# Optimization of the Heap Leaching Process through Changes in Modes of Operation and Discrete Event Simulation

^{1}

^{2}

^{3}

^{4}

^{5}

^{6}

^{*}

## Abstract

**:**

_{2}SO

_{4}) as reagent and adding chloride in the case of sulfide ores (secondary sulfides). The incorporation of uncertainty allows the creation of models that maximize the productivity, while confronting the geological uncertainty, as the extraction program progresses. The model seeks to increase the expected recovery from leaching, considering a set of equiprobable geological scenarios. The modeling and simulation of this productive phase is developed through a discrete event simulation (DES) framework. The results of the simulation indicate the potential to address the dynamics of feed variation through the implementation of alternating modes of operation.

## 1. Introducion:

#### 1.1. Overview

#### 1.2. Heap Leaching

^{2+}) dissolves in the leaching solution as it percolates the heap. The realization of tests at the laboratory level and in pilot plants determine the effectiveness of a heap. The amount of ore to be treated can vary considerably from hundreds to more than one million tons [12], depending on the mine.

## 2. Materials and Methods

#### 2.1. Discrete Event Simulation

_{n}, and event n + 1 will occur at time t

_{n}

_{+1}, as the simulation clock jumps directly to the instant t

_{n}

_{+1}. Upon advancing to t

_{n}

_{+1}, the system statistics and state variables are updated, and this process repeated until a termination condition is met [23].

#### 2.2. Mathematical Modeling of Heap Leaching

_{t}, k

_{τ}are kinetic constants associated with the characteristics of the heap and grade of the mineral respectively, and n

_{τ}is the order of the reaction. The subscript τ represents a time scale that depends on the phenomenon to be modeled. To solve Equation (1), an initial condition is required. Mellado et al. introduced a delay (i.e., a time ω where R

_{t}begins to change (R

_{t}(ω) = 0)); the general solution for ${\mathrm{n}}_{\mathsf{\tau}}=1$ is given by (see Mellado et al. [29] for the general solution):

^{*}in Equations (4)–(6) respectively:

_{θ}and k

_{τ}are kinetic constants, μ

_{s}is the surface velocity of the leaching flow in the heap, ε

_{b}is the volumetric fraction of the bulk solution in the heap, ω is the delay of the reaction, D

_{Ae}is the effective diffusivity of the solute within the pores of the particles, ε

_{o}is the porosity of the particles, and r is the radius of the particles.

#### 2.3. Adjustment of the Analytical Model for the Recovery of Copper from Copper Oxides

#### 2.4. Adjustment of Analytical Model for Copper Recovery from Secondary Copper Sulfides

#### 2.5. Adjustment of Analytical Models for Copper Recovery from Secondary Copper Sulfide Ores Adding Chlorides

#### 2.6. Modeling and Simulation of Heap Leaching Using a DES Framework

- Mode A: Leaching of copper oxides.
- Mode B: Leaching of copper sulfide minerals (secondary sulfides).

## 3. Discussion of Results

#### 3.1. Simulated Scenarios

- Scenario 1 (standard operation): Leaching of copper oxides and secondary copper sulfides adding sulfuric acid only. The leaching of secondary sulfides with sulfuric acid slows down the process of extracting ore from the rock, increasing the time required until the marginal extraction of ore is negligible [12,34].

#### 3.2. Comparison of Samples

_{0}:µ

_{2}= µ

_{1}

_{2}represents the average production in thousands of tons of the leaching phase considering changes in the modes of operation, and μ

_{1}represents the average value of production considering a single mode of production. The alternate hypothesis is given by:

_{a}:µ

_{2}> µ

_{1}

## 4. Conclusions

#### 4.1. Conclusions

#### 4.2. Future Work

- Include other modes of operation and analytical models that incorporate more operational variables to the process, together with parameters that have a significant impact on recovery.
- Study the impact on an industrial scale of operating the leaching process with alternating modes of operation, including the analysis operating and capital costs.

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 3.**Copper recovery from oxide and sulfide ores using H

_{2}SO

_{4}and chlorides as an additive.

Curve/Statistic | MAD | MSE | MAPE |
---|---|---|---|

R(t) (Oxides) | 1.008 × 10^{−2} | 1.222 × 10^{−4} | 1.28 × 10^{−2} |

**Table 2.**Statistics of analytical models of leaching of secondary copper sulfides adding sulfuric acid.

Curve/Statistic | MAD | MSE | MAPE |
---|---|---|---|

R(t) (Oxides) | 6.63 × 10^{−}^{4} | 5.068 × 10^{−7} | 8.93 × 10^{−4} |

Curve/Statistic | MAD | MSE | MAPE |
---|---|---|---|

R(t) (Chloride 20 g/L) | 1.68 × 10^{−4} | 4.59 × 10^{−7} | 5.40 × 10^{−4} |

R(t) (Chloride 50 g/L) | 9.17 × 10^{−5} | 5.23 × 10^{−7} | 5.89 × 10^{−4} |

Configuration | Recovery (%) |
---|---|

Leaching of secondary copper sulfides with sulfuric acid | 40.5 |

Leaching of secondary copper sulfides adding chlorides (20 g/L) | 46.5 |

Leaching of secondary copper sulfides adding chlorides (50 g/L) | 58.1 |

Leaching of copper oxides with sulfuric acid | 64.6 |

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**MDPI and ACS Style**

Saldaña, M.; Toro, N.; Castillo, J.; Hernández, P.; Navarra, A. Optimization of the Heap Leaching Process through Changes in Modes of Operation and Discrete Event Simulation. *Minerals* **2019**, *9*, 421.
https://doi.org/10.3390/min9070421

**AMA Style**

Saldaña M, Toro N, Castillo J, Hernández P, Navarra A. Optimization of the Heap Leaching Process through Changes in Modes of Operation and Discrete Event Simulation. *Minerals*. 2019; 9(7):421.
https://doi.org/10.3390/min9070421

**Chicago/Turabian Style**

Saldaña, Manuel, Norman Toro, Jonathan Castillo, Pía Hernández, and Alessandro Navarra. 2019. "Optimization of the Heap Leaching Process through Changes in Modes of Operation and Discrete Event Simulation" *Minerals* 9, no. 7: 421.
https://doi.org/10.3390/min9070421