frame after the froth began to overflow. Bubbles bursting or coalescence were observed as bubbles became bigger. When the bubbles burst in one frame, bubble parameters were obtained from the previous frame, such as burst bubble size, volume and the number of the burst bubbles. The bubble size was obtained by reading the two horizontal pixels with the longest distance of the burst bubble. Then, the pixels were converted into actual distance. The burst bubble volume was taken as hemisphere to estimate. Burst fraction indicated the ratio of the total burst volume to the whole air volume introduced in the column during the overflow period, represented as follows:

V burst Burst fraction ¼ ¼ Arate  t

Pn

1 i¼1 2

 43  p  Arate  t

2.3.4. Height over weir The height over weir was usually used in calculating air recovery (Hadler et al., 2010, 2012; Qu et al., 2013; Park and Wang, 2015). It was usually measured using image processing software or laser distance meter. The height over weir was also obtained by image processing using Matlab in this research. The images were obtained from the video first. Then the images were cropped and converted from the truecolor RGB images into the grayscale intensity images. The Find function of Matlab was applied to return the place of the pixels on the interface of the froth surface and the background. The height over weir at the center of the overflowing weir was used to present the height variation during the flotation process. At last, data correction by video observation was used to ensure the data accuracy. In this research, the height data was obtained every second to plot the figure. Since the starting time of overflowing for each experiment was different, the froth height over weir was analyzed using the 20 frames extracted every second during the first 20 s after overflowing.

 3 di 2

ð4Þ

where Vburst is the total burst volume (mm3), Arate is the aeration rate (mm3/s), t is the flotation time during the overflow (s), n is the number of the bubbles burst in time t and di (mm) is the bubble size of different burst bubbles. Since the burst parameters are variables of the overflowing froth, the variables were extracted by the images frame by frame from the beginning to the end of the overflow.

3. Results and discussion 3.1. Flotation results The flotation experiments were conducted at different frother dosages and froth depths. The froth depth refers to the distance between the levels of the overflow weir and the pulp before flotation. The results were shown in Fig. 4.

J. Tan et al. / Minerals Engineering 92 (2016) 9–20

Fig. 4(a) shows that the ash content and yield increase with the frother dosage when the froth depth is 19.5 mm. Frother can prevent the bubble coalescence and enhances the froth stability (Barbian et al., 2003; Farrokhpay, 2011). It is also found that the water recovery increases with the frother dosage, which is proportional to the ash content. This is consistent with the findings of many researchers, namely the entrained gangue minerals in the concentrate increase with the water recovery and the correlation between the entrainment and the water recovery shows a linear trend (Neethling and Cilliers, 2002, 2009; Neethling et al., 2003; Zheng et al., 2006b; Liu and Peng, 2014; Wang et al., 2015). However, for the froth depth of 69.5 mm in Fig. 4(b), the ash content, yield and water recovery are lower. Deeper froth has longer froth retention time and lower froth recovery (Tao et al., 2000). The bubble burst and coalescence occurs more frequently, which results in the detachment of particles and enhances the froth drainage. It should also be noted that the concentrate ash content, yield and water recovery in Fig. 4(b) first reach the maximum and then slightly decrease. This may be caused by the decrease of froth stability beyond the frother critical concentration (Qu et al., 2013). The ash content, yield and water recovery in Fig. 4 (b) get their maximums at 82 g/t frother dosage, while in Fig. 4(a) they keep increasing. 3.2. Related parameters based on froth images 3.2.1. Gray value Several gray images of different frother dosages, flotation time and average gray value were shown in Fig. 5. Low gray value indicates dark froth with more low ash content coal particles attached,

13

while the high gray value represents the bright froth with more water and high ash clay minerals in the froth. Fig. 5 indicates that the gray value increases with the frother dosage and the flotation time. The gray values of froth images as a function of flotation time are shown in Fig. 6. It is found that the gray value increases with the flotation time in Fig. 6(a) when the froth depth is 19.5 mm. The dark coal particles with low ash content are easy to float so they overflow first. Afterward, particles with higher ash content continued to overflow and the gray value of froth images increased. The gray value at 27 g/t frother dosage increases slowly with flotation time in Fig. 6(a), which indicates that the flotation rate is the slowest. The gray value at 27 g/t frother dosage is also the lowest, which is caused by the slow flotation rate of the dark floatable materials. The froth was the darkest with less high ash particles and water content. This is consistent with the lowest concentrate ash content in the flotation results. It is also found that the flotation rate at 82 g/t frother dosage is the fastest with the highest gray value in the first 20 s. This is consistent with the frother critical concentration found in the flotation results of the froth depth of 69.5 mm in Fig. 4(b). However, the flotation results of the froth depth of 19.5 mm in Fig. 4(a) shows that the yield and ash content kept increasing and the maximum is obtained at 206 g/t frother dosage. This is because the gangue minerals continuously overflowed due to the high frother concentration remained in the slurry, which is interpreted by the continuously increasing gray value at 206 g/t frother dosage after 20 s. For the deeper froth in Fig. 6(b), the gray value at the frother dosage of 82 g/t is almost the maximum, which is also consistent with the flotation results in Fig. 4(b). The deeper froth means the

Fig. 4. Flotation results at different frother dosages (materials: 60 g of coal and 1 L of tap water; collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s).

Fig. 5. The gray images of different frother dosages, flotation time and average gray value (from left to right: A: 27 g/t, 20 s, 79; B: 55 g/t, 10 s, 92; C: 55 g/t, 20 s, 139; D: 82 g/t, 20 s, 153).

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Fig. 6. The gray value of froth images at different frother dosages and froth heights (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; gray value: average gray value of all pixels of the cropped froth images during the overflow period).

longer froth retention time, which enhances the drainage and reduces the entrainment. Hence, lower water content and less entrainment contribute to the slowly increased gray value of the deeper froth. Fig. 7 shows the correlation between the gray value and the concentrate ash content at different frother dosages. The gray value was obtained by averaging the gray values every second during the overflow period at each frother dosage. The gray value and the ash content at the froth depth of 19.5 mm simultaneously increase with the increasing frother dosage. While both the gray value and the ash content first increase and then slightly decrease at the froth depth of 69.5 mm. It could be concluded that the gray value correlates with the concentrate ash content very well. 3.2.2. Homogeneity for bubble size estimation The images randomly obtained at different flotation time under the condition of 82 g/t frother dosage and 19.5 mm froth depth are shown in Fig. 8. The bubble size increases with the flotation time. This can be explained by the fact that the frother concentration decreases as the floatable materials overflowed and the bubble bursting and coalescence occur more frequently. This size change in batch flotation is consistent with the research conducted by Citir et al. (2004).

Fig. 7. The correlation between the gray value and the concentrate ash content at different frother dosages (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; gray value: average gray value of all gray values every second during the overflow period).

The texture homogeneity as a function of offset at different flotation time is shown in Fig. 9. The offsets in horizontal direction are defined as [zeros (50,1) (1:50)0 ], namely offsets from [0,1], [0,2] to [0,50]. The distances are from 1 pixel to 50 pixels which are defined according to the bubble size range in the flotation image. The large value of the homogeneity obtained at the larger offset could indicate the larger bubbles on the froth. The offset value could be the measure of the bubble size, while the homogeneity represent how much the same gray levels exists with the distance of the offset. The results in Fig. 9(a) illustrate the bubble size distribution of the images in Fig. 8 very well. The texture homogeneity as a function of offset at 206 g/t frother dosage is shown in Fig. 9 (b). It is found that the bubble size stay very small along the flotation time of 50 s. This correlates with the flotation results in Fig. 4 (a) and the reason analysis in Fig. 6(a). The remained frother of high concentration causes the small bubble size and continuous overflowing froth with water and entrained particles, which contribute to the highest concentrate ash content at 206 g/t frother dosage. Texture homogeneity as a function of offset in the first 20 s after overflow is shown in Fig. 10. The homogeneity decreases with the increasing frother dosage in Fig. 10(a). Since frother can inhibit bubble coalescence, the smaller average bubble size is found at higher frother dosage. The decreasing homogeneity is correlated with the increasing concentrate ash content in the flotation results. For the froth depth of 69.5 mm in Fig. 10(b), the smallest homogeneity is found at the frother dosage of 82 g/t, which is consistently with the peak concentrate ash content in the flotation results. Fig. 11 shows the correlation between the homogeneity and the concentrate ash content at different frother dosages. The homogeneity was calculated by averaging the homogeneity values every second during the first 20 s after overflow at each frother dosage. Both the homogeneity and the concentrate ash content at the froth depth of 19.5 mm and 69.5 mm are negatively correlated. Above all, the homogeneity is shown to be a representative froth variable in concentrate ash content analysis. 3.2.3. Bubble burst parameters The number and size of the burst bubbles are shown in Fig. 12 (a) and (b). The number and size in y axis are the average burst number and size per second which are calculated every 8 s. The burst bubble number at 27 g/t frother dosage is the smallest, while the burst bubble size is the highest. The burst bubble number of 55 g/t and 82 g/t frother dosage decreases with the flotation time, while the bubble size increases with the time. It can be interpreted

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Fig. 8. The images obtained under the condition of 82 g/t frother dosage and 19.5 mm froth depth (images from left to right were selected randomly from the time of 18–20 s, 28–30 s, 38–40 s and 48–50 s).

(a)

(b)

1 18-20s 28-30s 38-40s 48-50s

0.9

18-20s 28-30s 38-40s 48-50s

0.9

0.8

Homogeneity

0.8

Homogeneity

1

0.7

0.6

0.5

0.7

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0.5

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0.4 0

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Horizontal Offset

20

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Horizontal Offset

Fig. 9. Texture homogeneity as a function of offset at different flotation time at the froth depth of 19.5 mm (frother: 2-octanol, a. 82 g/t and b. 206 g/t; collector: kerosene, 330 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; homogeneity: a statistic measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal and increases with the bubble size; horizontal offsets: offsets is a parameter of the graycomatrix which is a function in Matlab to create GLCM from image. Horizontal offsets represent the distances (from 1 pixel to 50 pixels) in horizontal direction used in creating GLCM).

(a)

(b)

1 27 g/t 55 g/t 82 g/t 206 g/t

0.9

27 g/t 55 g/t 82 g/t 206 g/t

0.9 0.8

Homogeneity

0.8

Homogeneity

1

0.7 0.6

0.7 0.6

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Horizontal Offset

0

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Horizontal Offset

Fig. 10. Texture homogeneity as a function of offset in the first 20 s after overflow at different frother dosage (froth depth: (a) h = 19.5 mm and (b) H = 69.5 mm; collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; homogeneity: a statistic measures the closeness of the distribution of elements in the GLCM to the GLCM diagonal and increases with the bubble size; horizontal offsets: Offsets is a parameter of graycomatrix which is the function in Matlab to create GLCM from image. Horizontal offsets represent the distances (from 1 pixel to 50 pixels) in horizontal direction used in creating GLCM).

by the insufficient frother concentration remained and the severe bubble coalescence. However, the number and size of the burst bubbles at the frother dosage of 206 g/t show a reverse rule. The number increases while the size decreases along with the flotation time. It can be illustrated by the fact that the frother concentration was overdosed at the beginning and then went down closely to the critical froth concentration.

The burst bubble size and concentrate ash content at different frother dosages and froth depths are shown in Fig. 13. It is found that the burst bubble size decreases with the increasing concentrate ash content and they are closely negatively correlated. The burst bubble is shown to be an appropriate froth variable relating to the concentrate ash content when the frother dosage is changing.

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Fig. 11. The correlation between the homogeneity and the concentrate ash content at different frother dosages (froth depth: (a) h = 19.5 mm and (b) H = 69.5 mm; collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; homogeneity: it was calculated by averaging the homogeneity values every second during the first 20 s after overflow at each frother dosage).

The burst volume was recorded at different time points during the whole flotation time. There are different ways to represent the burst volume as a function of time. The average burst volume per

second calculated by a short time range (every 2 s) can represent the fluctuation characteristics, while the average burst volume calculated by a long time range (every 8 s) can indicate the trend comparison of burst volume as shown in Fig. 14(a) and (b). The fluctuation of burst volume in Fig. 14(a) could be interpreted by the burst process. The peaks and valleys correspond to the coarsening and burst processes of bubbles on the top froth. The Fig.14(a) also shows that the fluctuation range decreases with the increasing frother dosage. The burst bubble size at lower frother dosage is larger after coalescence for many times and the bubble burst shows obvious synergistic effect due to the oscillation caused by one bubble as observed. The fluctuation range of burst volume becomes narrow as the burst bubble size decreases and the overflow velocity increases at higher frother dosages. The comparison of the burst volume at different frother dosages is shown in Fig. 14(b). The burst volume decreases with the frother dosage except for the burst volume at the frother dosage of 27 g/t. As the frother dosage increases, the froth should become more stable with less bubble burst. The water recovery in Fig. 4 also indicates that the froth become more stable as the frother dosage increases. The abnormal burst volume at low frother dosage is also found in Fig. 15. The burst fraction and concentrate ash content at different frother dosages and froth depths are shown in Fig. 15. Except the abnormal burst volume of 27 g/t frother dosage, the burst fraction decreases with the increasing frother dosage and negatively correlates with the concentrate ash content. The abnormal burst volume

Fig. 12. The number (a) and size (b) of the burst bubbles represented by the average of every 8 s (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; number and size: the number and average size of the burst bubbles during the overflow period).

Fig. 13. The burst bubble size and concentrate ash content at different frother dosages and froth depths (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; burst bubble size: the average size of the burst bubbles during the overflow period).

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Fig. 14. The burst volume represented by the average of every 2 s (a) and 8 s (b) (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; burst volume: The burst volume of the burst bubbles during the overflow period).

Fig. 15. The burst fraction and concentrate ash content at different frother dosages and froth depths (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; burst fraction: The ratio of the total burst volume to the whole air volume introduced in the column during the overflow period).

may be caused by the less water and fewer coarse particles in the froth as shown in Table 2. The froth with less water is relatively rigid with lower overflowing speed. Since fine particles with high hydrophobicity attached on the bubble could greatly prevent the froth from collapse for a very long time and coarse particles with high hydrophobicity could accelerate the froth collapse (Liang et al., 2015), the concentrates at the frother dosage of 27 g/t are with lower burst fraction. 3.2.4. Height over weir The froth height over weir of the first 20 s after overflowing is shown in Fig. 16. It is found that the height over weir in Fig. 16 (a) at 27 g/t frother dosage is obviously higher than the others and the fluctuation range is wide. It could be interpreted by the coalescence and burst of large bubbles on the top of the froth.

The fluctuation of the height over weir at 82 g/t and 206 g/t can be characterized by low fluctuation range and high frequency. The low fluctuation range indicates that the bubble size on the froth surface was very small due to the large frother dosage. The high frequency represents the high overflowing velocity as observed. Similar results can also be found when the froth depth is 69.5 mm. The fluctuation range of the height over weir could indicate the bubble size burst on the top of the froth to some extent, which correlates with the concentrate ash content. Hence, the sum of square is proposed to characterize the fluctuation range. It is interpreted by the sum of squares of the height difference between the positive and negative peaks. The sum of squares was calculated using the height peaks of the first 20 s after overflow and it is illustrated in Fig. 17 and Eq. (5).

Table 2 The yield of different size fractions in flotation concentrate. Frother (g/t)

Yield (%) h = 19.5 mm

27 55 82 206

H = 69.5 mm

500–250 lm

250–74 lm

74 lm

500–250 lm

250–74 lm

74 lm

0.73 12.34 16.89 16.99

5.87 23.02 24.39 23.68

10.34 23.26 25.82 34.70

0.65 10.41 14.78 14.27

2.54 17.52 19.60 19.44

5.79 19.39 22.39 20.52

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Fig. 16. The height over weir at different frother dosages and froth heights (collector: kerosene, 330 g/t; frother: 2-octanol, 27 g/t  206 g/t; aeration rate: 0.1 m3/h; flotation time: 50 s; height over weir: The height between the column weir and the center of the top froth surface).

Fig. 17. The calculation of sum of squares illustrated by the overflow weir and the curve of the height over weir.

2

2

Sum of squares ¼ ðh1  h2 Þ þ ðh2  h3 Þ þ . . . 2

þ ðhm2  hm1 Þ þ ðhm1  hm Þ

2

ð5Þ

h is the peak height over weir and m is the number of the peaks in the first 20 s after overflow. The sum of squares after calculation is shown in Table 3. The sum of squares decreases with the increasing frother dosage with the froth depth of 19.5 mm. Small sum indicates small burst bubble size, less coalescence, as well as high concentrate ash content. But the sum of squares at the frother dosage of 27 g/t is not the case. Although the burst bubble size (fluctuation range) of 27 g/t is larger as the average height shows, the bad mobility (fluctuation frequency) seems to dominate the results. The sum of squares is the result of combined effects of both burst bubble size and overflowing velocity. Therefore, the average height is also calculated to provide additional information to explain the results in Table 3. Similar results are also found when the froth height is 69.5 mm. It is notable that the sum of square at 206 g/t frother dosage is not in accord with the ash content. Just as the case of the frother dosage of 27 g/t, the ash content at 206 g/t frother dosage is not the highest due to the higher average height over weir, which indicates more bubble coalescence compared with that of 82 g/t frother dosage. The sum of square is very sensitive to the concentrate with moderate ash content as shown in Table 3, namely a very large value of the sum of square. The value of the sum of square could dramatically decrease by the smaller burst bubble size with higher concentrate ash content or slower overflow velocity with lower concentrate ash content.

Table 3 The sum of squares and the average height in different operation conditions. Frother (g/t)

h = 19.5 mm Sum of squares (mm2)

Average height (mm)

27 55 82 206

225 600 164 145

38 26 23 22

Frother (g/t)

H = 69.5 mm Sum of squares (mm2)

Average height (mm)

27 55 82 206

380 680 318 115

32 27 26 30

Besides, only Park and Wang (2015) studied the overflowing froth height separately as a function of time to analyze the air recovery. It was found that the air recovery, overflowing froth length and height would become stable within 10–30 s and the experimentally obtained air recovery had a large errorbar at 40 s. It is also in accordance with this study that the fluctuation range increases with the batch flotation time due to the increasing burst bubble size. 4. Conclusion The ash content of coal flotation concentrate was investigated at different frother dosages based on froth images in this research. Some variables of froth property related to the ash content were extracted and analyzed. The gray value could indicate the concentrate ash content, as well as the overflowing speed of floatable materials. The froth with high ash content particles has larger gray

J. Tan et al. / Minerals Engineering 92 (2016) 9–20

value due to more reflective spots with more water and entrained gangue minerals. The homogeneity was another froth variable closely correlated to concentrate ash content. This texture feature also characterized the bubble size well as the images of the coal flotation froth were not suitable for segmentation. The homogeneity increased with the increasing bubble size and the decreasing ash content. The bubble burst parameters were also used to analyze the flotation performance, including burst bubble size, burst bubble number, burst volume and burst fraction. The burst bubble size and burst fraction negatively correlated with the concentrate ash content as the frother dosage changes. The height over weir at different flotation time was also studied. The fluctuation range and frequency could indicate the burst bubble size and overflowing velocity to some extent. The sum of squares and the average height over weir were used to analyze the overflowing froth. The study on the correlations between concentrate ash content and froth properties based on froth images is very helpful to understand the flotation results and is of great importance for further flotation prediction and control. Acknowledgements This work was supported by Natural Science Foundation of China (Projects 51374205 and 51474213) and the Doctoral Foundation of Ministry of Education of China (Grant No. 20110095120021). We also want to thank the support of A Priority Academic Program Development of Jiangsu Higher Education Institutions. References Aktas, Z., Cilliers, J., Banford, A., 2008. Dynamic froth stability: particle size, airflow rate and conditioning time effects. Int. J. Miner. Process. 87 (1–2), 65–71. Aldrich, C., Moolman, D.W., Bunkell, S.J., Harris, M.C., Theron, D.A., 1997. Relationship between surface froth features and process conditions in the batch flotation of a sulphide ore. Miner. Eng. 10, 1207–1218. Aldrich, C., Marais, C., Shean, B.J., Cilliers, J.J., 2010. Online monitoring and control of froth flotation systems with machine vision: a review. Int. J. Miner. Process. 96, 1–13. Bailey, M., Gomez, C.O., Finch, J.A., 2005. Development and application of an image analysis method for wide bubble size distributions. Miner. Eng. 18, 1214–1221. Barbian, N., Ventura-Medina, E., Cilliers, J.J., 2003. Dynamic froth stability in froth flotation. Miner. Eng. 16, 1111–1116. Barbian, N., Hadler, K., Ventura-Medina, E., Cilliers, J.J., 2005. The froth stability column: linking froth stability and flotation performance. Miner. Eng. 18, 317– 324. Barbian, N., Hadler, K., Cilliers, J.J., 2006. The froth stability column: measuring froth stability at an industrial scale. Miner. Eng. 19, 713–718. Barbian, N., Cilliers, J., Morar, S., Bradshaw, D., 2007. Froth imaging, air recovery and bubble loading to describe flotation bank performance. Int. J. Miner. Process. 84, 81–88. Bartolacci, G., Pelletier Jr., P., Tessier Jr., J., Duchesne, C., Bossé, P.-A., Fournier, J., 2006. Application of numerical image analysis to process diagnosis and physical parameter measurement in mineral processes — Part I: Flotation control based on froth textural characteristics. Miner. Eng. 19, 734–747. Bhondayi, C., Moys, M.H., 2014. Measurement of a proxy for froth phase bubble sizes as a function of froth depth in flotation machines. Part 1. Theoretical development and testing of a new technique. Int. J. Miner. Process. 130, 8–19. Cao, B., Xie, Y., Gui, W., Wei, L., Yang, C., 2013. Integrated prediction model of bauxite concentrate grade based on distributed machine vision. Miner. Eng. 53, 31–38. Cheng, D., 2005. Detection of ash of coal by means of neutron induced prompt gamma-ray analysis. Master thesis, Northeast Normal University, China (in Chinese). Citir, C., Aktas, Z., Berber, R., 2004. Off-line image analysis for froth flotation of coal. Comput. Chem. Eng. 28, 625–632. Cole, K.E., Morris, G.D.M., Cilliers, J.J., 2010. Froth touch samples viewed with Scanning Electron Microscopy. Miner. Eng. 23, 1018–1022. Farrokhpay, S., 2011. The significance of froth stability in mineral flotation—a review. Adv. Colloid Interface Sci. 166, 1–7. Forbes, G., 2007. Texture and bubble size measurements for modelling concentrate grade in flotation froth systems. Ph.D. thesis, University of Cape Town. Hadler, K., Cilliers, J.J., 2009. The relationship between the peak in air recovery and flotation bank performance. Miner. Eng. 22, 451–455. Hadler, K., Smith, C.D., Cilliers, J.J., 2010. Recovery vs. mass pull: the link to air recovery. Miner. Eng. 23, 994–1002.

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