# Multi-Stage Flotation for the Removal of Ash from Fine Graphite Using Mechanical and Centrifugal Forces

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Size and Chemical Analyses

_{50}, d

_{80}, and d

_{90}values for the graphite sample were determined as 25.52 µm, 43.65 µm, and 55.57 µm, respectively. Water, volatile, ash, and carbon content analyses were performed according to a previously described method for chemical analysis of graphite (air-dried basis; State Standard of the People’s Republic of China: GB/T 3521-2008).

#### 2.3. Mineralogy of the Ore

#### 2.4. Mechanical Flotation Tests

_{g}) was 0.70 cm/s, which defined as the volumetric air flow rate per unit cross-section. In each flotation test, tap water was added to maintain a constant pulp level and a froth layer of 1 cm. Kinetic study was carried out to select suitable flotation time. Following a flotation kinetic study where a maximum plateau was reached at 3-min flotation, the pulp was floated for 3 min. A detailed description of the working process of the mechanical flotation cell is reported in the literature [31]. User-Defined Design (Expert-design 8.0, Stat-Ease Inc., Minneapolis, MN, USA) software was employed. Experimental conditions, including the collector dosage (Factor A), frother dosage (Factor B), and pulp density (Factor C) of the mechanical flotation cell are presented in Table 2.

#### 2.5. Column Flotation Tests

## 3. Results and Discussion

#### 3.1. Characterization

_{90}of 56 µm.

#### 3.2. Mechanical Flotation Cell Tests

#### 3.2.1. Rougher Flotation

#### 3.2.2. Multi-Stage Flotation

#### 3.3. Flotation Column Tests

#### 3.3.1. Rougher Flotation

#### 3.3.2. Multi-Stage Flotation

^{2}centrifugal force was re-cleaned in multi-stage flotation circuits using a flotation column. The effects of the pulp density of the Cleaner 1 flotation process on the concentrate of the multi-stage flotation circuits are listed in Table 5.

#### 3.4. Comparison of Flotation Separation Efficiencies

_{C}is as follows [39]:

_{C}is the grade of valuable material reporting to the concentrate; G

_{Max}is the mass fraction of valuable material in the floatable component; G

_{NF}is the mass fraction of valuable material in the non-floating component; G

_{T}is the grade of valuable material in the tank (or in the tailing from the tank); b is a dimensionless parameter.

_{Max}, G

_{NF}, and b were determined from fitting Equation (1) to the experimental results of the mechanical flotation cell and flotation column.

_{Max}) and the grade of the non-floating component (G

_{NF}) were virtually identical for the two flotation devices. It is expected that the type of flotation device does not have an impact on the flotability of the ore. The ratio of entrainment to true flotation (b) when using the flotation column (0.0014–0.0018) was much smaller than that obtained when a mechanical flotation cell was employed (0.0291–0.0409) at the similar level of the pulp density of the Cleaner 1 flotation process. Hence, it was concluded that the use of the flotation column exhibited a reduction of entrainment and enlargement of true flotation compared with the mechanical flotation cell.

## 4. Conclusions

_{90}value of 55.57 µm.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A. Analysis of Variance (ANOVA)

_{i}is the model prediction for the ith observation and n is the number of observations. The model mean square is the average squared error for the observation data or the sum-of-squares divided by the number of observations:

^{2}values of 0.98 and 0.93, respectively. Joglekar and May [40] suggested that for a good model fit, the coefficient of determination should be ≥0.8. Therefore, we concluded that the predicted values fitted the observed values reasonably well and thus, that Equations (A1) and (A2) fitted the experimental data listed in Table 2.

Statistics | Yield | Ash Content |
---|---|---|

Sum of square | 1882.89 | 16.07 |

Degree of freedom | 6 | 6 |

Mean sum of square | 313.82 | 2.68 |

R^{2} | 0.98 | 0.93 |

F-value | 13.26 | 48.72 |

Prob > F | <0.0001 | <0.0001 |

## Appendix B. Calculation of the Centrifugal Acceleration in the Flotation Column

_{cen}) in the centrifugal force field is described as:

_{t}(r) represents the tangential speed at column radius r. The tangential speed was calculated from:

_{pipe}is the inside diameter of the circulating pipe; P

_{cir}is the measured circulation pressure; P

_{hydro}is the hydrostatic pressure of the entrance to the centrifugal force field; ρ is the density of the slurry; S is resistance coefficient of the circulation pipe; L is the length of the pipe between the measuring point and the outlet of the pipe in the centrifugal field; and g is the gravitational acceleration. The resistance coefficient of the pipe is evaluated by Manning’s formula [41]:

P_{cir} (10^{6} Pa) | J_{g} (cm/s) | V_{t} (r = D/2) (m/s) | a_{cen} (m/s^{2}) | Values of Parameters | ||
---|---|---|---|---|---|---|

0.12 | 0.71 | 6.87 | 945 | D (mm) | P_{hydro} (Pa) | L (m) |

0.14 | 0.99 | 7.52 | 1130 | 100 | 17,640 | 0.5 |

0.16 | 1.16 | 8.11 | 1314 | D_{pipe} (mm) | ρ (g/cm^{3}) | n (µm) |

0.18 | 1.45 | 8.66 | 1499 | 13 | 1.5 | 12 |

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**Figure 5.**Response surface plots illustrating the interaction effects of the parameters on the ash content of the concentrate during rougher flotation in the mechanical flotation cell.

**Figure 6.**Effects of centrifugal acceleration (

**a**) 20 cm froth depth and froth depth (

**b**) 1130 m/s

^{2}centrifugal force on rougher flotation performance of the flotation column.

**Figure 7.**Comparisons of flotation separation efficiency between the mechanical flotation cell and flotation column.

Sample | Size (µm) | Concentrate FC_{ad} (%) | Flotation Machine | No. of Stages | Reference |
---|---|---|---|---|---|

Chotanagarpur (India) | <144 | 88.30 | C-I | 5 | [25] |

88.00 | C-II | 2 | |||

Um Qureia (Egypt) | >45 | 79.60 | C-I | 4 | [26] |

78.60 | C-II | 2 | |||

<45 | 45.20 | C-I | 4 | ||

46.10 | C-II | 2 | |||

Rajunagfena (India) | <210 | 79.00 | C-I | 6 | [27] |

80.10 | C-II | 2 | |||

Jharkhand (India) | <186 | 39.45 | C-I | 1 | [28] |

<144 | 89.65 | C-II | 3 |

_{ad}(%) = % fixed carbon in the concentrate (air-dried basis).

**Table 2.**Levels of factors A, B, and C together with experimental and predicted results of the mechanical flotation cell.

Run | Level of Factors | Yield (%) | A_{ad} (%) | ||||
---|---|---|---|---|---|---|---|

A (g/t) | B (g/t) | C (g/L) | Observed (S.D.) | Predicted | Observed (S.D.) | Predicted | |

1 | 500 | 125 | 90 | 50.00 (1.24) | 61.73 | 10.86 (0.16) | 10.88 |

2 | 1000 | 250 | 90 | 70.46 (0.24) | 66.53 | 10.90 (0.24) | 10.95 |

3 | 2000 | 500 | 90 | 80.03 (1.91) | 74.98 | 11.06 (0.27) | 11.10 |

4 | 3000 | 1000 | 90 | 79.34 (0.51) | 80.30 | 10.77 (0.08) | 10.94 |

5 | 3000 | 1500 | 90 | 83.41 (1.44) | 81.90 | 11.18 (0.21) | 11.34 |

6 | 3000 | 750 | 270 | 83.41 (0.73) | 81.90 | 11.35 (0.27) | 11.24 |

7 | 3000 | 3000 | 90 | 83.41 (0.88) | 81.90 | 11.35 (0.11) | 11.24 |

8 | 3000 | 750 | 360 | 84.37 (0.32) | 83.08 | 11.35 (0.28) | 11.24 |

9 | 3000 | 750 | 180 | 90.31 (0.13) | 86.68 | 11.89 (0.25) | 11.54 |

10 | 3000 | 750 | 60 | 90.37 (0.70) | 85.46 | 12.05 (0.22) | 12.15 |

11 | 3000 | 750 | 90 | 90.81 (0.67) | 92.59 | 12.2 (0.16) | 12.14 |

12 | 3000 | 750 | 90 | 93.74 (0.28) | 91.47 | 12.59 (0.06) | 13.05 |

13 | 3000 | 750 | 90 | 94.97 (0.96) | 96.26 | 14.21 (0.07) | 13.95 |

14 | 5000 | 2500 | 180 | 88.86 (2.24) | 91.13 | 11.53 (0.04) | 11.5 |

15 | 5000 | 2500 | 180 | 93.02 (0.48) | 96.03 | 12.41 (0.14) | 12.59 |

16 | 5000 | 1667 | 180 | 93.57 (0.67) | 96.70 | 12.52 (0.21) | 12.59 |

17 | 5000 | 1250 | 90 | 93.60 (1.57) | 96.70 | 13.04 (0.16) | 12.73 |

18 | 7000 | 3500 | 180 | 91.25 (1.85) | 94.22 | 11.66 (0.12) | 11.72 |

19 | 7000 | 2333 | 180 | 94.65 (1.54) | 95.47 | 13.11 (0.15) | 13.31 |

20 | 7000 | 1750 | 90 | 94.67 (0.83) | 89.24 | 13.26 (0.04) | 13.09 |

Fixed Carbon | Ash | Water | Volatile Matter |
---|---|---|---|

80.90 | 15.43 | 0.43 | 3.42 |

**Table 4.**Effect of pulp density of the Cleaner 1 flotation process on the concentrate of the multi-stage flotation circuits using a mechanical flotation cell (%).

Flotation Circuit | Pulp Density of the Cleaner 1 Flotation Process (g/L) | |||||||
---|---|---|---|---|---|---|---|---|

150 | 100 | 50 | 25 | |||||

Yield (S.D.) | A_{ad} (S.D.) | Yield (S.D.) | A_{ad} (S.D.) | Yield (S.D.) | A_{ad} (S.D.) | Yield (S.D.) | A_{ad} (S.D.) | |

Rougher | 93.02 (3.92) | 12.24 (0.22) | 93.22 (3.11) | 12.30 (0.06) | 93.22 (2.75) | 12.25 (0.09) | 93.22 (0.54) | 12.29 (0.18) |

Cleaner 1 | 81.7 (3.96) | 10.99 (0.04) | 83.56 (0.3) | 10.61 (0.23) | 79.83 (0.30) | 9.85 (0.16) | 67.39 (2.18) | 9.38 (0.06) |

Cleaner 2 | 70.78 (3.4) | 9.71 (0.09) | 76.72 (5.5) | 9.77 (0.14) | 64.50 (5.3) | 8.85 (0.29) | 43.92 (2.95) | 7.98 (0.14) |

Cleaner 3 | 61.08 (0.57) | 8.84 (0.24) | 70.26 (4.41) | 9.19 (0.29) | 47.70 (1.21) | 8.06 (0.01) | ||

Cleaner 4 | 53.66 (5.49) | 8.38 (0.01) | 61.78 (1.64) | 8.74 (0.17) | 26.83 (3.21) | 7.24 (0.20) | ||

Cleaner 5 | 45.83 (1.62) | 8.01 (0.09) | ||||||

Cleaner 6 | 39.63 (2.00) | 7.81 (0.20) |

Flotation Circuit | Pulp Density of the Cleaner 1 Flotation Process (g/L) | |||
---|---|---|---|---|

60 | 30 | |||

Yield | A_{ad} | Yield | A_{ad} | |

Rougher | 94.53 (2.10) | 11.52 (0.15) | 94.27 (0.37) | 11.39 (0.28) |

Cleaner 1 | 93.33 (0.92) | 10.67 (0.02) | 92.00 (2.17) | 9.87 (0.25) |

Cleaner 2 | 92.41 (4.62) | 10.12 (0.28) | 89.97 (1.49) | 9.09 (0.02) |

Cleaner 3 | 91.91 (1.60) | 9.89 (0.25) | 77.53 (1.99) | 7.97 (0.29) |

Cleaner 4 | 88.87 (0.52) | 9.10 (0.27) | ||

Cleaner 5 | 83.90 (1.05) | 8.53 (0.05) |

**Table 6.**Summary of the parameters from Equation (1) as fitted to the data in Figure 7.

Parameter | Pulp Density of the Cleaner 1 Flotation Process (g/L) | |||||
---|---|---|---|---|---|---|

Mechanical Flotation Cell | Flotation Column | |||||

150 | 100 | 50 | 25 | 60 | 30 | |

G_{Max} | 0.97 | 0.96 | 0.94 | 0.96 | 0.92 | 0.92 |

G_{NF} | <0.001 | <0.001 | <0.001 | <0.001 | 0.13 | 0.14 |

b | 0.0454 | 0.0387 | 0.0291 | 0.0409 | 0.0014 | 0.0018 |

R^{2} | 0.80 | 0.94 | 0.60 | 0.95 | 0.98 | 0.99 |

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**MDPI and ACS Style**

Bu, X.; Zhang, T.; Peng, Y.; Xie, G.; Wu, E.
Multi-Stage Flotation for the Removal of Ash from Fine Graphite Using Mechanical and Centrifugal Forces. *Minerals* **2018**, *8*, 15.
https://doi.org/10.3390/min8010015

**AMA Style**

Bu X, Zhang T, Peng Y, Xie G, Wu E.
Multi-Stage Flotation for the Removal of Ash from Fine Graphite Using Mechanical and Centrifugal Forces. *Minerals*. 2018; 8(1):15.
https://doi.org/10.3390/min8010015

**Chicago/Turabian Style**

Bu, Xiangning, Tuantuan Zhang, Yaoli Peng, Guangyuan Xie, and Erdong Wu.
2018. "Multi-Stage Flotation for the Removal of Ash from Fine Graphite Using Mechanical and Centrifugal Forces" *Minerals* 8, no. 1: 15.
https://doi.org/10.3390/min8010015