# Use of Discrete Element Modelling to Evaluate the Parameters of the Sampling Theory in the Feed Grade Sampler of a Sulphide Gold Plant

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## Abstract

**:**

## 1. Introduction

## 2. Configuration of the Sampler and Simulations

- Movement direction: perpendicular to the flow;
- Cutter aperture (A): 60 mm;
- Cutter edge angle (γ): 70°;
- Cutter angle (α): 60°;
- Cutter velocity (V
_{max}): 45 cm/s; - Solids feed rate: 73 t/h.

- The Young’s Modulus (or Loading Stiffness) for particles was 1 × 10
^{7}N/m^{2}, and for boundaries, 1 × 10^{11}N/m^{2}; - The constant adhesive model was used, and the adhesive distance was based on 1/2 particle diameter of the smallest group of particles;
- The restitution coefficient for all particles and all types of interactions was 0.3;
- The friction coefficient for particle/belt interactions was 0.7;
- The friction coefficient for particle/boundary interactions was 0.5.

## 3. Materials and Methods

- Bulk density;
- Particle density;
- Size distribution;
- Gold analysis by size;
- Internal friction angle;
- Repose angle;
- Moisture.

- Sliding friction coefficient;
- Rolling friction coefficient;
- Attractive force;
- Particle size;
- Particle shape.

- Cutter aperture (A);
- Cutter angle (α);
- Cutter edge angle (β);
- Cutter velocity (V
_{max}); - Solids feed rate in the sampler.

_{j}= (Mfg/Mft)/(Mig/Mit) × 100,

## 4. Results

#### 4.1. Physical Parameters Characterization

#### 4.2. Particle Interactions Calibration

^{2}= 96.61%) = 8.39 + 9.84 × A − 7.03 × B + 5.5 × C + 32.81 × A × B + 2.5 × A × C + 16.25 × B × C − 37.5 × A × B × C,

^{2}= 99.95%) = 20.79 + 8.98 × A + 13.36 × B + 6.42 × C − 2.34 × A × B − 11.72 × A × C − 10.47 × B × C + 79.69 × A × B × C,

^{2}= 98.14%) = 26.5 − 6.88 × A + 0.62 × B − 5.91 × C + 12.5 × A × B + 9.38 × A × C + 11.88 × B × C + 6.2 × A × B × C,

^{2}= 98.83%) = 25.39 + 1.72 × A + 17.34 × B + 3.97 × C + 20.3 × A × B + 2.81 × A × C − 3.44 × B × C + 9.4 × A × B × C,

#### 4.3. Simulations

#### 4.3.1. Cutter Aperture

#### 4.3.2. Cutter Angle

#### 4.3.3. Cutter Edge Angle

#### 4.3.4. Cutter Velocity

#### 4.3.5. Solids Feed Rate

## 5. Conclusions

- Cutter aperture (A): 4 times the diameter of the largest particle;
- Cutter angle (α): ≥50°;
- Cutter edge angle (γ): ≥50°;
- Cutter velocity (V
_{max}): ≤45 cm/s; - Solids feed rate in the sampler: All the simulations presented acceptable results for extraction ratio.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**AngloGold Ashanti CDS—Geographical location of the plant in Brazil (illustrative without scale).

**Figure 2.**Parameters for design samplers, adapted from [4].

**Figure 3.**3-D geometry of the of the cross-stream cutter installed plant feed stream (

**left**). Side view of the cutter as implemented in Rocky and real pictures of the cutter (

**right**): (

**a**) beginning (

**b**) middle (

**c**) end of cut.

**Figure 5.**Comparison between laboratory test and DEM simulatons using calibrated contact parameters (Solution 2): (

**a**) Lifting cylinder test, (

**b**) Shear box test, and (

**c**) Draw down test.

**Figure 7.**Close up view of the cutter in operation in two diferent DEM simulations. Particles’ velocity in cutter’s top: dark blue low velocity and light blue high velocity. (

**a**) Simulation 05: 4D; (

**b**) Simulation 01: 1D.

**Figure 8.**Top view of the system showing particles inside the cutter. Particles are colored according to their velocity being: dark blue low velocity and light blue high velocity. (

**a**) Simulation 05: 60°, (

**b**) Simulation 04: 50°, (

**c**) Simulation 03: 40°, (

**d**) Simulation 02: 30°, (

**e**) Simulation 01: 20°.

**Figure 11.**Snapshots of the DEM simulation of the case 03 (35°) showing the fines stuck in the slope of the cutter, red represents 2.5 mm particles and yellow represents 6.3 mm particles.

**Figure 12.**Snapshot of DEM simulations showing particles being dragged to the sample, coloured by particle size, with red being smallest (2.5 mm) and blue largest (15 mm).

Parameters | Level | |
---|---|---|

Low | High | |

Sliding friction coefficient | 0.1 | 0.9 |

Rolling friction coefficient | 0.1 | 0.9 |

Attractive force | 0.5 | 1.0 |

Levels | Cutter Aperture | Cutter Velocity | Cutter Angle | Cutter Edge Angle | Solids Feed Rate |
---|---|---|---|---|---|

mm | cm/s | ° | ° | t/h | |

1 | 15 (1D) | 45 | 20 | 1 | 60 |

2 | 22.5 (1.5D) | 60 | 30 | 20 | 73 |

3 | 30 (2D) | 75 | 40 | 35 | 90 |

4 | 45 (3D) | 90 | 50 | 50 | 105 |

5 | 60 (4D) | 105 | 60 | 70 | 120 |

Parameters | Unit | Value | Std. |
---|---|---|---|

Moisture (w.b.) | % | 2.30 | 0.16 |

Bulk density | g/cm^{3} | 1.70 | 0.10 |

Particles density | g/cm^{3} | 2.83 | 0.01 |

Repose angle (lifting cylinder test) | ° | 29 | 1.91 |

Internal friction angle (shear box test) | ° | 59 | 2.08 |

Repose angle (draw down test) | ° | 28 | 2.80 |

Internal friction angle (draw down test) | ° | 67 | 2.56 |

Group n° | Passing % | Size mm | Mass Distribution % | Gold Grade g/t |
---|---|---|---|---|

1 | 100 | 15.0 | 5% | 1.98 |

2 | 95 | 13.3 | 15% | 2.23 |

3 | 80 | 10.0 | 30% | 2.77 |

4 | 50 | 6.3 | 25% | 2.47 |

5 | 25 | 2.5 | 25% | 3.54 |

Response | Low Value | Target | High Value |
---|---|---|---|

Repose angle (lifting cylinder test) | 12° | 29° | 34° |

Internal friction angle (shear box test) | 25° | 59° | 90° |

Repose angle (draw down test) | 22° | 28° | 50° |

Internal friction angle (draw down test) | 28° | 67° | 70° |

Solution | Variables | Composed Desirability | ||
---|---|---|---|---|

Rolling Friction Coefficient | Sliding Friction Coefficient | Attractive Force | ||

1 | 0.89 | 0.61 | 0.72 | 0.79 |

2 | 0.69 | 0.90 | 0.58 | 0.78 |

3 | 0.62 | 0.90 | 0.60 | 0.76 |

Response | Target | Solution 1 | Solution 2 | Solution 3 |
---|---|---|---|---|

Repose angle (lifting cylinder test) | 29 | 32 | 30 | 40 |

Internal friction angle (shear box test) | 59 | 61 | 60 | 58 |

Repose angle (draw down test) | 28 | Material didn’t flow | 28 | 36 |

Internal friction angle (draw down test) | 67 | 66 | 65 |

Parameter | Lot | Sample | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Size (mm) | 2.5 | 6.3 | 10.0 | 13.3 | 15.0 | 2.5 | 6.3 | 10.0 | 13.3 | 15.0 |

Size distribution (%) | 25.0 | 25.0 | 30.0 | 15.0 | 5.0 | 25.3 | 24.8 | 29.8 | 15.5 | 4.6 |

Grade per group (g/t) | 3.54 | 2.47 | 2.77 | 2.23 | 1.98 | 3.54 | 2.47 | 2.77 | 2.23 | 1.98 |

Total grade (g/t) | 2.767 | 2.770 |

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**MDPI and ACS Style**

Magalhães, M.F.; Chieregati, A.C.; Ilic, D.; de Carvalho, R.M.; Lemos, M.G.; Delboni, H.
Use of Discrete Element Modelling to Evaluate the Parameters of the Sampling Theory in the Feed Grade Sampler of a Sulphide Gold Plant. *Minerals* **2021**, *11*, 978.
https://doi.org/10.3390/min11090978

**AMA Style**

Magalhães MF, Chieregati AC, Ilic D, de Carvalho RM, Lemos MG, Delboni H.
Use of Discrete Element Modelling to Evaluate the Parameters of the Sampling Theory in the Feed Grade Sampler of a Sulphide Gold Plant. *Minerals*. 2021; 11(9):978.
https://doi.org/10.3390/min11090978

**Chicago/Turabian Style**

Magalhães, Marcus Félix, Ana Carolina Chieregati, Dusan Ilic, Rodrigo Magalhães de Carvalho, Mariana Gazire Lemos, and Homero Delboni.
2021. "Use of Discrete Element Modelling to Evaluate the Parameters of the Sampling Theory in the Feed Grade Sampler of a Sulphide Gold Plant" *Minerals* 11, no. 9: 978.
https://doi.org/10.3390/min11090978