Development of an analytical model for copper heap leaching from secondary sulfides in chloride media in an industrial environment Technical paper

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Manuel Saldaña
Eleazar Salinas-Rodríguez
Jonathan Castillo
Felipe Peña-Graf
Francisca Roldán


In multivariate analysis, a predictive model is a mathematical/statistical model that relates a set of independent variables to dependent or response variable(s). This work presents a descriptive model that explains copper recovery from secondary sulfide minerals (chalcocite) taking into account the effects of time, heap height, superficial velocity of leaching flow, chloride concentration, particle size, porosity, and effective diffusivity of the solute within particle pores. Copper recovery is then modelled by a system of first-order differential equations. The results indicated that the heap height and superficial velocity of leaching flow are the most critical independent variables while the others are less influential under operational conditions applied. In the present study representative adjustment parameters are obtained, so that the model could be used to explore copper recovery in chloride media as a part of the extended value chain of the copper sulfides processing.


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Saldaña, M., Salinas-Rodríguez, E., Castillo, J., Peña-Graf, F., & Roldán, F. (2022). Development of an analytical model for copper heap leaching from secondary sulfides in chloride media in an industrial environment: Technical paper. HEMIJSKA INDUSTRIJA (Chemical Industry), 76(4), 183–195.
Chemical Engineering - Simulation and Optimization

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Flanagan DM. Copper. In Mineral Commodity Summaries 2021. Reston, VA, USA: U.S. Geological Survey; 2021; 52–3. ISBN 9781411343986.

Villela D, Kutscher C, Castillo E. Sulfuros primarios: desafíos y oportunidades. Comisión Chilena del Cobre (COCHILCO). Santiago, Chile: 2017.

ICSG. Copper: Preliminary Data for January 2020. International Copper Study Group (ICSG): Lisbon, Portugal: 2020.

Pérez K, Toro N, Gálvez E, Robles P, Wilson R, Navarra A. Environmental, economic and technological factors affecting Chilean copper smelters – A critical review. Journal of Materials Research and Technology 2021; 15: 213–25. https: //

Navarra A, Wilson R, Parra R, Toro N, Ross A, Nave JC, Mackey PJ. Quantitative methods to support data acquisition modernization within copper smelters. Processes 2020; 8(11): 1–22. https: //

Lazo A, Lazo P, Urtubia A, Lobos MG, Gutiérrez C, Hansen HK. Copper Analysis by Two Different Procedures of Sequential Extraction after Electrodialytic Remediation of Mine Tailings. International Journal of Environmental Research and Public Health 2019; 16(20): 3957. https: //

Rodríguez F, Moraga C, Castillo J, Gálvez E, Robles P, Toro N. Submarine tailings in chile—a review. Metals (Basel) 2021; 11(5): 1–17. https: //

Toro N, Rodríguez F, Rojas A, Robles P, Ghorbani Y. Leaching manganese nodules with iron-reducing agents – A critical review. Minerals Engineering 2021; 163: 106748. https: //

Dijkstra R. Economical abatement of high-strength SO2 off-gas from a smelter. J South Afr. Inst. Min. Metall. 2017; 117(11): 1003–7. https: //

Daibova EB, Lushchaeva I v, Sachkov VI, Karakchieva NI, Orlov V v, Medvedev RO, Nefedov RA, Shplis ON, Sodnam NI. Bioleaching of Au-Containing Ore Slates and Pyrite Wastes. Minerals 2019; 9(10): 1–11. https: //

Conić V, Stanković S, Marković B, Božić D, Stojanović J, Sokić M. Investigation of the optimal technology for copper leaching from old flotation tailings of the copper mine bor (Serbia). Metallurgical and Materials Engineering 2020; 26(2): 209–22. https: //

Casas JM, Martinez J, Moreno L, Vargas T. Bioleaching model of a copper-sulfide ore bed in heap and dump configurations. Metallurgical and Materials Transactions B: Process Metallurgy and Materials Processing Science 1998; 29(4): 899–909. https: //

Behrad Vakylabad A, Nazari S, Darezereshki E. Bioleaching of copper from chalcopyrite ore at higher NaCl concentrations. Minerals Engineering 2022; 175: 107281. https: //

Ghorbani Y, Franzidis J-P, Petersen J. Heap leaching technology – current state, innovations and future directions: A review. Mineral Processing and Extractive Metallurgy Review 2015: 08827508.2015.1115990. https: //

Kevin Pérez , Norman Toro, Eduardo Campos AN and MHR. Extraction of Mn from Black Copper Using Iron Acid Medium. Metals (Basel) 2019; 9(10): 1–10. https: // //

Hernández PC, Taboada ME, Herreros OO, Graber TA, Ghorbani Y. Leaching of chalcopyrite in acidified nitrate using seawater-based media. Minerals 2018; 8(6). https: //

Toro N, Ghorbani Y, Turan MD, Robles P, Gálvez E. Gangues and Clays Minerals as Rate-Limiting Factors in Copper Heap Leaching: A Review. Metals 2021, Vol 11, Page 1539 2021; 11(10): 1539. https: //

Cerda CP, Taboada ME, Jamett NE, Ghorbani Y, Hernández PC. Effect of pretreatment on leaching primary copper sulfide in acid-chloride media. Minerals 2018; 8(1): 1–14. https: //

Pradhan N, Nathsarma KC, Srinivasa Rao K, Sukla LB, Mishra BK. Heap bioleaching of chalcopyrite: A review. Minerals Engineering 2008; 21(5): 355–65. https: //

Castillo J, Sepúlveda R, Araya G, Guzmán D, Toro N, Pérez K, Rodríguez M, Navarra A. Leaching of white metal in a NaCl-H2SO4 system under environmental conditions. Minerals 2019; 9(5). https: //

Velásquez-Yévenes L. The kinetics of the dissolution of chalcopyrite in chloride media: PhD Thesis, Murdoch University, Australia. 2009.

Velásquez-Yévenes L, Nicol M, Miki H. The dissolution of chalcopyrite in chloride solutions Part 1. The effect of solution potential. Hydrometallurgy 2010; 103(1–4): 108–13. https: //

Nicol M, Miki H, Velásquez-Yévenes L. The dissolution of chalcopyrite in chloride solutions Part 3. Mechanisms. Hydrometallurgy 2010; 103(1–4): 86–95. https: //

Torres CM, Ghorbani Y, Hernández PC, Justel FJ, Aravena MI, Herreros OO. Cupric and chloride ions: Leaching of chalcopyrite concentrate with low chloride concentration media. Minerals 2019; 9(10). https: //

Nicol M, Basson P. The anodic behaviour of covellite in chloride solutions. Hydrometallurgy 2017; 172(June): 60–8. https: //

Pérez K, Toro N, Saldaña M, Salinas-Rodríguez E, Robles P, Torres D, Jeldres RI. Statistical Study for Leaching of Covellite in a Chloride Media. Metals (Basel) 2020; 10(4): 477. https: //

Toro N, Moraga C, Torres D, Saldaña M, Pérez K, Gálvez E. Leaching Chalcocite in Chloride Media—A Review. Minerals 2021; 11(11): 1197. https: //

Cisternas LA, Gálvez ED. The use of seawater in mining. Mineral Processing and Extractive Metallurgy Review 2018; 39(1): 18–33. https: //

Bogdanović GD, Petrović S, Sokić M, Antonijević MM. Chalcopyrite leaching in acid media: a review. Metallurgical and Materials Engineering 2020; 26(2): 177–98. https: //

Yévenes LV, Miki H, Nicol M. The dissolution of chalcopyrite in chloride solutions: Part 2: Effect of various parameters on the rate. Hydrometallurgy 2010; 103(1–4): 80–5. https: //

Dimitrijević M, Urošević D, Milić S, Sokić M, Marković R. Dissolution of copper from smelting slag by leaching in chloride media. Journal of Mining and Metallurgy, Section B: Metallurgy 2017; 53(3): 407–12. https: //

Petronijević N, Stanković S, Radovanović D, Sokić M, Marković B, Stopić SR, Kamberović Ž. Application of the Flotation Tailings as an Alternative Material for an Acid Mine Drainage Remediation: A Case Study of the Extremely Acidic Lake Robule (Serbia). Metals 2020, Vol 10, Page 16 2019; 10(1): 16. https: //

Sokić M, Marković B, Stanković S, Kamberović Ž, Štrbac N, Manojlović V, Petronijević N. Kinetics of Chalcopyrite Leaching by Hydrogen Peroxide in Sulfuric Acid. Metals 2019, Vol 9, Page 1173 2019; 9(11): 1173. https: //

Córdoba EM, Muñoz JA, Blázquez ML, González F, Ballester A. Leaching of chalcopyrite with ferric ion. Part I: General aspects. Hydrometallurgy 2008; 93(3–4): 81–7. https: //

Molinos-Senante M, Donoso G. Water scarcity and affordability in urban water pricing: A case study of Chile. Utilities Policy 2016; 43: 107–16. https: //

Saleth RM, Dinar A. Institutional changes in global water sector: trends, patterns, and implications. Water Policy 2000; 2(3): 175–99. https: //

Ministerio del Medio Ambiente. Informe del Estado del Medio Ambiente. Ministerio Del Medio Ambiente. 2020. https: // Accessed December 12, 2021.

IPPC. The Working Group I contribution to the Sixth Assessment Report addresses the most up-to-date physical understanding of the climate system and climate change, bringing together the latest advances in climate science. In: Climate Change 2021: The Physical Science Basis. Cambridge University Press; 2021. ISBN 9780080967899. https: // Accessed December 30, 2021.

Bárcena A, Prado A, Samaniego J, Pérez R. La Economía del Cambio Climático en Chile. Comisión Económica para América Latina y el Caribe (CEPAL): Santiago, Chile: 2012. http: // Accessed November 19, 2021.

Torres D, Toro N, Galvez E, Castillo D, Bermudez SA, Navarra A. Temporal Variography for the Evaluation of Atmospheric Carbon Dioxide Monitoring. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing 2022; 15: 80–8. https: //

Santibañez F. El cambio climático y los recursos hídricos de Chile. Agricultura Chilena: Reflexiones y Desafíos 2016: 147–78. https: // Accessed July 03, 2021.

Roldán F, Salazar I, González G, Roldán W, Toro N. Flow-Type Landslides Analysis in Arid Zones: Application in La Chimba Basin in Antofagasta, Atacama Desert (Chile). Water 2022, Vol 14, Page 2225 2022; 14(14): 2225. https: //

Fuentes F, García C. Ciclo económico y minería del cobre en Chile. Revista CEPAL 2016; Abril: 165–92. https: // Accessed September 23, 2021.

Conejeros V, Pérez K, Jeldres RI, Castillo J, Hernández P, Toro N. Novel treatment for mixed copper ores: Leaching ammonia – Precipitation – Flotation (L.A.P.F.). Minerals Engineering 2020; 149 (December 2019) : 106242. https: //

Ortlieb L. Eventos El Niño y episodios lluviosos en el desierto de Atacama: el registro de los últimos dos siglos. Bulletin de l’Institut Français d’Études Andines 1995; 24(3): 519–37

Vargas G, Ortlieb L, Rutllant J. Aluviones históricos en Antofagasta y su relación con eventos El Niño/Oscilación del Sur. Revista Geológica de Chile 2000; 27(2): 157–76. https: //

Arens FL, Airo A, Feige J, Sager C, Wiechert U, Schulze-Makuch D. Geochemical proxies for water-soil interactions in the hyperarid Atacama Desert, Chile. CATENA 2021; 206: 105531. https: //

Jordan TE, Kirk-Lawlor NE, Nicolás Blanco P, Rech JA, Cosentino NJ. Landscape modification in response to repeated onset of hyperarid paleoclimate states since 14 Ma, Atacama Desert, Chile. GSA Bulletin 2014; 126(7–8): 1016–46. https: //

Placzek CJ, Matmon A, Granger DE, Quade J, Niedermann S. Evidence for active landscape evolution in the hyperarid Atacama from multiple terrestrial cosmogenic nuclides. Earth and Planetary Science Letters 2010; 295(1–2): 12–20. https: //

Kappes DW. Precious Metal Heap Leach Design and Practice. Mineral processing plant design, practice, and control. Vancouver, Canada: Society for Mining, Metallurgy, and Exploration; 2002; 12

Schlesinger M, King M, Sole K, Davenport W. Extractive Metallurgy of Copper. Fifth Ed. Amsterdam, The Netherlands: Elsevier Ltd; 2011. ISBN 9780080967899.

Saldaña M, Rodríguez F, Rojas A, Pérez K, Angulo P. Development of an empirical model for copper extraction from chalcocite in chloride media. Hem Ind 2020; 74(5): 285–92. https: //

Saldaña M, Gálvez E, Robles P, Castillo J, Toro N. Copper Mineral Leaching Mathematical Models - A Review. Materials 2022, Vol 15, Page 1757 2022; 15(5): 1757. https: //

Saldaña M, Neira P, Gallegos S, Salinas-Rodríguez E, Pérez-Rey I, Toro N. Mineral Leaching Modeling Through Machine Learning Algorithms − A Review. Frontiers in Earth Science 2022; 10: 560. https: //

Mellado ME, Cisternas LA, Gálvez ED. An analytical model approach to heap leaching. Hydrometallurgy 2009; 95(1–2): 33–8. https: //

Mellado ME, Casanova MP, Cisternas LA, Gálvez ED. On scalable analytical models for heap leaching. Computers and Chemical Engineering 2011; 35(2): 220–5. https: //

Mellado ME, Gálvez ED, Cisternas LA. On the optimization of flow rates on copper heap leaching operations. International Journal of Mineral Processing 2011; 101(1–4): 75–80. https: //

Mellado M, Cisternas L, Lucay F, Gálvez E, Sepúlveda F. A Posteriori Analysis of Analytical Models for Heap Leaching Using Uncertainty and Global Sensitivity Analyses. Minerals 2018; 8(2): 44. https: //

Dixon DG, Hendrix JL. A mathematical model for heap leaching of one or more solid reactants from porous ore pellets. Metallurgical Transactions B 1993; 24(6): 1087–102. https: //

Dixon DG, Hendrix JL. Theoretical basis for variable order assumption in the kinetics of leaching of discrete grains. AIChE Journal 1993; 39(5): 904–7. https: //

Dixon DG, Hendrix JL. A general model for leaching of one or more solid reactants from porous ore particles. Metallurgical Transactions B 1993; 24(1): 157–69. https: //

Torres D, Trigueros E, Robles P, Leiva WH, Jeldres RI, Toledo PG, Toro N. Leaching of pure chalcocite with reject brine and mno2 from manganese nodules. Metals (Basel) 2020; 10(11): 1–19. https: //

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: //

Liu B. Uncertainty Theory. In Uncertainty Theory. 4th Ed., Springer-Verlag Berlin Heidelberg: Germany. 2007. https: //

Jaynes ET. Probability Theory. Cambridge: Cambridge University Press; 2003. https: //

Saldaña M, González J, Jeldres R, Villegas Á, Castillo J, Quezada G, Toro N. A Stochastic Model Approach for Copper Heap Leaching through Bayesian Networks. Metals (Basel) 2019; 9(11): 1198. https: //

Taha HA. Operations Research: An Introduction. 10th Ed., Essex, England: Pearson Education Limited; 2017. ISBN 9780134444017.

Petersen J. Heap leaching as a key technology for recovery of values from low-grade ores – A brief overview. Hydrometallurgy 2016; 165: 206–12. https: //

McCoy JT, Auret L. Machine learning applications in minerals processing: A review. Minerals Engineering 2019; 132 (November 2018): 95–109. https: //

Peña-Graf F, Órdenes J, Wilson R, Navarra A. Discrete Event Simulation for Machine-Learning Enabled Mine Production Control with Application to Gold Processing. Metals 2022, Vol 12, Page 225 2022; 12(2): 225. https: //