# A Decision Support System for Changes in Operation Modes of the Copper Heap Leaching Process

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview

- Ore feed analysis: The data corresponding to the mineral feed includes the parameters of the raw feed, among which are: percentage of leachable oxides and sulfides, particle size, leaching flow rate, and level of chlorides added to the acid solution.
- Domain ontology development: Representation of knowledge about the dynamics of the leaching process, mainly indicating the configurations of the assets typical of a certain mode of operation.
- Rules, facts, and knowledge base: Generation of operation rules based on a specific subset of configurations in the mineral’s feed parameters that enter the process.
- Operational parameters and expected recovery levels: Identification of the operational parameters that significantly impact the response and determination of expected recovery levels is determining or estimating a tipping point where mineral recovery is negligible or becomes asymptotic.
- Knowledge of domain experts: Experts in the domain have the functions of generating the operating rules based on their knowledge of the dynamics of the process and the validation of the sequence of operating modes recommended by the algorithm or designed system.

#### 2.2. LX Process Modeling

#### 2.3. Rules-Based System

#### 2.4. Knowledge Representation

#### 2.5. Planning of Operating Modes

_{2}SO

_{4}and chlorides at different concentrations. This dynamic behavior of the feeding, considering the variable leaching time, to complete the process when the mineral recovery in the leaching behaves asymptotically, supposes high variations in the valid lifetimes of the heap (as shown in Figure 1a) due to lower leaching kinetics of sulfide minerals when exposed only to H

_{2}SO

_{4}, which implies increases in operating costs.

- Mode A: Leaching of oxidized copper ores in acidic media.
- Mode B: Leaching of sulfide copper ores using H
_{2}SO_{4}, and chlorides as a catalyst agent. - Mode X: Mixed leaching of oxidized and sulfurized minerals in acidic media at low chloride concentrations (This mode of operation corresponds to a transition mode, between the leaching of oxides with H
_{2}SO_{4}and chloride-adhering sulfides).

#### 2.6. Validation Using Performance Measures

- Accuracy (Acc): Corresponds to the proportion of correctly classified cases from all the examples in the dataset. This indicator can be calculated with the data from the confusion matrix (see Equation (1)).Accuracy = (TP + TN)/(TP + TN + FP + FN)
- Precision (p): The proportion of true positives (TP) among the elements is predicted as positive (see Equation (2)). Precision refers to the spread of the set of values obtained from repeated measurements of a quantity.Precision = TP/(TP + FP)
- Recall (r): The proportion of predicted true positives among all items classified as positive (see Equation (3)).Recall = TP (TP + FN)
- Specificity: (True Negative Rate) measures the proportion of negatives that are correctly identified (that is, the proportion of those who do not have the condition (not affected) who correctly identify as people who do not have the condition).Specificity = TN/(TN + FP)
- F1 score: The F1 value is used to combine the precision and recall measurements into a single value. This is practical because it makes it easier to compare the combined performance of precision and recall between various solutions. F1 score is calculated by taking the harmonic mean between precision and recall, as shown in Equation (5).F1 score = Precision × Recall/(Precision + Recall)
- Matthew’s correlation coefficient (MCC): An indicator that relates what is predicted with what is real, creating a balance between the classes, considering the instances correctly and incorrectly classified in classes that are pretty different in size and with a significant number of observations (see Equation (6)).MCC = (TN × TP − FP × FN)/([(TN + FN) × (FP + TP) × (TN + FP) × (FN + TP)]
^{0.5}) - Kappa index: An indicator that represents the proportion of agreements observed beyond random with respect to the maximum possible agreement. It is used to evaluate the concordance or reproducibility of categorical measurement instruments and is defined as shown in Equation (7).ĸ = (P
_{o}− P_{e})/(1 − P_{e}) | P_{e}= [(TP + FP) × (TP + FN) + (TN + FN) × (TN + FP)]/N^{2}

## 3. Implementation

- 3.1. Implementation of knowledge representation
- 3.2. Expert module
- 3.3. Recommendation module

#### 3.1. Implementation of Knowledge Representation

- Heap/Pile: Accumulations of mineralized material carried out in a mechanized way, forming a kind of continuous cake or embankment of varying height. The piles are slightly inclined to allow the drainage and capture of the solutions and are watered with a reagent solution to extract the mineral.
- Operation mode: Configuration of productive resources in order to adapt to the characteristics of the feed. For this knowledge model, three modes have been considered: MODE
_{A}, MODE_{B}, and MODE_{X}. The detail of each operation mode and conditions of changes are not of interest in this phase of the work. - Mineral: Inorganic solid substance, formed by one or more defined chemical elements that are organized in an internal structure.
- Reagent: A chemical element that establishes an interaction with other substances in the framework of a chemical reaction, generating a substance with different properties called a product.
- Operating conditions: State of the variables of interest in a given mode of operation. Some variables are days of operation, irrigation ratios, type of reagent, total reagent added, mineral recovery, and update of the amount of mineral extracted from the heap.
- Mineral recovery: Output variable or ore recovery function.

- it_is_a_type: is the relationship between concepts that belong to the same hierarchy.
- depends_on: is the relationship established between the concepts involved or influence in copper recovery.
- leach: is the relationship between leaching agents and the type of material.
- operates_according_to: is the relationship between the heap and the operation mode. Sets the operating mode to be applied to a stack according to its characteristics.

- Axiom 1: if P
_{1}, P_{2}are heaps and OM1, OM2 are operating modes (the operating modes can exist independently of batteries and correspond to ways in which batteries have been operated previously), and if OM1 corresponds to P1, and OM2 corresponds to P2, then: P1 ∩ P2 = ∅. - Axiom 2: if P1 is a leaching heap and OM1, OM2 are modes of operation, and P <oper> OM1 and P <oper> OM2, then: OM1 ≠ OM2 where <oper> represents the univocal correspondence of the operation of a stack according to an operation mode.
- Axiom 3: if P1, P2 are leaching heaps, M1, M2, and C1, C2 are the type of mineral and the operating conditions of the pile, respectively, and it is known that C1 <corresp> P1, C2 <corresp> P2 and M1 ≠ M2, then C1 ∩ C2 = ∅. <corresp> represents the relationship between a Stack where a specific material and operating conditions are established in a heap.

- Percentage of oxides in the feed (%O);
- Percentage of sulfides (secondary) in the feed (%S);
- Granulometry (d);
- Surface velocity of the leaching flow (μ
_{s}); and - Chloride at concentrations of 20 g/L (Cl20) and 50 g/L (Cl50) (see Table 1).

- Operation mode; and
- Copper recovery.

#### 3.2. Expert Module

#### 3.3. Recommendation Module

## 4. Results and Discussion

#### 4.1. Implementation of the Recommendation System

#### Ontology Modeling

- Operating conditions
- ◦
- Days of operation
- ◦
- Irrigation ratios
- ◦
- Types of reagents
- ◦
- Total reagent added

- Modes of operation
- ◦
- Mode A
- ◦
- Mode B
- ◦
- Mode X

- Heap
- ◦
- Physical characteristics
- ⬝
- Heap height
- ⬝
- Granulometry

- ◦
- Chemical characteristics
- ⬝
- Grade of oxides
- ⬝
- Grade of primary sulfides
- ⬝
- Grade of secondary sulfides

- Types of reagents
- ◦
- H
_{2}SO_{4} - ◦
- Cl

- Mineral recovery
- Type of mineral in the feed (Mineral)
- ◦
- Oxides
- ◦
- Sulfides

#### 4.2. Evaluation of Recommendations

#### 4.3. Discussion

## 5. Conclusions and Future Works

- The first decision support system was presented that allows decision support to the hydrometallurgical phase of heap leaching.
- An inference system was formalized and developed to recommend a mode of operation based on variations in feeding.
- This inference engine was integrated into a recommendation system that generates predictions of the responses.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Proposal to improve copper recovery through variation in operating modes. Leaching of oxidized minerals and copper sulfides using only H

_{2}SO

_{4}as the leaching agent (

**a**), configuration of operating modes (Modes A and B) according to mineral feed (

**b**), and updating of operating curves in the event of variation in leaching agents (

**c**).

**Figure 3.**Class hierarchy of the ontology for the definition of operation modes (

**a**) and hierarchy of properties associated with the classes of the ontological representation (

**b**).

**Figure 4.**Accuracy versus pruning parameter (α) (

**a**) and accuracy for fitting 10 trees using 10 subsets (

**b**).

**Figure 7.**Modes of operation proposed by the recommendation system (

**a**), historical modes of operation (

**b**), and modes of operation recommended by expert knowledge (

**c**) in the heap leaching phase.

Cl/Sulfides | Non-Existent | Medium | High |
---|---|---|---|

Cl20 | 0 | 1 | 0 |

Cl50 | 0 | 0 | 1 |

System | Historical | ||
---|---|---|---|

Real/Predicted | A | B | X |

A | 2982 | 47 | 146 |

B | 17 | 769 | 127 |

X | 94 | 81 | 2487 |

Statistical/Mode | A | B | X |
---|---|---|---|

Accuracy | 0.9550 | 0.9597 | 0.9336 |

Precision | 0.9392 | 0.8423 | 0.9343 |

Recall | 0.9641 | 0.8573 | 0.9011 |

Specificity | 0.9472 | 0.9754 | 0.9561 |

Accuracy | 0.9550 | 0.9597 | 0.9336 |

**Table 4.**Confusion matrix between system recommendations versus historical operating modes and domain expert recommendations.

System | Historical | Expert | ||||
---|---|---|---|---|---|---|

Real/Predicted | A | B | X | A | B | X |

A | 592 | 7 | 17 | 587 | 13 | 22 |

B | 8 | 198 | 21 | 12 | 188 | 21 |

X | 12 | 13 | 212 | 16 | 19 | 202 |

**Table 5.**Performance statistics of the proposed recommendation system versus historical data and domain expert.

Indicator | Modo | Proposal/Historical | Proposal/Expert |
---|---|---|---|

Accuracy | A | 0.95926 | 0.94167 |

B | 0.95463 | 0.93981 | |

X | 0.94167 | 0.92778 | |

Precision | A | 0.96104 | 0.94373 |

B | 0.87225 | 0.85068 | |

X | 0.89451 | 0.85232 | |

Recall | A | 0.96732 | 0.95447 |

B | 0.90826 | 0.85455 | |

X | 0.84800 | 0.82449 | |

Specificity | A | 0.94872 | 0.92473 |

B | 0.96636 | 0.96163 | |

X | 0.96988 | 0.95808 | |

F1 score | A | 0.96417 | 0.94907 |

B | 0.88989 | 0.85261 | |

X | 0.87064 | 0.83817 | |

MCC | A | 0.91699 | 0.88090 |

B | 0.86161 | 0.81480 | |

X | 0.83351 | 0.79189 | |

Kappa index | A | 0.91696 | 0.88082 |

B | 0.86133 | 0.81480 | |

X | 0.83301 | 0.79171 |

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**MDPI and ACS Style**

Saldaña, M.; Neira, P.; Flores, V.; Robles, P.; Moraga, C. A Decision Support System for Changes in Operation Modes of the Copper Heap Leaching Process. *Metals* **2021**, *11*, 1025.
https://doi.org/10.3390/met11071025

**AMA Style**

Saldaña M, Neira P, Flores V, Robles P, Moraga C. A Decision Support System for Changes in Operation Modes of the Copper Heap Leaching Process. *Metals*. 2021; 11(7):1025.
https://doi.org/10.3390/met11071025

**Chicago/Turabian Style**

Saldaña, Manuel, Purísima Neira, Víctor Flores, Pedro Robles, and Carlos Moraga. 2021. "A Decision Support System for Changes in Operation Modes of the Copper Heap Leaching Process" *Metals* 11, no. 7: 1025.
https://doi.org/10.3390/met11071025