# A Method of Ore Blending Based on the Quality of Beneficiation and Its Application in a Concentrator

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

_{2}O

_{3}), which is called “red ore” by the workers and is a high-grade ore. The green part not far away is rich in ferrous ions, including ferrous carbonate (FeCO

_{3}) and ferrous silicate (FeSiO

_{3}). This part is challenging to beneficiate and is called “green ore” by the workers. Above them, the black part of the ore is mainly composed of iron tetroxide (Fe

_{3}O

_{4}). Workers call it magnetic iron, which is a very high-quality raw material. These ores are concentrated in one mining site, which shows that the nature of the ore on site is very complicated. This kind of complex raw ore leads to high real-time requirements for ore blending.

#### 2.1. Constraints on Ore Blending

_{2}O

_{3}and Fe

_{3}O

_{4}, LQC is FeCO

_{3}and FeSiO

_{3}. The MPV refers to the minimum production volume at each ore mining site. The geological reserves refer to the maximum amount of each ore that can be produced.

#### 2.2. ABC-BPNN Model

_{j}

^{max}and X

_{j}

^{min}are the upper bound and lower bound of the optimization problem. $\delta $ is a random number uniformly distributed between (0, 1).

_{i}to generate candidate solution V

_{i}according to the following formula. If V

_{i}is better than X

_{i}, replace it.

_{i}is the fitness function of food source X

_{i}, which is proportional to food source quality. That is, the greater fitness value of a food source, the higher probability of selection by onlookers. When the onlooker selects the food source, it is updated according to Equation (2).

#### 2.2.1. Data Preprocessing

#### 2.2.2. Describing Function

_{i}is the amount of ore produced at the mine outlet of No.i.

#### 2.2.3. Normalization

_{max}is the maximum value of the input data, and P

_{min}is the minimum value of the input data.

#### 2.2.4. Fitting and Saving Function

_{i}, O

_{i}); i = 1, 2, …, n be the training subset with size n, the MSE is calculated as follows.

_{i}is the actual output of the ith sample, d

_{i}is the predicted value of the ith sample.

#### 2.3. Optimization Model

- (1)
- Performance Index:$$\mathrm{min}\left(|{J}_{f}\left({X}_{i}\right)-\epsilon |\right),i=1,2,\cdots ,m$$$$\mathrm{max}{Z}_{l}\left({X}_{i}\right),i=1,2,\cdots ,m$$
- (2)
- Constraints:
- (a)
- Raw Ore Constraints$${J}_{f}\left({X}_{i}\right)=f\left[h\left({X}_{i}\right),k\left({X}_{i}\right),l\left({X}_{i}\right)\right],{X}_{i}\in {\rm Z}$$$${M}_{c}={\displaystyle \sum _{i=1}^{m}{X}_{i}}={W}_{r}$$$$MP{V}_{i}={x}_{i\mathrm{min}}\le {x}_{i}\le {x}_{i\mathrm{max}}=G{R}_{i}$$
- (b)
- Mixed ore properties constraints$${h}_{\mathrm{min}}\left({X}_{i}\right)\le h\left({X}_{i}\right)\le {h}_{\mathrm{max}}\left({X}_{i}\right)$$$${k}_{\mathrm{min}}\left({X}_{i}\right)\le k\left({X}_{i}\right)\le {k}_{\mathrm{max}}\left({X}_{i}\right)$$$${c}_{\mathrm{min}}\left({X}_{i}\right)\le c\left({X}_{i}\right)\le {c}_{\mathrm{max}}\left({X}_{i}\right)$$

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Maximum Training | Learning Rate | Minimum Error | Number of Input | Number of Output |
---|---|---|---|---|

2500 | 0.1 | 0.0001 | 3 | 1 |

Test Error | Training Error |
---|---|

0.0788 | 0.0309 |

Algorithm | Mean | SD |
---|---|---|

ABC-BP | 76.0725 | 0.0309 |

PSO-BP | 77.1132 | 0.0421 |

NA-BP | 75.8654 | 0.0674 |

No | Ore Grade T (%) | Iron Content M (%) | High Quality Content G (%) | Low Quality Content B (%) | Minimum Production Volume (Unit) | Geological Reserves (Unit) |
---|---|---|---|---|---|---|

1 | 34.54 | 20.32 | 18.24 | 4.31 | 0 | 100 |

2 | 29.26 | 15.48 | 12.87 | 4.25 | 0 | 100 |

3 | 32.03 | 3.21 | 0 | 3.17 | 0 | 100 |

4 | 31.87 | 2.50 | 0 | 2.56 | 0 | 100 |

Total Ore (Unit) | Concentrate Recovery (%) | Upper Grade of Ore (%) | Lower Grade of Ore (%) | Upper of High Quality (%) | Lower of High Quality (%) | Upper of Low Quality (%) | Lower of Low Quality (%) |
---|---|---|---|---|---|---|---|

100 | 73.8 | 33 | 29 | 12 | 9 | 4.5 | 3 |

Modeling Method | Mining No.1 | Mining No.2 | Mining No.3 | Mining No.4 | Ore Dressing Index |
---|---|---|---|---|---|

Original method | 16 | 24 | 32 | 28 | 79.45 |

This method | 27 | 27 | 31 | 15 | 82.35 |

No. | Ore Dressing Index | Result |
---|---|---|

1 | >80 | Excellent |

2 | 70–80 | Good |

3 | 60–70 | Qualified |

4 | 50–60 | Relatively poor |

5 | 40–50 | Poor |

6 | <40 | Unavailable |

ODI | Concentrate Grade | Tailing Grade | Concentration Ratio | Cost (CNY/t) |
---|---|---|---|---|

Excellent | 67.5% | 7.5–8.5% | 2.93–3.03% | 383 |

Good | 67.5% | 8.5–9.5% | 3.03–3.14% | 407 |

Qualified | 67.5% | 9.5–10.5% | 3.14–3.26% | 447 |

Relatively poor | 67.5% | 10.5–11.5% | 3.26–3.39% | 511 |

Poor | 67.5% | 11.5–13.5% | 3.39–3.72% | 609 |

Unavailable | 67.5% | More than 13.5% | More than 3.72% | 796 |

Scheme | Mining No.1 | Mining No.2 | Mining No.3 | Mining No.4 | Mining No.5 | Mining No.6 | Mining No.7 | Mixed Ore Grade (%) | Profit (CNY) |
---|---|---|---|---|---|---|---|---|---|

Method 1 | 41 | 24 | 15 | 6 | 14 | 2 | 5 | 54.30 | 46.00 |

Method 2 | 50 | 24 | 6 | 6 | 15 | 2 | 5 | 54.08 | 50.24 |

Method 3 | 41 | 24 | 15 | 6 | 14 | 2 | 5 | 54.56 | 45.04 |

Method 4 | 50 | 24 | 6 | 6 | 15 | 2 | 5 | 54.36 | 49.64 |

This method | 50 | 20 | 5 | 5 | 13 | 2 | 4 | 54.22 | 58.11 |

Scheme | Mining No.1 | Mining No.2 | Mining No.3 | Mining No.4 | Mining No.5 | Mining No.6 | Mining No.7 | Mining No.8 | Mining No.9 | Mixed Ore Grade (%) | Profit (CNY) |
---|---|---|---|---|---|---|---|---|---|---|---|

Method 1 | 41 | 24 | 0 | 15 | 0 | 6 | 14 | 2 | 5 | 54.30 | 94.12 |

Method 2 | 50 | 24 | 0 | 6 | 0 | 6 | 15 | 2 | 5 | 54.08 | 102.71 |

Method 3 | 41 | 0 | 24 | 15 | 0 | 6 | 14 | 2 | 5 | 54.56 | 93.49 |

Method 4 | 50 | 0 | 24 | 6 | 0 | 6 | 15 | 1 | 5 | 54.36 | 102.35 |

Method 5 | 41 | 24 | 0 | 0 | 15 | 6 | 13 | 1 | 5 | 55.28 | 83.68 |

Method 6 | 50 | 24 | 0 | 0 | 6 | 6 | 14 | 2 | 5 | 54.51 | 98.85 |

This method | 46 | 23 | 3 | 6 | 3 | 6 | 14 | 2 | 4 | 54.18 | 112.10 |

Scheme | Mining No.1 | Mining No.2 | Mining No.3 | Mining No.4 | Mining No.5 | Mining No.6 | Mining No.7 | Mining No.8 | Mining No.9 | Mixed Ore Grade (%) | Profit (CNY) |
---|---|---|---|---|---|---|---|---|---|---|---|

Method 1 | 42 | 23 | 0 | 15 | 0 | 6 | 15 | 2 | 5 | 53.71 | 54.12 |

Method 2 | 42 | 32 | 0 | 6 | 0 | 6 | 15 | 2 | 5 | 54.03 | 59.83 |

Method 3 | 42 | 18 | 5 | 0 | 15 | 6 | 15 | 2 | 5 | 54.00 | 49.35 |

Method 4 | 42 | 29 | 3 | 0 | 6 | 6 | 15 | 2 | 5 | 54.01 | 57.94 |

This method | 36 | 26 | 3 | 13 | 2 | 5 | 14 | 2 | 4 | 54.15 | 67.36 |

Scheme | Mining No.1 | Mining No.2 | Mining No.3 | Mining No.4 | Mining No.5 | Mining No.6 | Mining No.7 | Mining No.8 | Mining No.9 | Mixed Ore Grade (%) | Profit (CNY) |
---|---|---|---|---|---|---|---|---|---|---|---|

Method 1 | 45 | 20 | 0 | 0 | 15 | 6 | 14 | 2 | 5 | 54.40 | 56.41 |

Method 2 | 45 | 0 | 20 | 0 | 15 | 6 | 14 | 2 | 5 | 54.63 | 56.09 |

Method 3 | 45 | 20 | 0 | 15 | 0 | 6 | 15 | 2 | 5 | 53.83 | 69.35 |

Method 4 | 45 | 0 | 20 | 15 | 0 | 6 | 15 | 2 | 5 | 54.04 | 68.92 |

This method | 35 | 27 | 1 | 13 | 5 | 6 | 13 | 2 | 4 | 54.21 | 80.27 |

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**MDPI and ACS Style**

Liu, B.; Zhang, D.; Gao, X.
A Method of Ore Blending Based on the Quality of Beneficiation and Its Application in a Concentrator. *Appl. Sci.* **2021**, *11*, 5092.
https://doi.org/10.3390/app11115092

**AMA Style**

Liu B, Zhang D, Gao X.
A Method of Ore Blending Based on the Quality of Beneficiation and Its Application in a Concentrator. *Applied Sciences*. 2021; 11(11):5092.
https://doi.org/10.3390/app11115092

**Chicago/Turabian Style**

Liu, Bingyu, Dingsen Zhang, and Xianwen Gao.
2021. "A Method of Ore Blending Based on the Quality of Beneficiation and Its Application in a Concentrator" *Applied Sciences* 11, no. 11: 5092.
https://doi.org/10.3390/app11115092