MATHEMATICAL MODELLING OF CALICHE HEAP LEACHING

Javier Ignacio Ordóñez Contreras

Thesis presented in accordance to the requirements to obtain the degree of Ph.D. in Mineral Process Engineering

Supervisors Ph.D. Luis Cisternas & Ph.D. Luis Moreno

Laboratory of Optimization and Modelling Department of Chemical and Mineral Process Engineering Universidad de Antofagasta Antofagasta

November 18, 2013 Abstract

Caliche is a mineral composed of a high proportion of water-soluble species that is naturally present in northern Chile, in the regions of Tarapacá and Antofagasta. The most important products obtained from this mineral are nitrates and iodine. Nitrate is used for the manufacture of fertilizers and iodine in medical and technological applications. Chile is the world's largest producer of iodine and natural nitrates in the world.

One of the stages in the production of these resources is the leaching of caliche, which takes place in both vats as heaps depending on the grade and granulometry of mineral. In the case of heap leaching, this involves irrigation with water or recirculated solutions at the top and the liquid obtained is taken to iodine extraction plant, where the iodate is transformed to metallic iodine. The solution is subsequently conducted to evaporation pools to obtain crystalline sodium nitrate and other salts.

Mining operations that exploit caliche are located in northern Chile, where the availability of fresh water is low, so that companies have had to adapt their processes with water scarcity. However, this condition has a limit, since to maintain productivity levels to the gradual decrease of grades, caliche operating volumes must be increased and therefore, the water requirements. This has resulted in the need to find new water sources that address the growing demand. An alternative that has been studied and gradually integrated by companies is seawater, which has proven to be compatible with the processing of caliche.

Models that represent the heap leaching minerals have been a commonly used tool for both the understanding of the phenomena involved and finding solutions for optimal management. The development of mathematical models for heap leaching has been concentrated mainly in metallic minerals, such as: gold, silver, copper and zinc, while for caliche the information is scarce.

Dissolution phenomena of caliche soluble species obey to reactions based on solubilities, whereas the metallic minerals are governed by chemical reactions. An important difference is that caliche has a high fraction of soluble minerals formed by different species that are dissolving simultaneously at different rates, which makes modelling of caliche leaching a

v complex system. The high fraction of soluble species cause that the gradual decrease in the size of the particles and, therefore, the entire heap.

The contribution of this thesis is based on three pillars, which are: 1) pilot scale experimental tests of caliche leaching, incorporating seawater as one of the leaching agents, 2) phenomenological modelling based on fundamental principles for the dissolution of soluble species of caliche and 3) modelling using hybrid models for caliche leaching, which combine empirical results with fundamental principles.

In the experiments, how the dissolution of caliche is affected by varying some operating parameters such as: irrigation rate, initial column height and leaching agent was addressed. The phenomenological model developed for soluble species accurately described nitrate and iodine dissolution. The hybrid modelling was used to estimate recoveries of the most important ions of caliche with good agreement; the model considers two scales, one for the heap and other for the particles. It was found that sodium sulphate precipitates in certain situations due to the common ion effect. This phenomenon was modelled, considering the solubilities for a simplified system of three minerals, which was able to reproduce the trends observed in the column experiments for these ions.

These findings are an important contribution to the knowledge on caliche heap leaching, since scientific information the scientific and public domain information about modelling and testing of caliche leaching in heaps is scarce

Keywords: Caliche, heap leaching, phenomenological modelling, hybrid modelling, seawater.

vi Resumen

El caliche es un mineral compuesto por una alta proporción de especies solubles en agua que se encuentra naturalmente presente en el norte de Chile, en las regiones de Tarapacá y Antofagasta. Los productos más importantes que se obtienen de este mineral son: nitratos y yodo. El nitrato es empleado para la fabricación de fertilizantes y el yodo en aplicaciones médicas y tecnológicas. Chile es el principal productor mundial de yodo y nitratos naturales en el mundo.

Una de las etapas para la producción de estos recursos es la lixiviación del caliche, la cual se realiza tanto en bateas como en pilas dependiendo de la ley y granulometría del mineral. En el caso de la lixiviación en pilas, este consiste en la irrigación con agua o soluciones recirculadas en la parte superior y el líquido obtenido es llevado a una planta de extracción de yodo, donde el yodato es transformado a yodo metálico y subsecuentemente a pozas de evaporación para obtener nitrato de sodio cristalizado.

Las operaciones mineras que explotan caliche se encuentran exclusivamente en el norte de Chile, lugar donde la disponibilidad de agua fresca es baja, por lo que las compañías han tenido que desarrollar sus procesos con escasez hídrica. Sin embargo, esta condición tiene un límite muy delicado, puesto que para mantener niveles de productividad ante el decrecimiento gradual de las leyes hay que aumentar los volúmenes de explotación de caliche y por consiguiente, de agua requerida. Esto ha repercutido en la necesidad de buscar nuevas fuentes de agua que hagan frente a la creciente demanda. Como una alternativa que ha sido estudiada y paulatinamente incorporada por las compañías está el agua de mar, que ha demostrado ser compatible con el procesamiento hidrometalúrgico del caliche.

La generación de modelos que representen la lixiviación en pilas de minerales ha sido una herramienta habitualmente empleada tanto para el entendimiento de los fenómenos involucrados como para la búsqueda de soluciones de manejo óptimos. El desarrollo de modelos matemáticos para pilas de lixiviación se ha concentrado mayoritariamente en minerales metálicos, tales como: oro, plata, cobre y cinc, mientras que para caliche la información es escasa.

vii Los fenómenos de disolución de las especies solubles del caliche obedecen a reacciones basadas en las solubilidades, mientras que para los minerales metálicos las reacciones están gobernadas por óxido-reducción. Esta diferencia establece otras variaciones que hacen de la modelación de las pilas de lixiviación de caliche un sistema complejo, tales como la disminución gradual del tamaño de las partículas y, por tanto, de toda la pila y la disolución simultánea de distintas especies a distintas velocidades.

La contribución de esta tesis se enmarca en tres grandes ejes, los que son: 1) pruebas experimentales escala piloto de lixiviación de caliche, incorporando el agua de mar como uno de los lixiviantes, 2) modelación fenomenológica basada en principios fundamentales para la disolución de especies solubles del caliche y 3) modelación híbrida de la lixiviación de caliche basada en términos empíricos junto con conceptos fenomenológicos.

Los resultados más destacables de este trabajo responden a los objetivos planteados. Con respecto a los experimentos se establecieron los comportamientos de disolución para cada una de las especies que forman el caliche y cómo estos se ven afectados al variar algunos parámetros operacionales como la tasa de riego, altura inicial de columna y agente lixiviante, siendo este último el más relevante. El modelo fenomenológico desarrollado para especies solubles describió de forma precisa la disolución de nitrato y yodo en base al concepto de multi-tanques bien agitados en serie. Por otra parte, la modelación híbrida estimó las recuperaciones de los iones más importantes del caliche de manera satisfactoria a través de una definición multi-escala de la pila de lixiviación, esto es manejando dos escalas complementarias de tamaño y tiempo para la pila y las partículas que la conforman. A partir de las observaciones experimentales se encontró que determinados iones interactúan, trayendo consigo la precipitación de sulfato de sodio como consecuencia del efecto de ion común. Este fenómeno fue modelado a través de una expresión fenomenológica que considera los productos de solubilidad para un sistema simplificado de 3 minerales. Este modelo se ajustó en gran medida a los valores de concentración experimentales obtenidos en las columnas de lixiviación.

Estos resultados revisten un importante aporte al conocimiento sobre la lixiviación de caliche en pilas, puesto que la información científica y de dominio público disponible acerca de la modelación y experimentación de la lixiviación de caliche en pila es escasa.

viii Supervisors

Luis Cisternas, PhD Laboratory of Optimization and Modelling Department of Chemical and Mineral Process Engineering Universidad de Antofagasta, Antofagasta, Chile

Luis Moreno, PhD School of Chemical Science and Engineering Royal Institute of Technology, Stockholm, Sweden

List of papers

This thesis is based on the following papers that were published in ISI journals:

I. Gálvez, E.D., Moreno, L., Mellado, M.E., Ordóñez, J.I., Cisternas, L.A., 2012. Heap leaching of Caliche minerals: Phenomenological and analytical models – Some comparisons. Minerals Engineering 33, 46–53.

II. Ordóñez, J.I., Moreno, L., Gálvez, E.D., Cisternas, L.A., 2013. Seawater leaching of caliche mineral in column experiments. Hydrometallurgy 139, 79–87.

III. Ordóñez, J.I., Moreno, L., Mellado, M.E., Cisternas, L.A., 2013. Modeling validation of caliche ore leaching using seawater. International Journal of Mineral Processing. In Press.

Additionally, results were reported in events, through publications in proceeding books:

IV. Moreno, L., Ordóñez, J.I., Gálvez, E.D., Cisternas, L.A., 2012. Seawater heap leaching of caliche ores, experiments and modelling. 4th International seminar on process Hydrometallurgy, Hydroprocess 2012, 11-13 July 2012, Santiago, Chile. 66–74.

V. Ordóñez, J.I., Moreno, L., Cisternas, L.A., Gálvez, E.D., Mellado, M.E., 2012. An analytical model for heap leaching of caliche ores. 4th International seminar on process Hydrometallurgy, Hydroprocess 2012, 11-13 July 2012, Santiago, Chile. 244–253.

VI. Ordóñez, J.I., Valdez, S., Moreno, L., Cisternas, L.A., 2013. Some improvements of caliche heap leaching. 5th International seminar on process Hydrometallurgy, Hydroprocess 2013, 10-12 July 2013, Santiago, Chile. 429-437.

ix Preface

This thesis titled Mathematical modelling of caliche heap leaching presents the work done during the PhD studies that started in April 2010 and finished in December 2013. The activities were realised at the Laboratory of Optimization and Modelling, Department of Chemical Engineering and Mineral Processing, University of Antofagasta, Chile.

The document is arranged in 7 chapters. Initially, the introduction gives a general context about the motivation and the subject of this investigation. The second chapter is an overview of caliche and its processing. In chapter 3, mathematical modelling applied to heap leaching is described, followed by a chapter of the methodology and results of column leaching experiments. Chapter 5 refers the description of developed models and their implementation. The Chapter 6 summarizes the papers which were published and that were written under this thesis. The final chapter provides a space of discussion about the main findings of the work, the general conclusions and final remarks. As appendices, the ISI published papers are attached to this thesis.

Acknowledgements

This dissertation is the result of almost 4 years of intense work, where many people have been involved, both in the execution of this thesis as by enriching my doctoral experience every day.

I wish to express my deep thanks to Luis Cisternas and Luis Moreno, my supervisors and mentors, whose experience and immense knowledge allowed me to complete my studies satisfactorily through their lucid advice and provoking in me a great admiration.

I am grateful to the team of the Laboratory of Modelling and Optimization and in general to the all great "family" of the graduate program of Mineral Processing Engineering. Thank for entrusting me the mission of to be his representative for 2 years and for those pleasant days that we shared playing tennis, in english sessions, in festive evenings among many other activities.

Finally, I thank CONICYT, who gave me the financial support to carry out my studies through national doctoral fellowship.

xi CONTENT

ABSTRACT ...... V RESUMEN ...... VII PREFACE ...... XI CHAPTER 1. INTRODUCTION ...... 19 1.1. BACKGROUND ...... 19 1.2. AIM OF THESIS ...... 20 CHAPTER 2. CALICHE AND ITS PROCESSING...... 21 2.1. CALICHE ...... 21 2.2. PROCESSING OF CALICHE AND LEACHING ...... 24 2.3. INDUSTRY OF CALICHE ...... 27 CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING ...... 31 3.1. EMPIRICAL MODELS ...... 31 3.2. PHENOMENOLOGICAL MODELS ...... 32 3.3. HYBRID MODELS ...... 32 3.4. CALICHE HEAP LEACHING MODELLING ...... 33 CHAPTER 4. COLUMN LEACHING EXPERIMENTS ...... 35 4.1. METHODOLOGY ...... 35 4.2. EXPERIMENTAL RESULTS ...... 40 CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING ...... 47 5.1. PHENOMENOLOGICAL MODEL ...... 47 5.2. HYBRID MODEL ...... 50 CHAPTER 6. SUMMARY OF PAPERS ...... 55 CHAPTER 7. CONCLUSIONS AND FINAL REMARKS ...... 73 7.1. MAJOR FINDINGS OF THE THESIS ...... 73 7.2. GENERAL CONCLUSIONS ...... 74 7.3. FINAL REMARKS AND RECOMMENDATIONS ...... 75 CHAPTER 8. REFERENCES ...... 77 APPENDIX A. PAPERS ...... 81

xiii LIST OF TABLES

Table 2.1. Historical analysis of caliche minerals (Extracted from Lauterbach, 2004).Concentrations in wt%...... 25 Table 2.2. Main companies of caliche expoitation, their annual production and water consumption. Values between parentheses correspond to projected values with pending environmental qualification (SEA, 2013)...... 30 Table 4.1. Chemical analysis of water-soluble content forming caliche (wt%)...... 36 Table 4.2. Mineralogical analysis of caliche...... 36 Table 4.3. Chemical analysis of leaching solutions used in experiments (kg/m3)...... 38 Table 4.4. Column leaching experiments...... 40 Table 4.5. Mineralogical analysis of residue RS6S...... 42 Table 6.1. Values used in the simulations...... 57 Table 6.3. Values used in simulations of hybrid model...... 69

Table 6.4. Fitted values of K2,i - parameter...... 69 Table 6.5. Parameter values used in the sensitivity analysis...... 70 Table 6.6. Prediction of experiments and determination coefficients...... 71

xv LIST OF FIGURES

Figure 2.1. Layers of common caliche deposits (Taken from Ericksen, 1983)...... 23 Figure 2.2. Industrial heap leaching (SQM, 2013)...... 26 Figure 2.3. Processing of caliche to produce potassium nitrate and iodine (Ordóñez et al., 2013)...... 27 Figure 2.4. Main products of caliche processing...... 28 Figure 2.5. Geographical distribution of caliche exploitation operations...... 29 Figure 4.1. Granulometry of caliche used in leaching experiments...... 37 Figure 4.2. Column leaching system...... 39 Figure 4.3. Crystals of sodium sulphate that appeared into columns after 5 days of leaching (experiment SW3S)...... 41 Figure 4.4. Dissolution of the most important ions. □: RS, q=0.006 m3/m2/h, H=0.6 m; Δ: TW, q=0.006 m3/m2/h, H=1.0 m; ◊: SW, q=0.006 m3/m2/h, H=0.6 m ...... 43

Figure 4.5. Recovery of ions at VL/VB equals to 1.2...... 46 Figure 5.1. Column formed by N well-stirred tanks in series as volume unit of a heap...... 48 Figure 5.2. Multiscale dimension of heap leaching (Adapted from Dixon and Hendrix, 1993a)...... 50 Figure 6.1. Relative recovery of the soluble species as a function of time for different a) irrigation rate, b) particle diameter and c) Initial heap height. The lines are the analytical model, and the markers are the simulated experimental data...... 58 Figure 6.2. Fitting of phenomenological model using concentrations obtained from experiments (Dotted: SW and Solid: TW and Dashed: LX) for a) Nitrate and b) Iodine...... 64 Figure 6.3. Experimental (markers) and simulated outlet concentration (lines) using the chemical reaction model for columns: a) SW, q=0.006 m3/m2/h, H=0.6 m, b) TW, q=0.006 m3/m2/h, H=1.0 m and c) LX, 0.006 m3/m2/h, H=0.6 m...... 65 Figure 6.4. Experimental (markers) and modelled (lines) recoveries for SW3S experiment...... 70 Figure 6.5. Experimental (markers) and modelled (lines) recoveries for RS6S experiment...... 70 Figure 6.6. Predictability analysis for RS6S (left) and DS6L (right) experiments, fitting SW3S and SW3L...... 72

xvii CHAPTER 1. INTRODUCTION

CHAPTER 1. INTRODUCTION

1.1. Background

Modelling is a useful tool that allows understanding and improving the performance of certain processes, through different approaches. A comprehensive description of phenomena is commonly provided by phenomenological models, while by simpler expressions as empirical models the management or design of processes is easier.

For the mining industry, particularly for heap leaching process, a wide spectrum of applied models can be found, which describe the phenomena under different approaches. However for caliche heap leaching the information related with the use of mathematical models is scarce as consequence that this industry is small and the high complexity of dissolution phenomenon.

The caliche heap leaching is a system that comprises a high quantity of soluble minerals, whose dissolution depends on the solubility of these components. Along leaching, a size diminution of particle and heap occurs. Moreover, the dissolution is frequently done simultaneously for some species with different kinetic rates and the control of dissolution of some species is exerted by other ions. In this sense, mathematical models can be used to explore and clarify the complex phenomena of heap leaching, for this there is a need for novel mathematical models formulation for caliche dissolution, incorporating fundamental principles such as: mass transfer, convection and diffusion transport.

Considering that mining industry is an important actor of the Chilean economy, applied tools for improving the processes are needed. In this way, the formulation of hybrid models is also interesting to develop. Empirical observations mixed with expressions that consider fundamental concepts would be useful for optimization and design tasks associated with heap leaching.

19 CHAPTER 1. INTRODUCTION

Moreover, actual mining operations are located in places with scarce water resources; therefore the use of other sources of water as seawater is a topic that has a niche of research under the concept of sustainability, especially for caliche, where the concentrations in seawater for the main ions is far with respect their solubility limits.

1.2. Aim of thesis

The aim of this thesis is the understanding of caliche heap leaching, which is addressed by experiments and modelling. In column experiments, the use of different leaching agents, irrigation rates, column heights were considered. Models taking into account the most important processes occurring in caliche heap leaching were developed, which may be used in optimization and design tasks. Two models are formulated: phenomenological and hybrid models. These models were validated by using the column leaching experiments.

20 CHAPTER 2. CALICHE AND ITS PROCESSING

CHAPTER 2. CALICHE AND ITS PROCESSING

2.1. Caliche

Caliche is the name of the mineral formed by a high proportion of water-soluble species and the most important source of natural nitrate (also known as saltpetre or Chilean nitrate) and iodine minerals. The most important products that are obtained from caliche are: sodium nitrate, that is used in the elaboration of fertilizer and in the developing of molten salts applied in thermal storage (Valencia et al., 2008; Chandía, 2012), sodium sulphate, which is employed as additive for chemical and metallurgical processes, and finally, iodine and its derivatives, that are the central products of caliche processing from an economical point of view and are used in food, health and technological industries as a contrast medium in X-ray and as additive in the production of LCD screens (Valencia et al., 2008; Pokorny and Maturana, 1997).

Regarding the mineralogy and among the soluble minerals, the most abundant species are:

Nitratine (NaNO3), Halite (NaCl), Bloedite (Na2Mg(SO4)2·4H2O), Polyhalite

(K2Ca2Mg(SO4)4·2H2O) and Glauberite (CaNa2(SO4)2). Other less abundant minerals are: borates, chromates, chlorates, perchlorates and iodates, the latter one in form of Lautarite

(Ca(IO3)2) and Hectorfloresite (Na9(IO3)(SO4)4). On other hand, the insoluble species are represented mainly by Anhydrite (CaSO4), Gypsum (CaSO4·2H2O), Quartz (SiO2) and other silicates (Ericksen, 1983; Jackson and Ericksen, 1994; Pokorny et al., 1997; Valencia et al., 2008).

Besides Chile, the saltpetre can be extracted in Spain, Iran, Egypt and India, but only in Northern Chile the deposits of nitrate and iodine (caliche) are commercially exploitable (Valencia et al., 2008). The geographic distribution of caliche is confined to the Tarapacá and Antofagasta regions for an area that extends about 20,000 km2. A characteristic of the deposits is that its distribution is concentrated in the oriental face of the coastal range at 1,200 m.a.s.l.

21 CHAPTER 2. CALICHE AND ITS PROCESSING

Minerals that are extremely rare to find in nature such as: nitrates, sulphate-nitrates, iodates, and sulphate-iodates constitute the ore of caliche, accompanying sulphates, chlorides and, to a much lesser extent, borates and carbonates. Most nitrate deposits are under a superficial layer, forming thin crusts on soil surface as consequence of natural differential leaching during their formation. A notable stratification resulting from the dissolution and re-deposition of more soluble minerals by the infrequent rains in the zone is observed. As a result, the nitrate is often found a couple of metres in depth, being scarce in the surface, where less soluble species such as sulphate minerals predominate (Figure 2.1). The deposits are commonly composed by 5 layers which are: Chuca, Costra, Caliche, Conjelo and Coba.

The Chuca layer is the upper mantle, loose soil dark gray to brown that contains nitrate law no more than 2% and iodine grades around 80 to 180 ppm. Its thickness is 10 – 30 cm, in specific cases can reach up to 1 m. Gypsum, clay, rock fragments are the main constituents, but at the bottom of this layer, thick white powdery salt material can be found, predominantly sodium sulphates such as: thenardite, bloedite, humberstonite and gypsum.

The Costra is presented as a conglomerate of various bonded insoluble salts, being the predominant sulphates and chlorides. Typically has a nitrate grade of 5% and iodine content from 15 to 25 ppm.

The under layer is the Caliche, which is presented as gaps or sandstone. The particles are cemented by various salts, among which predominate nitrates, chlorides, sulphates, magnesium, potassium and iodine salts. The grades of nitrate vary from 6 to 25% and iodine between 280 and 700 ppm.

Conjelo and Coba are the strata below Caliche and are composed mainly of soluble salts from the predominantly chlorides and sulphates. Below these layers are volcanic rocks that form the Andes range.

22 CHAPTER 2. CALICHE AND ITS PROCESSING

Figure 2.1. Layers of common caliche deposits (Taken from Ericksen, 1983).

At the moment, the geological explanation about the formation of ores of caliche is not completely clarified, there being a numerous theories about the sources of nitrate accumulation, which are described by Ericksen (1983) but submitted by various authors. Some of them are:

. Decomposition of plants associated with continental lakes or seaweed and other marine plants that remained in partially dried arms of sea. . Nitrification and leaching of guano or nitrification and fixation of atmospheric nitrogen by bacteria

23 CHAPTER 2. CALICHE AND ITS PROCESSING

. Accumulation of windblown ammoniacal particulate from guano spread along the coast of northern Chile. . Bacterial decomposition of plant and animals remains, during Tertiary and Quaternary geological ages, when the northern Chile climate was less arid. . Leaching of nitrate-rich salts or volcanic rocks of Jurassic age. . Accumulation of nitrate from subsurface saline waters and brines of salars.

None of these theories are able to explain completely the origin of caliche deposits.

2.2. Processing of caliche and leaching

The commercial exploitation of caliche started in 1830 for the production of nitrate to supply the explosives industry. Late 19th century the production of nitrates had become the leader industry of Chile and the main provider of nitrates around the world (Bermúdez, 1987). In 1913 was achieved the chemical synthesis of ammonium nitrate in a large scale through Haber-Bosch process, replacing potassium nitrate produced from caliche (Wisniak and Garcés, 2001). Under this panorama, the preponderance of Chile as nitrate supplier fell to levels never before reached. At present, the extraction of caliche lives a new impulse based on iodine. Iodine is a non metallic element that is internationally traded as a commodity with an important presence in medical/food and technological industries, both sectors with high value-added applications.

The processing of caliche starts with the extraction of the mineral from the soil by removing the sterile layer that covers caliche, using blasting or mechanical equipment. Then, and depending on the mineralogy and granulometry, the mineral is arranged in heaps of about 10 m for coarse particles. Comminution by crushers (jaw and cone) is used to reduce the size for vat leaching of fines, managing material with a size less than 0.4 mm (Wheeler, 2010).

The gradual diminution of nitrate mineral grades (Table 2.1), together with an increase of economic and environmental costs has resulted in the search of techniques less intensive and more massive in the mineral hydro-processing as heap leaching. This metallurgical methodology that was firstly implemented to gold industry in the early 70’s and currently

24 CHAPTER 2. CALICHE AND ITS PROCESSING

employed in the extraction of various metals such as copper, silver and zinc. The caliche industry adopted the heap leaching methodology at the middle of 80’s.

Table 2.1. Historical analysis of caliche minerals (Extracted from Lauterbach, 2004).Concentrations in wt%.

Extraction period Component Up to 1920 1960 – 1970 1970 – 2000 NaNO3 20 – 50 7 – 9 6.5 – 8 NaCl 20 10 – 15 5 – 10 Na2SO4 12 – 15 12 – 16 12 – 20 I2 0.03 0.03 0.03 Na2B4O7 0.4 – 0.6 0.4 – 0.6 0.4 – 0.6 K 1.0 – 2.0 0.4 – 1.5 0.3 – 1.2 KClO4 0.03 0.03 0.03 Mg 0.2 – 0.3 0.2 – 0.8 0.2 – 1.2 Ca 0.4 – 3.3 0.4 – 2.3 0.5 – 2.8 H2O 1.0 – 2.0 1.1 – 1.8 1.1 – 1.8 Insoluble 6 – 14 53 – 68 60 – 69

The leaching of caliche is a solid-liquid mass transfer process by which the mineral is watered by a solvent, frequently water or intermediate solutions obtained from downstream steps, dissolving the soluble content of the solid matrix and transferring it to the liquid phase (Havlík, 2008; Fleming, 1992). The percolate (or enriched solution) is treated to separate the species of interest. Unlike metallic ores leaching, where the dissolution is governed by chemical reactions, the caliche processing is by dissolution based on differences of solubilities (Wadsworth, 1987; Valencia et al., 2008).

During the first years, caliche was processed in mobile installations, dissolving into heated iron tanks by direct flame. The resulting brines were subsequently evaporated in crystallization ponds. With this technique only high grade minerals were able to be commercially leached (over 50% nitrate). In 1853 a new process was introduced, allowing poorer caliches (over 30% nitrate). Caliche was dissolved in steam heated tanks and the installations became permanent and the production rates were incremented importantly. Greater improvements, such as Shanks leaching process that used double wall steam-heated tanks were incorporated in 1878, whereupon caliche ores with about 13% of nitrate were processed (Donald, 1936ab; Wisniak and Garcés, 2001).

25 CHAPTER 2. CALICHE AND ITS PROCESSING

Industrially, heaps built by the accumulation of 600 to 900 thousand tons (Figure 2.2), are irrigated with fresh water or mixed solution between water and residual liquids that comes from iodine extraction plant with a nominal irrigation rate of 2 L/h/m2 (Sirocco, 2013; SQM, 2013) Nowadays, the feasibility to use seawater as a leaching agent is being studied due to the scarcity of fresh water in northern Chile (Taboada et al., 2012; Torres et al., 2013).

Figure 2.2. Industrial heap leaching (SQM, 2013).

The solution obtained from leaching is accumulated and sent to iodine extraction plant, where by chemical reduction reactions, the iodine is recovered. After that, remained liquid is sent to evaporation ponds, place where the crystallization of sodium nitrate and sodium sulphate is done. The sodium nitrate collected in evaporation ponds is reacted with potassium chloride (obtained from salt lakes), resulting potassium nitrate, a final product used as fertilizer. A general overview of caliche processing is shown in Figure 2.3.

26 CHAPTER 2. CALICHE AND ITS PROCESSING

Crushing Leaching vats Potassium chloride (from Salar) Caliche extraction Crystallization Melting and Heap leaching Iodine plant NPT plant plant Prilling plant

Prilled iodine Prilled sodium nitrate Crystallization and Drying Evaporation ponds

Prilled potassium Prilling nitrate

Figure 2.3. Processing of caliche to produce potassium nitrate and iodine (Ordóñez et al., 2013).

2.3. Industry of caliche

Products and production

The main products obtained from the exploitation of caliche ores are iodine and nitrate salts (Anderson, 2013). Marginally, other by-products are also extracted, as sodium sulphate that is used in industrial applications (Figure 2.4).

The worldwide production of iodine in 2012 was estimated in almost 30,000 tons, where the main producers are Chile, Japan and United States. Meanwhile the first country produces iodine from the caliche exploitation, the others two reach their positions through underground brines related with natural gas deposits. Minor actors of this commodity are Azerbaijan, China, Russia and Turkmenistan (USGS, 2013).

It is possible to appreciate that the first producer of caliche's products is SQM, company with wide history in this activity. In recent years, new companies and expansion projects have appeared, strongly influenced by the demand and prices of iodine. The Tarapacá's region is the leader in the production of iodine. Although the price of iodine grew notably between 2003 and 2012, was in the last 5 years when the increment of prices has achieved their maximal rates, around 5,350 US$/t by year, reaching close to 44,000 US$/t (SONAMI, 2013; USGS, 2013).

27 CHAPTER 2. CALICHE AND ITS PROCESSING

Prilled iodine Prilled sodium nitrate Prilled potassium nitrate

Figure 2.4. Main products of caliche processing.

The iodine applications include a wide range of uses; however the main areas are related with human and animal health and dietary. It is estimated that two thirds of iodine and its derivatives are used in that. On other side, in industrial fields, the demand has increased as consequence of the strong irruption of technological products, which are based in LCD screens and where iodine is one of the components.

Concerning to nitrates, they are classified in two groups depending of the application field: fertilizer and industrial salts. The fertilizers involve potassium nitrate, sodium nitrate and sodium-potassium nitrate. Chile leads the fabrication of this type of fertilizer, with about 50% of the world production. Jordan and Israel are the other most important actors of this market. The industrial salts are used as industrial additives and in solar plants to storage thermal energy. Chile is positioned at the head of the production of these salts.

The main application of nitrates obtained from caliche is as fertilizer, that are better than ones based on ammonia formulation, because they have more nutritional richness to also possess potassium and for crops more sensitive to salinity. Moreover, their solubilities allow be used in crops irrigated by fertirrigation systems.

28 CHAPTER 2. CALICHE AND ITS PROCESSING

Processing companies of caliche

Due to the commercially exploitable deposits are located exclusively in Chile, particularly in Tarapacá and Antofagasta regions, the main producers of natural nitrate and iodine are concentrated in these zones. A general geographical distribution is presented in Figure 2.5.

150 km N

Figure 2.5. Geographical distribution of caliche exploitation operations.

Use of seawater in heap leaching of caliche minerals

Due to that exploitation of caliche is carried out in locations with water scarcity, new sources of water such as seawater have been studied and, progressively, used for the production of iodine and nitrates. In various operations seawater is the only viable alternative for leaching, not only for non-metallic minerals but also for other minerals, such as copper ores.

29 CHAPTER 2. CALICHE AND ITS PROCESSING

Table 2.2. Main companies of caliche expoitation, their annual production and water consumption. Values between parentheses correspond to projected values with pending environmental qualification (SEA, 2013).

Caliche exploitation Production, Type of Water usage, Company Products capacity, t/year t/year process water m3/h ACF Minera S.A. 4,800,000 Iodine 1,450 Well water 108 (Nitrate) (60,000) Atacama Minerals 4,056,000 Iodine 1,500 Well water 483 S.A. Nitrate 115,000 Sulphate 300,000 Cosayach SCM 781,000 Iodide 260 Well water 32 (5,166,400) (1,800) (Well water) (148) Iodine 1,000 (6,000) Algorta Norte S.A. 18,250,000 Iodine 4,000 Seawater 540 Seawater (900) SCM Bullmine 16,100,000 Iodine 2,000 Seawater 540 Well water 90 SQM S.A. 37,000,000 Iodine 9,000 Well water 2,110 (93,000,000) (25,500) (Well water) (4,200) Nitrate 2,767,500 (Seawater) (1,800) (8,700,000)

For hydrometallurgical processing of caliche, the previous treatment of seawater is not needed; several industries use desalinated seawater by reverse osmosis in their processes. The direct use of seawater can be applied in operations that have adapted infrastructure to salinity conditions and where the mineralogical characteristics of mineral allow the use.

The used distances between the suction plant and the mine sites are about 70 km for caliche exploitation sites. It is increasingly common that companies that exploit caliche use seawater directly in their processes. Among the first cases that started the operation with this type of water was Algorta Norte; however companies that originally used well or superficial water have joined to a mixed supply, such as: SQM and Bullmine. The water consumptions or installed capacities and the type of water supply are shown in Table 2.2.

30 CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING

CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING

The heap leaching processes are complex systems that consider both physical and chemical phenomena and interactions between them such as: chemical reactions, dissolution, liquid stagnancy, diffusion, liquid and gas transport by convection, heat generation, etc (Ghorbani et al., 2011). For this reason, there is a great interest in to develop mathematical models, that allow understand, simulate, design and optimize processes (McBride et al., 2012; Padilla et al., 2008). Hydrometallurgical processes are, frequently, headed by leaching, for this reason any improvement on its performance may reflects global benefits at the end of process (Mooiman et al., 2005).

There are different strategies of modelling that can describe chemical phenomena, some of them are empirical, phenomenological and hybrid models, the latter are a combination of the above ones. In general, some criteria are defined for the use of each type of model, depending mainly of the objective to pursue.

3.1. Empirical models

The empirical modelling is the simplest way of representation and consists in the fitting of a curve with experimental or historical data to approach the behaviour of a system. Generally, this type of models is used when accurate predictions or extrapolation of data are not required, because the system is defined by the range of input variables, and therefore extrapolated information is not possible to obtain. Moreover, its simplicity results that the system is considered as a black box, so that only information about input and output variables is available. Empirical models frequently require little time and computational efforts to be solved, due to their formulation comes directly from experimental observations or historical data collected from operations (Mellado et al., 2011).

Bartlett (1992) used an empirical model based on extensive operation history and experimental data for continued operational planning and control and also can be used for scaling through experimental laboratory data (Roman et al., 1974). Empirical modelling of

31 CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING

agitated and column leaching also have been developed, for example Bouffard and Dixon (2007) compared the gold recoveries achieved in well-agitated tanks and columns experiments with simulated data from an empirical model, observing that the model is a good predictor for both type of leaching and for any particle size, especially at later stages.

3.2. Phenomenological models

The phenomenological models are expressions based on fundamental principles that govern a system. Usually a set of equations can accurately and consistently describe certain phenomena, so are suitable in processes where a thorough analysis is sought. However formulation of phenomenological models is more complex than empirical models and in many times they cannot response adequately the needs of industry, because they require a large number of data that sometimes are difficult to obtain or are expensive to determine experimentally.

In the context of heap leaching, Dixon and Hendrix (1993ab) proposed a phenomenological dimensionless model to porous spherical particles with the objective to use it in design and scaling heap leaching processes. In that work, the heap leaching is visualised as a multiscale phenomenon which are diffusive-type process for particle level and convective process referred to bed. The validation was realised through leaching tests in columns. De Andrade Lima (2004) developed a model, taking a heap leaching process of high size particles and low porosity. The modelling was performed dividing the column subsystem in flat layers instead of small columns

3.3. Hybrid models

By using hybrid models is possible to predict the behaviour of a system, overcoming the mathematical complexities of models based on differential equations (phenomenological type) and increasing the quantity of information of just fitted expressions (empirical type). The hybrid models can be used in optimization tasks because may give more information and perform multiple calculations in brief times, what is frequently needed in actual operations.

32 CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING

Mellado et al. (2009) presented a hybrid model for heap leaching of copper ores that captures the exponential trend of recovery through a Bernoulli-type equation.

Stochastic analysis of empirical models is not useful because these models do not consider variations of input variables. On the other hand, phenomenological models is certainly possible to evaluate these variations, however this process can become complex due to the nature of the expressions. In this sense, hybrid models are good target of stochastic studies (Mellado et al., 2011; Mellado et al., 2012).

3.4. Caliche heap leaching modelling

Modelling associated to heap leaching has been widely developed to metallic ores processing, both by phenomenological, empirical and hybrid expressions. In almost all cases the main phenomena is governed by chemical reactions. However for the exploitation of water-soluble minerals, like caliche, the information of public domain is scarce. This is due to on one side, the industry of caliche is small and the internal handling of information is less abundant and on other side, the process is a complex system given by its heterogeneity and highly soluble mineral composition, resulting in a reduction of particle size and consequently the heap as a result of the release material from collapsed particles to liquid phase.

Only recently in the literature has appeared information about modelling of caliche processing, particularly by heap leaching. The contributions come principally from the researching group of Modelling and Optimization laboratory of Universidad de Antofagasta. Since the exploitation of caliche focuses exclusively in northern Chile, the local emergence of research in its processing is explained. The first approach available is the research of Valencia et al. (2008), which formulated empirical kinetic expressions to model the process in terms of recovery of nitrate and magnesium species. Recovery is due to an exponential empirical expression that is in function of irrigation rate. Through experiences of column leaching was studied to better understanding of the present phenomena and to fit the model, where the results obtained were good.

33 CHAPTER 3. MATHEMATICAL MODELLING ON HEAP LEACHING

As part of this thesis have been developed 3 new articles that address the phenomena of heap leaching of caliche mineral through 2 large foci: modelling and experimental runs. In subsequent chapters they will be described.

34 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

CHAPTER 4. COLUMN LEACHING EXPERIMENTS

A relevant achievement of this thesis is the providing of experimental information about column leaching of caliche mineral, using actual operational conditions. In this sense, the methodology and the results obtained from the experiments is reviewed in this chapter, highlighting the observations that were used for the validation of proposed mathematical models.

4.1. Methodology

Caliche

The mineral used in the column leaching experiments was obtained from the northern Chile. The mineralogical, chemical and granulometric analysis were performed in order to characterize the material.

The used caliche has a high proportion of water-soluble content, about 30% and its appearance is soft and light brown. From the chemical analysis, it is possible to observe that sulphate is the most abundant anion, seconded by chloride and nitrate. According to the chemical composition of soluble fraction, the minor anions are borate, iodate and perchlorate. Concerning to the cations, sodium is by far the most abundant metallic ion. Magnesium, calcium and potassium are also present, but at lower levels (Table 4.1).

The chemical analysis of the ions considers gravimetric assay for sulphate, whereas for potassium, sodium, magnesium and calcium the analysis was by atomic absorption spectroscopy (AAS). Nitrate was quantified by molecular absorption spectroscopy – UV. Volumetry was used for chloride, iodine and boron. Perchlorate was detected by specific- electrode.

35 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

Table 4.1. Chemical analysis of water-soluble content forming caliche (wt%).

Anions Cations NO3- SO42- IO3- Cl- ClO4- BO33- Na+ K+ Mg2+ Ca2+ 3.674 9.410 0.046 4.194 0.036 0.060 5.575 0.579 0.971 0.597

According to the mineralogical analysis, the predominant soluble species are halite and nitratine, while albite and quartz are the most abundant non-soluble minerals. The high level of sulphate in caliche is present as many mineralogical forms, such as: glauberite, anhydrite and bloedite, which have a wide spectre of solubilities. For the other most abundant anion, chloride, the predominant mineral containing it is halite and at a lower level hidrochlorborite. On other side, nitrate is only present in caliche as nitratine, a high water-soluble mineral. The presence of sodium as the most important cation in the ore supports that a high level of sodium is shared by a large amount of species with different soluble nature, e.g. from nitratine to albite (insoluble). Like sodium, calcium, potassium and magnesium are widely spread in various species (many of them are complex salts), whilst potassium is only in polyhalite. Among the minor ions, borate is present as hydroclorborite and the remaining ones: iodate and perchlorate do not have mineralogical presence due to their low relative abundance (Table 4.2). The mineralogical composition of caliche was determined by X-ray diffraction using a D5000 diffractometer (Siemens).

Table 4.2. Mineralogical analysis of caliche.

Specie Formula % Albite NaAlSi3O8 26.3 Quartz SiO2 19.9 Halite NaCl 19.7 Nitratine NaNO3 9.5 Glauberite Na2Ca(SO4)2 9.1 Anhydrite CaSO4 7.3 Bloedite Na2Mg(SO4)2·4H2O 3.3 Loeweite Na12Mg7(SO4)13·15H2O 1.9 Polyhalite K2Ca2Mg(SO4)4·2H2O 1.6 Hydrochlorborite Ca2B4O4(OH)7Cl·7H2O 1.4

The material used in column leaching experiments was screened, using only particle sizes greater than 2.4 mm in order to avoid fines that can obstruct the column outlet. The

36 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

granulometric assay of caliche determines an average particle diameter of 6.8 mm with maximal values of 13.2 mm (Figure 4.1).

100

75

50

25 Cumulative finer, % finer, Cumulative

0 2.4 4.6 6.8 9.0 11.2 13.4 Particle size, mm

Figure 4.1. Granulometry of caliche used in leaching experiments.

Leaching solutions

The column leaching experiments use four different leaching agents: seawater, tap water, loaded solution and diluted loaded solution. Seawater (SW) was obtained from the coast of Antofagasta through submarine outfall and subsequently filtered by a membrane filter with 0.2 μm pore diameter. Tap water (TW) was obtained directly from the sanitary system. Both waters was stored in plastic containers and for seawater, them was covered in order to avoid the algae proliferation. Due to in actual operations the leaching agents are frequently recirculated, the use of loaded solutions in the experiments was considered. This rich solution (RS) was prepared by stirring fine caliche (<2.4 mm) with seawater at a solid:liquid ratio of 1:1 (kg:L) for 1 h and decantation for a day. The clarified liquid is considered the loaded solution. An intermediate leachant (DS) was also produced by dilution of charged

37 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

solution to 50% using seawater as dissolvent. The chemical analyses of these leaching solutions are given in Table 4.3.

Table 4.3. Chemical analysis of leaching solutions used in experiments (kg/m3).

Leaching solution

Seawater Tap water Diluted solution Rich solution

Anions NO3- 0.211 0.000 15.017 29.300 SO42- 2.661 0.130 28.060 53.716

IO3- 0.000 0.010 0.099 0.198

Cl- 19.709 0.350 39.131 59.879

ClO4- 0.120 0.010 0.011 0.012

BO33- 0.161 0.000 0.197 0.384

Cations Na+ 11.124 0.190 33.760 56.274 K+ 0.361 0.020 2.707 5.023

Mg2+ 1.576 0.030 4.505 7.697

Ca2+ 0.171 0.090 0.417 0.465

Leaching system

The columns employed for the experiments are made of PVC with a diameter of 20 cm and height of 1.5 m (Figure 4.2). To avoid stratification and channeling, caliche was loaded in small batches for every column. The leaching system consists in a feed tank having an outlet in its bottom side. From there, a hose transport the leaching solution to the column. The liquid is dripped at the top of the column and the bed is covered by a thin sponge that distributes it homogeneously. The control of the flow was exerted manually with the use of external valves. The use of peristaltic pumps was implemented subsequently, and the control was more stable. At the bottom of the column, a plastic grid with aperture size of 3 cm was settled and upon it a finer plastic mesh was placed in order to avoid the outlet by mineral collapse. A recipient in the outlet receives the solution. At every sampling, the volume of liquid and density were determined for recovery calculations.

38 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

Figure 4.2. Column leaching system.

Liquids samples were taken at every time and solid samples at the beginning and at the end of experiments. The ions that were quantified in solid and liquid samples were: nitrate, sulphate, chloride, sodium, iodine, magnesium and potassium. Calcium, boron and perchlorate were also analysed in solids and in some liquid samples, for the beginning, middle and end of the experiments.

Experimental design

The column leaching experiments were carried out using 4 leachants, 3 irrigation rates and 3 initial heights. The nominal rates and initial heights used in experiments are: 3, 4 and 6 L/h/m2 and 60, 80 and 100 cm, respectively. A comprehensive list of the conditions used en each column is showed in Table 4.4.

39 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

Table 4.4. Column leaching experiments.

Experiment Leaching agent Irrigation rate (m3/m2/h) Bed height (m) SW3S Seawater 0.003 0.6 SW6S Seawater 0.006 0.6 SW3L Seawater 0.003 1.0 TW6L Tap water 0.006 1.0 RS6S Rich solution 0.006 0.6 DS6L Seawater + Rich solution 0.006 1.0 DS4M Seawater + Rich solution 0.004 0.8

4.2. Experimental results

Concentration variation during leaching

The time used for experiments was 20 days, which was adequate to reach equilibrium between the concentration for almost all ions at the leachates and at the leaching solutions (Table 4.3). In order to compare the leaching performance of all the experiments, which were conducted under different conditions of irrigation and bed height, the variation of the concentration is analysed in terms of the volume ratio between leaching solution that passed through the column and the initial bed volume (VL/VB).

It is clearly observed that caliche is formed by ions that have different dissolution behaviour, which are classified in three groups depending on their ability to be dissolved. The first family are composed by nitrate, iodate and perchlorate, being the most soluble species, because their concentrations fell abruptly for volume ratios of about 0.5 for nitrate and 0.7 for iodine and perchlorate. The maximal concentrations of these ions were achieved at the beginning of leaching.

A second group of ions have slower kinetic, these species are: potassium, magnesium and sodium. Their dissolutions are related with the concentration of other species, for this reason, the fall of concentration appeared with a delay at the beginning of the experiments.

Finally, a third group was assigned for the slowest dissolution ions, which were sulphate and chloride. Sulphate increased its concentration until to reach a saturation point, at about 0.3

VL/VB and then decreased gradually.

40 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

At the initial stage of leaching, when the concentration of sulphate is increasing, a precipitation phenomenon occurs as a consequence of the high dissolution rate of sodium compounds belonging of group I (mainly sodium nitrate), because fast output of nitrate provokes an increase of free sodium levels into the column, which interacts with sulphate and resulting in the formation of sodium sulphate crystals (Figure 4.3).

1 cm

Figure 4.3. Crystals of sodium sulphate that appeared into columns after 5 days of leaching (experiment SW3S).

Figure 4.4 shows the general dissolution of all considered ions for each type of leaching solution. In all of the cases, the release of ions is dependent of the concentration in the feeding (directly related with the extractive capability), reaching the lowest concentrations by TW column and the highest by RS column. In the plot, the columns irrigated with diluted charged solution were not considered, but their responses were intermediate between columns leached with seawater and charged solution.

The minerals remaining in residues corroborate that, even for the more charged solutions, the removal of soluble components is complete. The presence of silicates is predominant and gypsum ratifies its low solubility (Table 4.5).

41 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

Table 4.5. Mineralogical analysis of residue RS6S.

Specie Formula % Quartz SiO2 33.24 Albite NaAlSi3O8 26.63 Muscovite KAl2Si3AlO10(OH)2 15.89 Orthoclase KAlSi3O8 14.98 Gypsum CaSO4·2H2O 7.92 Calcite CaCO3 0.67 Nacrite Al2Si2O5(OH)4 0.67

Calcium has different dissolution behaviour than the other ions, because in all of the columns its outlet concentration constantly increased. This is attributed to the calcium speciation, because it is present in caliche associated with sulphate as gypsum and anhydrite, which have very low solubilities. For this, calcium dissolution is controlled by the sulphate levels, therefore calcium concentration increases when sulphate decreases. On other hand, boron showed faster dissolution kinetic and similar among the experiments.

In terms of dissolution trend and comparing the columns irrigated with seawater and tap water, no big differences were observed. Between them, the outlet concentration of chloride and sodium at the end were higher for the columns irrigated with seawater, due to the higher content of these ions in seawater.

42

225 160 1.5 160 2.0

3

3

3

3

3

g/m

kg/m

kg/m g/m 180 kg/m 120 120 1.5 1.0 135 80 80 1.0 90 0.5

40 concentration,Iodine 40 0.5

Nitrate concentration, k concentration,Nitrate Chloride concentration,Chloride

45 concentration,Sulphate Perchlorate concentration,k Perchlorate 0 0 0.0 0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

VL/VB VL/VB VL/VB VL/VB VL/VB

2.0 160 25 25 2.0

3

3

3

3

g/m

g/m 3 g/m 20 20

1.5 120 g/m 1.5 g/m

15 15 1.0 80 1.0 10 10

0.5 40 0.5

Sodium concentration, k Sodiumconcentration, 5 5

Potassium concentration,k Potassium

Boron concentration,k Boron

Calcium concentration, k concentration,Calcium Magnesium concentration, k concentration,Magnesium

0.0 0 0 0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 V /V V /V V /V V /V V /V L B L B L B L B L B

Figure 4.4. Dissolution of the most important ions. □: RS, q=0.006 m3/m2/h, H=0.6 m; Δ: TW, q=0.006 m3/m2/h, H=1.0 m; ◊: SW, q=0.006 m3/m2/h, H=0.6 m

43 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

The irrigation rate has an important effect on the dissolution behaviour and even though directly affects the decrease of concentration, is a nonlinear relationship because other factors are involved in the dissolution phenomenon such as: solubility concentration of controlling species, intrinsic dissolution kinetics and mass transfer resistance.

Since the leaching experiments were performed using caliche with small size (with an average particle diameter of 6.8 mm), the influence of the particle size was small and therefore the leaching of ions was mainly controlled by the solubilities and dissolution rates of each ion.

Effect of operational parameters on species recovery

The recovery of some ions was calculated by mass balance and considering the extracted mass and the fraction remained in the residue. The ions considered in the analysis of recovery include all of them that were chemically followed during the whole leaching, which are: nitrate, sulphate, iodate, chloride, sodium, potassium and magnesium. The remaining ions due to were not quantified continuously, no were considered for recovery calculation.

Although that all columns were run for 20 days, different irrigation rates and bed heights were used, for this reason the ratio of volume of leaching agent used by loaded caliche mass (or its volume) was different for each experiment. In order to compare the recoveries of experiences at the same leaching moment, the maximum value of the slowest column was employed, which was 1.2 for SW3S (Figure 4.5).

The highest recoveries were achieved for the leachants, irrigation rates and column heights in the following order: TW>SW>DS>RS, 0.006>0.004>0.003 m3/m2/h and 0.6>0.8>1.0 m. This is valid for all of the ions. According to these comparisons, the leaching agent appears to be the most important factor that affects the recovery.

As expected, the leaching agent that has the less concentration of ions, which is tap water, had the highest recoveries for almost all of the ions. Magnesium and sodium recoveries were slightly less than one of the seawater leached column, but the effect of an intensive irrigation had effect on this behaviour, which was corroborated analysing the responses at the end of the experiments, where tap water extracted more of these ions.

45 CHAPTER 4. COLUMN LEACHING EXPERIMENTS

The use of seawater was validated in the experiments since no significant differences were reached in comparison with tap water, even to chloride and sodium ions that are in greater presence in marine water, but far to their saturations. The effect of the employment of charged solutions, i.e. RS and DS is clearly observed, because for all of the ions the reached recoveries were the lowest among the seven experiments. This effect is even more pronounced for ions that dissolve more slowly such as sulphate, potassium and magnesium.

The sulphate recovery was the lowest in all of the leaching tests, possibly because the dissolution of this ion was initially controlled by the presence of other ions, such as sodium and calcium. Moreover, the cation dissolution appears to be highly influenced by the anions dissolution, due to that complex salts are an important fraction of caliche content.

Taller columns obtained greater recoveries than smaller ones, as can be evaluated for experiments SW3S and SW3L. By having more amount of leachable caliche and considering that the ions are soluble and with concentrations lesser than their solubilities, the outlet concentration is in general greater and therefore the recoveries also. Irrigation rate is the most important operational parameter in terms of its effect on the recovery of ions. The highest recoveries for all of the ions were achieved by the columns that were leached more intensely; however at the final time, the recoveries became more similar.

1.0

0.8

0.6

0.4

0.2

0.0 NO3 I2 Cl SO4 K Mg Na SW3S SW6S SW3L TW6L RS6S DS6L DS4M

Figure 4.5. Recovery of ions at VL/VB equals to 1.2.

46 CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING

CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING

This thesis aims to represent the caliche heap leaching by mathematical expressions to allow understand some phenomena involved in the ion-soluble dissolution and also to be handled for optimization and design purposes. For the first case, a phenomenological model was developed and for the second a hybrid analytical model was proposed; the formulation of both are reviewed in this chapter, mentioning the assumptions, approaches and scopes of each one, among other considerations.

5.1. Phenomenological model

Valencia et al. (2008) performed the first exercises to capture the dissolution behaviour of some components of caliche. In this thesis, the concepts previously managed were considered and an improved expression was obtained. The model based on fundamental principles was written considering that caliche heap leaching is carried out in a column as central volume unit of a heap, which are divided in tanks in series, where the height of each tank decrease with the time as consequence of dissolution of soluble components of caliche (Figure 5.1).

47 CHAPTER 5. MODELLING of caliche HEAP LEACHING

Figure 5.1. Column formed by N well-stirred tanks in series as volume unit of a heap.

The assumptions used in this model are:

. Non-porous and spherical particles with same initial size were considered. . The soluble and insoluble content are homogeneously distributed in the particles. . Only the soluble minerals that are superficially exposed are able to be dissolved. . Inert material is released from the particle after its collapsing as result of dissolution . A one-dimensional system is defined, assuming that the leaching axis is performed vertically and being the heap enough large.

The dissolution model of Brunner and Tolloczcko (Dokoumetzidis & Macheras, 2006) define that dissolution rate is related with the radius decreasing, and that is proportional to the product of the exposed area and the difference between the solubility, and instantaneous concentration, . Adapting this definition for each reactor (represented by the subscript ) and at time , results the expression 5.1.

5.1

From a material balance of a tank with a cross-sectional area A, the equation 5.2 is obtained.

48 CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING

5.2

where is the water volume in the reactor, is the irrigation rate through the column, and are the concentrations at the reactor and in the previous tank. is the number of particles in each reactor, which is calculated from the relation between the effective column volume and the nominal particle volume.

5.3

⁄

In equation 5.3, denotes the initial particle radius, is the column height and the porosity. Replacing the calculation of the quantity of particles in the balance, it is obtained:

5.4

Due to the volume is proportional to the column height, is possible to separate the derivative term and reorder the expression, resulting:

5.5

where is the height of the tank at time . For the calculation, a relation between the tank height and the particle radius is required, for that from a material balance of the tank and assuming a constant porosity, it is obtained equation 5.6.

5.6

[ ] [ ( ) ]

In this case, the column height is proportional to the particle volume, expressed by the term

. Deriving the height with respect to time and rearranging it in the equation 5.1, it is reached:

49 CHAPTER 5. MODELLING of caliche HEAP LEACHING

5.7 ( )

Finally, replacing the equations 5.1, 5.6 and 5.7 in the expression 5.5, the model that calculates the variation of concentration results:

5.8

5.2. Hybrid model

The developed analytical model was based on one described by Mellado et al. (2009) for leaching of copper ores, where the process is evaluated in terms of recovery of determined species along time and the leaching is considered as a multiscale phenomenon, where particles and heap have dissolution dynamics characteristics and works complementarily (Figure 5.2).

LOCAL HEAP AGRUPATION

Particle Air gaps Leachant solution

PARTICLE Mineral matrix Pores and channels

Figure 5.2. Multiscale dimension of heap leaching (Adapted from Dixon and Hendrix, 1993a).

50 CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING

Model developed for leaching of copper ores was used as starting point for modelling of caliche minerals. This model captures the exponential behaviour of recovery through Bernoulli-type equation. The model was compared with other reported models as the model proposed by Dixon and Hendrix, (1993ab), which is more complex; the comparison reached outstanding levels of representation with less computational effort.

The recovery is a dynamic quantity related proportional to the difference between the extracted material at long term, and one obtained at time , . This kinetic expression of order can be represented by:

5.9

Assuming an order of reaction equal to 1 ( ), the resulting equation is a Bernoulli-type expression with an exponential trend and asymptotic in the unity.

5.10 ( )

This expression is general and do not represent that occur in each scale of heap and particle, for this reason terms that give account of each scale were added. Dimensionless times for the heap, and for the particle, were defined, according to the following definitions:

5.11

5.12

The recovery is the global consideration of the recoveries of each scale, therefore is possible to calculate the global recovery from the sum of each partial recovery.

5.13

Due to are managing two level in one equation, it was necessary to incorporate a factor that denotes the importance of one level on the other, , which is a dimensionless parameter

51 CHAPTER 5. MODELLING of caliche HEAP LEACHING

defined as the relative importance of heap level with respect of the global recovery; is referred for particle. Replacing

( ( )) ( ( )) 5.14 [ ]

The parameter is the dimensionless delay. It was defined two dimensionless kinetic constants, and that are adjustable parameters that are related with each size scale. This hybrid-type model considers aspects related with principles as the definition of dimensionless times and also has empirical formulation coming from the exponential trend by Bernoulli equation.

Up to now, it has been describing the hybrid model developed for copper ores. As was previously described and in contrast to metallic-ores leaching, the caliche processing is headed by dissolution phenomenon that implies that the heap decreases its size as consequence of the diminution of particle radius when the soluble material is released and the subsequent collapsing. For this reason several modifications were done to the model of Mellado et al., 2009 (Equation 5.14).

One of the adjustment is related with the dimensionless times definition, because at particle level, is dependent of the transfer rate of species from solid matrix to the bed, both related with the mass transfer coefficient, , and the concentration solubility, .

5.15

The term was included with the objective to manage the same volume units.

On other hand, the dimensionless heap time, did not suffer modification, because the heap scale is only dependant of operational parameters. The variable notation was changed for the irrigation rate, , volumetric fraction of liquid, and the heap height, .

52 CHAPTER 5. MODELLING OF CALICHE HEAP LEACHING

5.16

An important aspect of caliche heap leaching is that height and particle size are variables that changes with the time. For this reason, the calculation of both parameters was done in function of recovery, in an iterative arrangement.

5.17 √

5.18

Finally, the hybrid model for global recovery calculation is expressed:

( ( )) ( ( )) 5.19 [ ]

53 CHAPTER 6. SUMMARY OF PAPERS

CHAPTER 6. SUMMARY OF PAPERS

The development of this thesis has led to the writing of three ISI papers, which are summarized in this chapter. The brief revision of each one is presented, but if the reader wants more details, is referred to appendices for their integral form.

Paper I: Heap leaching of caliche minerals: Phenomenological and analytical models – Some comparisons (Gálvez et al., 2012)

Aim

Although in Valencia et al. (2008) the first exercises to capture the dissolution behaviour of some components of caliche were done through mathematical models, in this article the process of caliche heap leaching is addressed under two different approaches: improving the phenomenological model previously developed by Valencia et al. (2008) and to propose a new adapted model for caliche based on the originally implanted expression for copper minerals (Mellado et al., 2009). Both expressions are compared and from the values simulated by phenomenological model the hybrid one was theoretically validated. The interpolation and extrapolation capacities are also determined for this model in order to prove the suitability of use it in optimization tasks.

Methodology/Modelling

Two models were considered in this work: a phenomenological and hybrid model, both with different applications. A transversal consideration of caliche heap leaching is that the wide variety of minerals that are dissolved simultaneously at different rates and the high fraction of water-soluble species imply a decreasing of particle and heap size during the leaching. For both modelling works, a one-dimensional columnar system is used as representative central element for a heap. Concerning to the geometry and chemical composition, the heap is composed by non-porous spherical particles with equal initial radius ( ) and homogenously distributed by inert and soluble material. The dissolution behaviour comprises the dissolution

55 CHAPTER 6. SUMMARY OF PAPERS

of soluble material spreads only in the surface of particles and the release of inert part leads the particle collapsing.

In the phenomenological model the heap is modelled as a column divided in mini-reactors disposed in series. At the beginning, these tanks have same quantity of material, therefore they have equal initial height ( ), but during the particle dissolution, their sizes changes with the time. The variation of particle radius in function of time is determined by a material balance of the particle and by the dissolution model of Bruner and Tolloczko (Dokoumetzidis and Macheras, 2006) that relates the changes of concentration along the time with the product between the exposed surface area and the difference between the solubility, , and the instantaneous concentration in each reactor , . From the interrelation of these expressions, assuming constant bed porosity, deriving and reordering the expression results:

6.1 ( )

where is the radius of the particle in each reactor, is the time, is a mass transfer coefficient, is the particle density, is the height of reactor , is the fraction of the soluble species in the particle, is the water flux through the column, is the water fraction in the bed, is the concentration in reactor and is the concentration that flows into reactor from reactor .

The hybrid model is based on the approach used for modelling of leaching copper ores (Mellado et al., 2009); a first-order kinetic model for caliche minerals was described. One of the most important issues of this model is the concept that leaching occurs on two different scales of size and time that are particle and heap levels. Assuming that the global recovery is in function of the every-scale recovery, it is obtained:

( ( )) ( ) 6.2 [ ]

where and are constants related with heap and particle scales, is the heap height at any time and is the grade of contribution of heap level in the global recovery and

56 CHAPTER 6. SUMMARY OF PAPERS

is equivalent to the fraction . In the same way, corresponds to the importance of particle scale.

Results and Discussion

Phenomenological model

To simulate data from the phenomenological model, different parameter values were used, which are detailed in Table 6.1.

Table 6.1. Values used in the simulations.

Entity Unit Central value Interval Heap height m 10 8 – 12 Number of small columns 10 5 – 20 Particle diameter m 0.15 0.10 – 0.20 Solid density kg/m3 2000 Mass transfer coefficient m/h 0.0001 0.00003 – 0.0003 Solubility kg/m3 200 100 – 400 Column porosity 0.45 Water porosity in column 0.015 Fraction of soluble material 0.40 Water flux m3/m2/h 0.005 0.004 – 0.006

In a first approach, the central value was used to show the properties of the phenomenological model. According to the expected, the decreasing of particle sizes is headed by the upper reactors, while the bottom tanks have a slower diminution rate of radius.

In the sensitivity analysis of this model, it was determined that recovery increased as the mass transfer coefficient increased. However, mass transfer coefficients greater than 0.0003 m/h seemed to have a lower effect on increasing the recovery, since recovery is controlled by salt solubility for high mass transfer coefficients. Solubility also has a large impact on the leaching process. For example, when solubility was duplicated, the time for salt depletion was reduced almost 50%. The number of reactors used for modelling determines the dispersion in the system and the results showed that recovery is almost independent of the number of reactors.

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Hybrid model

Through the simulated data of the phenomenological model, the hybrid model was fitted, being , , and the adjustable parameters and conducted using the operational parameters: heap height, particle diameter, and irrigation rate. The predictive capability of the model was tested using three scenarios with different number of fitting data. The results indicate that the fit of the analytical model to the simulated experimental data was good for the three cases with an average error of 1.8% (Figure 6.1). The recovery decreases with height, and longer times are required to obtain a high recovery and also decreases with the initial particle diameter. Finally, recovery increased with irrigation rate.

1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6

Recovery Recovery Recovery 0.4 0.4 0.4

q=0.003 m3/m2/h D=0.10 m H=8 m 0.2 0.2 0.2 q=0.005 m3/m2/h D=0.15 m H= 10 m q=0.006 m3/m2/h D=0.20 m H= 12 m 0.0 0.0 0.0 40 80 120 160 200 40 80 120 160 200 40 80 120 160 200 Time, d Time, d Time, d a) b) c)

Figure 6.1. Relative recovery of the soluble species as a function of time for different a) irrigation rate, b) particle diameter and c) Initial heap height. The lines are the analytical model, and the markers are the simulated experimental data.

The capability of interpolation/extrapolation was done by fitting the model with a subset of data points and then predicting other data points. For interpolation, the model was fitted using the data points obtained with the endpoints of the interval for each parameter, and the central value of the parameter is predicted. For extrapolation, the data for the central value and one endpoint value are used for fitting, and the other endpoint value was predicted.

The errors obtained in the fitting process were small, therefore the hybrid model describes the system well and it captures the recovery trends in spite of the variation of the parameters. The limited number of data points required for fitting is an important issue of

58 CHAPTER 6. SUMMARY OF PAPERS

this model. Although the small number of data points used in the fitting process, the predictions at other irrigation rates and even at other heap heights and particle diameters were satisfactory.

Conclusions

Once compared data sets, interpolation and extrapolation capability was tested. In general, low errors were obtained; the prediction capability was good and the behaviour of interpolation/extrapolation was stable using different operational parameters variation (Cs, q and H). Analytical hybrid model is suitable to be applied in optimization or design tasks and in postmodelling activities, even when the model requires to be solved a large number of times. On the other hand, the phenomenological model is useful in determining relationships between the different parameters and comprehension of the collateral phenomena associated to leaching as particle size diminution.

59 CHAPTER 6. SUMMARY OF PAPERS

Paper II Seawater leaching of caliche mineral in column experiments (Ordóñez et al., 2013)

Aim

The aim of this work is validate experimentally a previously developed phenomenological model for highly soluble species and to formulate a simple model for less soluble ions that precipitate into the column. Both expressions were validated using pilot column leaching experiments.

Methodology/Modelling

Column leaching

Leaching was performed in seven columns of 0.2 m of diameter for 20 days, using different operational conditions that are listed in Table 4.4. The use of seawater as a leachant was an important issue of this work, in order to test the potential replacing of solutions in the present context of fresh water scarcity. The mineral employed in the experiments comes from Northern Chile with a median size of 6.8 mm. A complete description of column leaching methodology is detailed in Chapter 4.

Modelling of leaching for highly soluble species

The model presented in Gálvez et al. (2012) was validated using experimental data of caliche column leaching. The description is extensively described in Chapter 3, being the final equation:

6.3 ( )

The mass transfer coefficient was the adjustable parameter and the fitting procedure was by the least square method.

61 CHAPTER 6. SUMMARY OF PAPERS

Modelling of leaching for less soluble species

A new phenomenological model that describes in a simple way the ionic interaction into the columns during caliche leaching was developed. The concentration of the sodium, at the beginning of leaching process, is very high due to the presence of the highly soluble sodium nitrate is leached increasing strongly the concentration of sodium. Some minerals containing sodium, such as sodium sulphate and sodium chloride may therefore reach the saturation and precipitate due to the effect of the common ion (Cisternas, 2009).

This model takes account the common ion phenomenon that leads precipitation of sodium sulphate through a material balance of theoretical reactors arranged in series and considers the product of solubility of some species that forming caliche. In this first approach only 3 sodium minerals ( ) and 4 ions ( ) were considered, resulting:

6.4 [ ( ) ]

where is the amount (mol) in each reactor and the molar concentration. Due to sodium is the unique cation associated with all the anions studied, the equation for it in each reactor is:

6.5 [ ( ) ]

According to the balance for the minerals that are formed by sodium i.e. sodium sulphate, sodium nitrate and sodium chloride, the obtained expression is:

6.6 ( )

In this equation, denotes the valence of the anion. For monovalent ions the value of is 1 and for sulphate (bivalent) mineral the magnitude is 2. The is the dissolution constant for each mineral and was considered the adjustable parameter of this model.

62 CHAPTER 6. SUMMARY OF PAPERS

Results and discussion

Final concentration for all ions and experiments resulted similar to the feeding levels, demonstrating that the employed times were adequate for the study. Among different leachants, the lowest responses were obtained for charged solutions, because their extracting capabilities are lower, while seawater and tap water leaching were the best. The use of tap water involves less fed water to obtain the lowest concentrations. The use of seawater does not result in appreciable differences with tap water performance, observing that for sodium and chloride the final levels were higher than for column irrigated with tap water, since salinity of seawater. Sulphate was leached with slower kinetic (Figure 4.4).

Calcium ion had a different trend of leaching, because while other ions decrease their levels, calcium increased its concentration. The low solubility of main species that are composed by calcium, such as gypsum and anhydrite and the control by sulphate levels on calcium at the outlet may be the reason for this behaviour.

Sodium sulphate precipitated into the columns after few days of leaching. This crystallization was due to the interaction between sulphate and the free sodium present in the column as consequence of the rapid release of nitrate.

The irrigation rate has an important effect on the concentration decreasing, but it is not a linear behaviour due to other factors are related such as dissolution of a third controlling species. The studied ions were divided in three categories according to their dissolution behaviours: most soluble - nitrate, iodine and perchlorate, intermediate soluble - sodium, potassium and magnesium and less soluble: sulphate and chloride

Validation of the phenomenological model proposed by Gálvez et al. (2012) and designed for highly soluble and non controlled by dissolution of third ions was done. Data obtained from the seven columns were considered and the fitting of the mass transfer coefficient ( ) was performed independently by the least square method for nitrate and iodine. The -parameter is important because describes the rate of dissolution of the species. The fitted values for nitrate for all experiments was, in general, three times greater than ones for iodine and the coefficients were more importantly affected by the irrigation rate than by other operational parameters such as leachant concentration and initial column height (Figure 6.2).

63 CHAPTER 6. SUMMARY OF PAPERS

225 1.5 SW, q=0.006 m/h, SW, q=0.006 m/h, H=0.6 m H=0.6 m

TW, q=0.006 m/h, 3 TW, q=0.006 m/h,

3 180

H=1.0 m H=1.0 m g/m

g/m LX, q=0.006 m/h, LX, q=0.006 m/h, H=0.6 m 1.0 H=0.6 m 135

90 0.5

45 concentration,k Iodine Nitrate concentration, k concentration,Nitrate

0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

a) VL/VB b) VL/VB Figure 6.2. Fitting of phenomenological model using concentrations obtained from experiments (Dotted: SW and Solid: TW and Dashed: LX) for a) Nitrate and b) Iodine.

For less soluble ions, i.e. sulphate and chloride a new model with simple formulation was performed, which considers the chemical interaction of 3 mineralogical species. The objective of this model is to reproduce the precipitation of sodium sulphate that is related with the common ion effect. Nitratine (sodium nitrate) and halite (sodium chloride) are 2 of the most abundant soluble components of caliche. At early times of leaching, the nitrate falls rapidly its concentration, remaining free sodium into the column. In a same way, but with a delay, chloride also leaves the column. All free sodium interacts with the sulphate that remained in the column after releasing of more soluble constituents. By this form, the reaction results in the precipitation of sodium sulphate as crystals.

The validation of the precipitation model was done, by fitting the dissolution constants for the sodium minerals and the agreement resulted satisfactorily (Figure 6.3). The simple approach of this model limits its application in actual processes, because mineralogical, chemical and granulometric simplifications were done. Although through this type of models is possible to understand one part of the leaching process. Data required are the main limitation of this model, because they are not extensively available in the literature. Multiple assumptions of values were realised.

64 CHAPTER 6. SUMMARY OF PAPERS

4 4 4 NO3 NO3 NO3 Cl Cl Cl 3 3 3 SO4 SO4 SO4

2 2 2

1 1 mol/LConcentration, 1

Concentration, mol/LConcentration, Concentration, mol/LConcentration,

0 0 0 0 200 400 0 200 400 0 200 400 a) Time, h b) Time, h c) Time, h Figure 6.3. Experimental (markers) and simulated outlet concentration (lines) using the chemical reaction model for columns: a) SW, q=0.006 m3/m2/h, H=0.6 m, b) TW, q=0.006 m3/m2/h, H=1.0 m and c) LX, 0.006 m3/m2/h, H=0.6 m.

Conclusions

Experiments of leaching in columns were performed, which showed different dissolution behaviours for various species: highly soluble and less soluble ions. In the first group, the concentration falling of nitrate, perchlorate and iodine is abrupt, while for the other species, such as sulphate and chloride, the diminution is gradual. Additionally, the use of desalinised seawater as water alternative was tested without appreciable differences in the leaching performance.

The decreasing of concentration was analysed using models. For nitrate and iodine, the phenomenological model proposed in Gálvez et al., 2012 was validated through fitting the mass transfer coefficient parameter. The results of this agreement showed that the leaching process of these ions may be represented adequately. Moreover, it was demonstrated that this parameter is dependent of the irrigation rate, in the way that increases as the irrigation is higher. For less soluble materials, a new model was developed focused on the precipitation of sodium sulphate, obtaining good levels of agreement.

In order to improve the modelling features, in subsequent works other aspects such as: mineralogy of ores, activity coefficients and use of larger particles may be considered.

65 CHAPTER 6. SUMMARY OF PAPERS

Paper III Modelling validation of caliche ore leaching using seawater (Ordóñez et al. In Press)

Aim

The aim of this article is validate the hybrid model developed in Gálvez et al. (2012) by using the experimental data collected by Ordóñez et al. (2013). This validation is performed adjusting some parameters and it includes a sensitivity and predictability analysis in order to demonstrate the applicability of this model in design and optimization tasks.

Methodology/Modelling

Column leaching

Leaching experiments were performed columns of 0.2 m of diameter during 20 days, testing different operational conditions that are listed in Table 4.4. The mineral used in the experiments comes from Northern Chile and its fine fraction (less than 2.4 mm) was discarded to avoid possible obstruction of column systems. A complete description of column leaching methodology is detailed in Chapter 4.

Modelling of recovery

As can be reviewed in Chapter 3.3, the hybrid model was developed in Gálvez et al. (2012) considering the leaching process as a multiscale phenomenon, where a particle and heap level is defined.

( ) ( ) 6.7 [ ]

However in this article several assumptions were done and new constants were defined in order to increase the stability of simulation and velocity of calculation.

67 CHAPTER 6. SUMMARY OF PAPERS

Delay time, is equal to zero, because the experimental time started with the first drop of leachate at the column outlet. and were defined as single values for all ions. The particle radius was assumed constant, due to the used granulometry was very small, therefore its diminution does not have effect on the recovery. Moreover, in order to use the model for tests irrigated with charged solutions, the term was replaced by . The resulting expression is the following, being the fitting parameters: , and .

6.8 [ ]

Results and Discussion

The experimental recoveries for all ions were calculated by mass balance for each experiment. Nitrate is highly soluble and was removed rapidly from all columns and together iodine, its recovery was similar between SW and TW experiments. For the other ions, TW resulted in higher levels because is the less concentrated leachant. As expected, in columns irrigated with charged solutions the recoveries were low for all ions, because the extraction capability decreased. The concentration of feeding appears to be the most important parameter that affects the recovery responses. Sulphate recovery was the lowest in all experiments as consequence of its low solubility and its initial dissolution control exerted by other ions such as sodium and calcium. Due to small particles were used in all of the experiments, the influence of their size is small on global recovery and the dissolution of all ions is, in a large extent, controlled by solubility limitations. For more details about experimental results, in Chapter 4 are deeply commented.

was defined as the operational solubility for each ion because no pure substances are obtained from caliche dissolution and was obtained by maximum concentrations achieved in leachates during experiments. The difference between and is the driving force of dissolution and has an important effect on the leaching behaviour. Some of the parameters were obtained from literature and others by empirical determination such as that is defined as the mass fraction of each ion (Table 6.2).

68 CHAPTER 6. SUMMARY OF PAPERS

Table 6.2. Values used in simulations of hybrid model.

Parameter Symbol Value Particle radius, m 0.003 Mineral density, kg/m3 1900 Fraction of retained solution 0.08 Limit recovery 0.99

The fitted parameters related with heap scale, and were 0.21 and 0.7, respectively. , specific of each ion, resulted with higher for the most soluble ions: nitrate and iodine, and the lowest for the less soluble, sulphate (Table 6.3). These behaviour is due to is related with the constant dissolution, . value shows that column scale had a higher effect on recovery than particle level, which reveals that due to small size used, no significant resistances are associated with particle scale.

Table 6.3. Fitted values of K2,i - parameter.

Ion , m/h NO3- 2.10*10-4 SO42- 1.30*10-6 IO3- 1.20*10-4 Cl- 6.40*10-6 Na+ 7.70*10-6 K+ 5.50*10-6 Mg2+ 6.70*10-6

The model captures the exponential trend of recovery of all ions with different levels of accuracy depending on the experiment analysed (Figure 6.4 and Figure 6.5). The differences of fitting quality could be attributed to the formation of preferential paths of leachant transport. A limitation of the model is that it does not consider collateral phenomena occurring such as precipitation of specific ions and dissolution control of third parties.

69 CHAPTER 6. SUMMARY OF PAPERS

1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6

Rm,Na

Recovery Recovery Recovery 0.4 0.4 0.4 Rx,Na Rm,NO3 Rm,Cl Rm,K Rx,NO3 Rx,Cl Rx,K 0.2 0.2 0.2 Rm,IO3 Rm,SO4 Rm,Mg Rx,IO3 Rx,SO4 Rx,Mg 0.0 0.0 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time, h Time, h Time, h

Figure 6.4. Experimental (markers) and modelled (lines) recoveries for SW3S experiment.

1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6 Rm,Na

Rx,Na

Recovery Recovery Recovery 0.4 0.4 0.4 Rm,NO3 Rm,Cl Rm,K Rx,NO3 Rx,Cl Rx,K 0.2 0.2 0.2 Rm,IO3 Rm,SO4 Rm,Mg Rx,IO3 Rx,SO4 Rx,Mg 0.0 0.0 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time, h Time, h Time, h

Figure 6.5. Experimental (markers) and modelled (lines) recoveries for RS6S experiment.

To determine the most important parameters that affect the recovery responses, a sensitivity analysis was done for , , and . Three values of each parameter were considered and the analysis was performed independently using the central values for the remaining parameters (Table 6.4).

Table 6.4. Parameter values used in the sensitivity analysis.

Parameter Units Values

m/h 3*10-5 1*10-4 4*10-4 3 kg/m 20 80 200 m 0.4 1.0 1.6 m3/m2/h 0.002 0.004 0.006

70 CHAPTER 6. SUMMARY OF PAPERS

Caliche specific properties had an important role of recovery at brief times in a direct relation, higher recoveries are obtained by species with high and . and (operational parameters) resulted in opposite responses. Taller initial beds obtain less values of recoveries, while q had a direct effect on recovery but with a limitation of the dissolution kinetic related with the specific property . Simulated recoveries of the model are strongly influenced by the intrinsic characteristics of the material and in a less manner by operational conditions, which play a role in a middle/large term of leaching.

For a predictability analysis, , and were initially fitted for some experiments and then, the values obtained were used to simulate data of other experiments carried out under different operation conditions ( , and ). All ion recoveries were predicted and as indicator of prediction quality, the determination coefficient was calculated. Three cases were studied, where two columns were fitted and 2 or 3 other experiments were predicted (Table 6.5).

Table 6.5. Prediction of experiments and determination coefficients.

Cases Fitted experiments Predicted experiments Case 1 SW3S - SW3L RS6S 0.92 DS6L 0.96 Case 2 SW3L - TW6L SW3S 0.97 RS6S 0.85 Case 3 TW6L - RS6S SW3S 0.97 SW3L 0.93 DS6L 0.94

The distribution of data reveals the soluble nature of ions, because a large quantity of recoveries of high soluble species was located in the upper part of the plot, while less soluble ions have data points more spread along leaching. Simulated recoveries of sodium, chloride and sulphate at brief times were frequently higher than experimental ones and less at longer times. This trend is attributed to the common ion effect, which is not addressed by the hybrid model. At longer times, the behaviour is opposite because a significant amount of sodium has been depleted from the column. The effect of sodium in columns irrigated with SW and TW was less notorious because the concentration of this ion is lower.

71 CHAPTER 6. SUMMARY OF PAPERS

The model showed to be a useful tool to predict recoveries of pilot experiments for a wide variety of ions, even for columns run under different operational conditions, since high values of were achieved by almost all predicted experiments (Figure 6.6).

1.0 1.0 R2 = 0.92 R2 = 0.96 0.8 0.8

0.6 0.6

0.4 0.4 Predicted recovery Predicted NO3 IO3 recovery Predicted NO3 IO3 Na K Na K 0.2 Mg Cl 0.2 Mg Cl SO4 SO4 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 Experimental recovery Experimental recovery

Figure 6.6. Predictability analysis for RS6S (left) and DS6L (right) experiments, fitting SW3S and SW3L.

Conclusions

This work contributes to validate the hybrid model with experimental data and analyse it in terms of the sensitivity and predictability studies. The fitting exhibited acceptable agreement considering the simplifications and assumptions that were used in the model. Its strength is that the values obtained for the particle-related constants ( ) are coherent with the values expected considering the dissolution kinetics of the different ions. The sensitivity analysis showed that the most important parameters were those intrinsic properties, such as the operational solubility and the mass transfer coefficient . The applicability of the model was tested by predictability analysis, which resulted in good agreements and established that is possible to determine the responses of a column through the model fitted with data of other tests.

72 CHAPTER 7. CONCLUSIONS AND FINAL REMARKS

CHAPTER 7. CONCLUSIONS AND FINAL REMARKS

This chapter provides the main findings of this thesis, some of them having been included on the published articles. Then, the conclusions of the work were indicated, which respond to the specific objectives and consolidate the contribution of this thesis. Additionally, final remarks and suggestions are indicated at the end of this chapter in order to canalise improvements and new studies related with the topic of leaching of soluble particles.

7.1. Major findings of the thesis

The results of conducted column leaching experiments constitute a contribution by itself, since information on caliche dissolution tests in pilot scale does not exist in the open literature. According to the behaviour of dissolution, three families of ions were categorized from highly soluble ions as nitrate, perchlorate and iodine to less soluble as sulphate and calcium, passing by ions with moderate solubility as potassium, sodium and magnesium.

An important aspect in the leaching tests is to study the operating conditions, and among them, the use of different leaching agents such as seawater. Leaching made with this leachant was similar to that made with tap water, which considers the seawater in a potential replacement of water sources due to its scarcity in northern Chile. Charged solutions were also tested due to in actual operations solutions are recirculated. The other parameters that were evaluated are initial bed heights and irrigation rates.

The highest concentration variations and recovery variations were obtained in the order of leachant, irrigation rate and bed height: Tap water > Seawater > Diluted solution > Charged solution, 0.006>0.004>0.003 m3/m2/h and 0.6>0.8>1.0 m. The responses of experimental observation were used also to validate the models that were developed in this work.

This thesis consisted in the development of models that are focused on caliche heap leaching process. To explain the leaching of caliche, a comprehensive phenomenological expression based on mass balance was developed, which evaluates the variations of

73 CHAPTER 7. CONCLUSIONS AND FINAL REMARKS

concentration of several ions during particle dissolution. The model was validated using experimental data by fitting the mass transfer coefficients of nitrate and iodine separately. The agreement was good and captured the fast concentration decrease even under different conditions of run.

An important observation from the experiments was the evidence of crystallization of sodium sulphate as consequence of dissolution control exerted by other shared ion such as sodium. A simple phenomenological model was developed in order to represent the ionic interaction causing this precipitation into columns. The model reproduces satisfactorily the phenomenon; however it can be considered as first approach due to the defined system is highly simplified to three sodium minerals.

On the other hand, a model describing the leaching in terms of recovery along time of different ions was realised, which has operational applicability due to its analytical empirical formulation is simple and gives important information with low computational effort. From its sensitivity analysis resulted that the most important parameters are whose ones related to particle level i.e. solubility concentration, and mass transfer coefficient, . A predictive analysis demonstrated that with few numbers of experiments is possible to determine responses of other treatments.

7.2. General conclusions

. One of the contributions of this thesis is the experimental data related with the dissolution of soluble ions forming caliche. From the results, the use of seawater was validated as a leachant with the same extractive capability than process water. . A phenomenological model has been developed, which describes accurately the phenomena involved in caliche heap leaching. The use of this model in the dissolution of highly soluble minerals such as nitrate and iodine was done with high levels of accuracy. . Good responses were also obtained for the precipitation of less soluble species as sodium sulphate through a second phenomenological model that considers the solubility products and the common ion effect.

74 CHAPTER 7. CONCLUSIONS AND FINAL REMARKS

. A hybrid model has been formulated representing the leaching of caliche as a multiscale process. The recoveries of 7 ions were simulated satisfactorily, for which a fitting procedure was performed.

7.3. Final remarks and recommendations

Through the different written articles is possible to track the main idea of this thesis that is understand the phenomena of caliche heap leaching and contribute to establish more controlled processes of this mineral by mathematical models. It is relevant to underline that there some challenges remain as substrate for subsequent studies:

. Extend the phenomenological precipitation/crystallization model to more realistic systems, due to in a first approach the crystallization phenomenon was represented with a simplified mineralogy of caliche (3 minerals), but caliche is composed by a wide quantity of species, for this reason in a second step, the incorporation of more species is required in order to approximate to real conditions of caliche ores. . Use of coarser particles for column leaching experiments is interesting to study, because with this size-type of particles, which are closest to macroparticles used in real leaching, the dissolution behaviours may vary as consequence of apparition of new controlling steps such as diffusion through large rocks and liquid transport through the bed. . One of the assumptions of the phenomenological model for the dissolution of soluble species is that the particles are formed by inert and soluble material distributed homogeneously and soluble fraction corresponds to a single species or a family of ions with equal dissolution kinetics. Given that composition of caliche is rich in soluble species of different nature, in a next step the model should be include at least two ions or family of ions with different leaching kinetics to analyze the dissolution of caliche ores with a higher degree of attachment to reality. . In a related work, the physical properties of caliche minerals are being determined in order to characterize the solid material such as density, porosity, capillary suction and permeability. The integration of the parameters to proposed models will soon be done.

75 CHAPTER 8. REFERENCES

CHAPTER 8. REFERENCES

Anderson, Steven T., 2013. 2011 Minerals Yearbook: Chile advance release, The mineral industry of Chile. U.S. Geological Survey USGS Report.

Bartlett, R.W., 1992. Simulation of ore heap leaching using deterministic models. Hydrometallurgy 29, 231-260.

Bermúdez, O., 1987. Breve Historia del Salitre: Síntesis Histórica desde sus Orígenes hasta Mediados del Siglo XX. Ediciones Pampa Desnuda, Santiago.

Bouffard, S.C., Dixon, D.G., 2007. Evaluation of kinetic and diffusion phenomena in cyanide leaching of crushed and run-of-mine gold ores. Hydrometallurgy 86, 63-71

Chandía, E., 2012. Diseño y análisis técnico-económico de una central solar termoeléctrica con almacenamiento térmico en el norte de Chile. Magister thesis Universidad de Chile.

Cisternas, L.A., 2009. Diagramas de fases y su aplicación. 1st edition, Reverté, Barcelona.

De Andrade Lima, L.R.P., 2004. A mathematical model for isothermal heap and column leaching. Brazilian Journal of Chemical Engineering 21, 435–447.

Dixon, D.G., Hendrix, J.L.,1993a. A mathematical model for heap leaching of one or more solids reactants from porous ore pellets. Metallurgical Transactions 24B,1087–1102.

Dixon, D.G., Hendrix, J.L., 1993b. General model for leaching of one or more solids reactants from porous ore pellets. Metallurgical Transactions 24B, 157–168.

Dokoumetzidis, A., Macheras, P., 2006. A century of dissolution research: From Noyes and Whitney to the Biopharmaceutics Classification Systems. International Journal of Pharmaceutics 321, 1–11.

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Donald, M.B., 1936a. History of the Chile nitrate industry. —I, Annals of Science, 1:1, 29-47.

Donald, M.B., 1936b. History of the Chile nitrate industry.—II, Annals of Science, 1:2, 193- 216.

Ericksen, G.E., 1983. The Chilean Nitrate Deposits. American Scientist 71, 366–374.

Fleming, C.A.,1992. Hydrometallurgy of precious metals recovery. Hydrometallurgy 30, 127– 162.

Gálvez, E.D., Moreno, L., Mellado, M.E., Ordóñez, J.I., Cisternas, L.A., 2012. Heap leaching of Caliche minerals: Phenomenological and analytical models – Some comparisons. Minerals Engineering 33, 46–53.

Ghorbani, Y., Becker, M., Mainza, A., Franzidis, J., Petersen, J., 2011. Large particle effects in chemical/biochemical heap leach processes – A review. Minerals Engineering 24, 1172– 1184.

Jackson J.C., Ericksen, G.E., 1994. An X-ray diffraction method for semiquantitative mineralogical analysis of Chilean nitrate ore. U.S. Geological Survey, Open-file Report 94 240, 1-28.

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78 CHAPTER 8. REFERENCES

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Mellado, M.E., Gálvez, E.D., Cisternas, L.A., Ordóñez, J.I., 2012. A posteriori analysis of analytical models for heap leaching. Minerals & Metallurgical processing 29 (2), 103–112.

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79 CHAPTER 8. REFERENCES

Taboada, M.E., Hernández, P.C., Galleguillos, H.R., Flores, E.K., Graber, T.A., 2012. Behavior of sodium nitrate and caliche mineral in seawater: Solubility and Physicochemical properties at different temperatures and concentrations. Hydrometallurgy 113-114, 160-166.

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80 APPENDIX A. PAPERS

APPENDIX A. PAPERS

. Heap leaching of Caliche minerals: Phenomenological and analytical models – Some comparisons. Minerals Engineering 33, 46–53.

. Seawater leaching of caliche mineral in column experiments. Hydrometallurgy 139, 79–87.

. Modeling validation of caliche ore leaching using seawater. International Journal of Mineral Processing. In Press.

81 APPENDIX A. PAPERS

Paper I

Heap leaching of Caliche minerals: Phenomenological and analytical models – Some comparisons

Minerals Engineering 33, 46–53.

Accessible at: http://dx.doi.org/10.1016/j.mineng.2011.11.009

83 Minerals Engineering 33 (2012) 46–53

Contents lists available at SciVerse ScienceDirect

Minerals Engineering

journal homepage: www.elsevier.com/locate/mineng

Heap leaching of caliche minerals: Phenomenological and analytical models – Some comparisons ⇑ Edelmira D. Gálvez a,b, Luis Moreno c,d, Mario E. Mellado b, Javier I. Ordóñez d, Luis A. Cisternas b,d, a Dept. of Metallurgical Engineering, Universidad Católica del Norte, Antofagasta, Chile b Centro de Investigación Científico Tecnológico para la Minería (CICITEM), Antofagasta, Chile c Dept. of Chemical Engineering and Technology, Royal Institute of Technology, Stockholm, Sweden d Dept. of Chemical and Mineral Process Engineering, Universidad de Antofagasta, Antofagasta, Chile article info abstract

Article history: Antofagasta, Chile, has one of the most important deposits of saltpetre in the world, which is called cali- Available online 9 December 2011 che. These deposits are mainly composed of nitrate, halite, sodium anorthite, and quartz. Minor species include anhydrite, glauberite, loeweite, calcite, polyhalite, probertite, and gypsum. Recently, several oper- Keywords: ations began to use heap leaching for the extraction of saltpetre. Modelling the heap leaching of caliche is Heap leaching not straightforward because of the many minerals and their different dissolution rates. Moreover, caliche Saltpetre may have a large fraction of soluble minerals, approximately 40%, which causes the heap to slump. In this Phenomenological models work, we present two models. The first, which is a phenomenological model, is an extension of the model Analytical models published by Valencia et al. (2008). The system is modelled as a column comprised of N small columns, and in each of these small columns, the height of the solids varies with time when the soluble minerals are dissolved. The liquid in each small column has the same composition (well-stirred reactor). The sec- ond model, which is an analytical model, is an extension of that published by Mellado et al. (2009) for low-grade minerals, such as copper and gold, which considers that the leaching phenomenon occurs on different scales of size and time. However, in this work, the time scale at the particle level is based on the Bruner and Tolloczko dissolution model. The objective of this work is to test the suitability of the analytical model as a tool for use in optimisation, for which the model needs to be solved many times. The phenomenological model was used to generate simulated experimental data. The results show that the analytical model may be a useful tool in optimisation. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction to leach caliche minerals. The leaching of piled minerals represents a valid alternative for low-grade caliche due to excellent economic Caliche minerals, which are found in Northern Chile, are primar- and technological possibilities and good levels of recovery when ily composed of nitrate (NaNO3), halite (NaCl), sodium anorthite compared with the vat-leaching technology typically utilised for ((Ca,Na)(SiAl)4O8), and quartz. Minor species include anhydrite, high-grade caliche. glauberite, loeweite, calcite, polyhalite, probertite, and gypsum The leaching of caliche differs from the leaching of copper, zinc, (Valencia et al., 2008). Soluble minerals found in caliche are not well gold, and other metals. Regarding caliche, there are several soluble identified. These soluble minerals are mixed with inert minerals, species but few in metal minerals. Copper, zinc, and gold minerals such as quartz and other silicates. The proportion of inert minerals are leached by chemical reactions, however, caliche is dissolved. is 50–60%. Caliche is an important raw material for obtaining so- The variation of heap height over time is significant for caliche but dium nitrate, potassium nitrate, sodium sulphate, and iodine not for metal ores. (Lauterbach and Ober, 1995). There are several works related to the modelling of heap leach- Heap leaching is used widely for the leaching of metals such as ing, including phenomenological models (Bouffard and Dixon, copper (Dixon and Hendrix, 1993; Casas et al., 1998; Thiel and Smith, 2001; Cariaga et al., 2005; Cross et al., 2006; Mellado and Cisternas, 2004). In Chile, since 1990, heap leaching with water has been used 2008) and empirical and hybrid models (Mellado et al., 2009, 2011). However, these works are applicable to poorly soluble minerals. To date, there is only one published manuscript related to highly solu- ⇑ Corresponding author at: Dept. of Chemical and Mineral Process Engineering, ble minerals (Valencia et al., 2008). Universidad de Antofagasta, Antofagasta, Chile. The objective of this work is to test the suitability of the analytical E-mail addresses: [email protected] (E.D. Gálvez), [email protected] (L. Moreno), [email protected] (M.E. Mellado), [email protected] (J.I. Ordóñez), model as a tool for use in optimisation, where the model needs to [email protected] (L.A. Cisternas). be solved a very large number of times (hundreds of thousands).

0892-6875/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mineng.2011.11.009 E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53 47

Nomenclature

2 1 A cross-sectional area of the modelled column (m ) Rl recovery at infinite generalised dimensionless time (–) 3 Cs solubility of soluble species (kg/m ) ri particle radius in small column i (m) 3 Ci concentration in small column i (kg/m ) t time (h) D particle diameter (m) us superficial bulk flow velocity (m/h) 3 Hheap heap height (m) Vwi water volume in small column i (m ) H initial height of the small columns (m) a fraction of soluble species (–) hi height of column i (m) e porosity of the column and heap (–) k mass transfer coefficient (m/h) ea air volume fraction (–) kl dimensionless kinetics constant (–) ew water volume fraction (–) kh, ks dimensionless adjusted parameters in Eq. (13) (–) u dimensionless parameter (–) N number of small columns (–) l generalised dimensionless time (–) Np number of particles in each small column (–) x dimensionless time delay (–) Pe Peclet number (–) q particle density (kg/m3) q water flux through the column (m3/m2 h) h dimensionless column-scale time (–) R initial particle radius (m) s dimensionless particle-scale time (–) Rt recovery at time t (–) p, b, c adjustable constants in Eq. (14) (–) Rl recovery at generalised dimensionless time l (–)

The phenomenological model is used to generate simulated experi- controlled by those soluble minerals that are found in large con- mental data. The analytical model is fitted using a subset of this data centrations. Minerals that are present in small amounts are dis- and is then used to predict the other data points. solved following the dissolution of the major minerals. Minerals that have a low dissolution rate may be separated from the particle 2. Heap leaching models simultaneously with the inert materials and be dissolved later. At present, this is not considered in the models. In this section, we present two models. The first, which is a To model the leaching of caliche minerals in heaps and to keep phenomenological model, is an extension of the model published the models sufficiently simple, several assumptions are needed. by Valencia et al. (2008). The system is modelled as a column com- These assumptions are listed below: prised of N small columns. In each of these small columns, the height of the solid varies with time when the soluble minerals The particles are spherical and are initially of the same size. are dissolved. The liquid in each small column has the same com- They are non-porous. position (well-stirred reactor). The second model, which is an The soluble minerals and the inert material are homogeneously empirical knowledge-based model, is an extension of that pub- distributed in the particle. lished by Mellado et al. (2009), which considers two time and size Only the soluble minerals that are on the particle surface are kinetics scales and considers particle radius and heap height to be dissolved. time-dependent properties. The inert materials that remain at the particle surface after the Modelling the heap leaching of caliche minerals is not trivial removal of the soluble minerals are separated from the particle due to factors such as (a) the caliche composition, which is a mix- surface when the surface collapses. ture of many minerals that may have different dissolution rates A one-dimensional system is used for the heap, i.e., it is and (b) the large fraction of soluble minerals, which reaches values assumed that the horizontal dimensions of the heap are large. of approximately 40%; therefore, the heap height will decrease Therefore, a column of caliche minerals in the centre of the heap appreciably when the soluble minerals are dissolved. is modelled. The main soluble anionic chemical species in the caliche miner- als are nitrate, chloride, sulphate, iodate, perchlorate, and tetrabo- Other situations that may be modelled are straightforward; one rate. The cationic species are sodium, potassium, magnesium, and example is the leaching of caliche formed by particles of different calcium. Due to the large fraction of soluble minerals, the heap col- sizes that dissolve simultaneously. lapses during the leaching process; therefore, its height decreases with time. A heap of caliche minerals is formed by rocks of differ- 2.1. Modelling the heap as well-stirred reactors in series ent sizes, from a few millimetres to hundreds of millimetres. It is expected that, initially, the minerals at or near the particle surface To take into account the variation of the heap height with time were solubilised. When a significant fraction of minerals has been in a simple way, the system is modelled as a column comprised of dissolved, it is expected that the inert materials that remain on the N small columns (Fig. 1). In each of these small columns, the height particle surface were removed (e.g., by the collapse of the particle of the solid varies with time when the soluble minerals are dis- surface). However, the removal of the inert material is not impor- solved. The liquid in each small column has the same composition tant; due to the high content of soluble minerals in the caliche (well-stirred reactor). Therefore, in each small column (reactor), all minerals, it is expected that the inert material that remains on the particles have the same size, ri(t). The initial height of the heap the particle surface will have a small resistance to mass transport. is divided into small columns of initial height H = Hheap/N, where Another issue is the dissolution rate of the different soluble Hheap is the initial height of the heap, H is the initial height of each minerals in the particle. Here, it is assumed that the minerals be- small column, and N is the number of small columns or well-stir- neath the particle surface will be dissolved only when these min- red reactors. erals are directly exposed to the action of the leaching solution When a column is represented by a series of small well-stirred at the particle surface. Therefore, mineral dissolution will be reactors, the dispersive term is omitted in the equations describing 48 E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53

All the reactors have the same number of particles because the reac- tors have the same volume and the initial particle size is the same. The small columns with height H are initially filled with caliche minerals; however, due to the dissolution of the soluble minerals, the column height decreases with time. It is assumed that the porosity of the bed is constant, i.e., the ratio between the void vol- ume and total volume is kept constant. The small column is as-

sumed to be water unsaturated with a water fraction of ew. Therefore, the total porosity, e, comprises the air porosity, ea, and the water content, ew. The number of particles in each reactor may then be calculated as

AHð1 eÞ Np ¼ : ð4Þ 4 3 3 pR Introducing the expression for the number of particles and the water content into Eq. (3),

dhiCi 3HAð1 eÞ 2 dri Aew ¼ qAðCi1 CiÞ ðr Þaq ð5Þ Fig. 1. An illustration showing the N small columns (or reactors). dt R3 i dt

where hi is the height of reactor i at any time t. Taking the derivative of the accumulation term and simplifying, the processes occurring in the column or bed. The dispersion is ta- 2 ken into account by the number of reactors used to model the dCi q 1 3Haq ð1 eÞ ri dri Ci dhi ¼ ðCi1 CiÞ 3 : ð6Þ heap. A system formed by a large number of small well-stirred dt ew hi R ew hi dt hi dt reactors is equivalent to having a high Peclet number, i.e., a small dispersion. The opposite is true for a small number of well-stirred A relationship between the height of the small column and the reactors (large dispersion). The relationship between the number radius of the particles in the column is required. This may be deter- of well-stirred reactors and the Peclet number is (Levenspiel, 1999) mined by performing a mass balance and assuming that the porosity is constant. In this case, the column height is directly proportional to 3 Pe ¼ 2N: ð1Þ the particle volume (ri ). Therefore, the following relationship may be written: This relationship is valid only for high Peclet numbers. For low "# Peclet numbers, the relationship is approximated, e.g., for 5 reac- 3 3 3 ðR ri Þ ri hi ¼ H 1 a ¼ H 1 a þ a : ð7Þ tors (Pe = 10), the error is 10%; however, for 10 reactors (Pe = 20), R3 R the error is only 5%. Regarding the dissolution of the soluble minerals, it is assumed Taking the derivative of Eq. (7) with respect to time, a relation- that the particles initially have the same radius, R. The variation of ship between dri/dt and dhi/dt may be obtained the particle radius with time is determined by the Bruner and Toll- oczko dissolution model (Dokoumetzidis and Macheras, 2006), in dhi 3Ha 2 dri 3H k 2 ¼ 3 ri ¼ 3 ri ðCs CiÞ: ð8Þ which the rate of dissolution is proportional to the product be- dt R dt R q tween the exposed surface area and the difference between the solubility and the instantaneous concentration in reactor i at time 2.2. Analytical model t. Therefore, the variation of the particle radius with time in reactor i is In this section, an analytical model based on the first-order kinetic equation is developed by following the approach used by dri k ¼ ðCs CiÞð2Þ Mellado et al. (2009). In that work, for first-order kinetics, the dif- dt aq 1 ference between the recovery at infinite time, Rl , and the recovery at dimensionless time l, R , was represented by where ri [m] is the radius of the particle in reactor i, t [h] is the time, l 3 k [m/h] is a mass transfer coefficient, q [kg/m ] is the particle den- 1 dðRl RlÞ 1 sity, and a is the fraction of the soluble species in the particle. Cs [kg/ ¼klðRl RlÞð9Þ 3 3 dl m ] is the solubility of the soluble species, and Ci [kg/m ] is the con- centration of the species in the leaching solution in reactor i at time where l is a generalised dimensionless time and kl is a dimension- t. The term in parentheses represents the driving force for the mass less kinetics constant in the same time scale. The subscript l is used transport. in all the variables and parameters to indicate that they represent Here, the equations are written assuming that only one mineral the kinetics at dimensionless time l. The initial condition for solv- is dissolving from the caliche minerals or that all the soluble min- ing Eq. (9) is that at dimensionless time x, the variable Rl begins to erals are dissolving at the same rate. The material balance in the change (x is the dimensionless delay of Rl). The solution to this well-stirred reactor i, with cross-sectional area A,is problem is known to be

1 klðlxÞ dV wiCi dri R ¼ R ð1 e Þ for l x: ð10Þ ¼ qAðC C ÞN ð4pr2Þqa ð3Þ l l dt i1 i p i dt Considering that the leaching phenomenon occurs on different 3 3 2 where Vwi [m ] is the volume of water in reactor i, q [m /m h] is the scales of size and time and in relation to different phenomena that 3 water flux through the column, Ci [kg/m ] is the concentration in participate in the leaching process, expressions similar to Eq. (9) 3 reactor i and Ci 1 [kg/m ] is the concentration that flows into reac- can be used to represent each of these phenomena. For the heap tor i from reactor i 1. Np is the number of particles in each reactor. leaching model in Dixon and Hendrix (1993), it is observed that E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53 49 the time scale at the heap level for the differential equations, after 200 the non-dimensionalisation procedure, is given in terms of the 180 dimensionless column scale time h, which is expressed as qt 160 h ¼ : ð11Þ ew Hheap 140

This simple observation leads to one kinetic constant for our 120 model in Eq. (10). Also, from the Bruner and Tolloczko dissolution 100 model, Eq. (2), the dimensionless time scale at the particle level is React 1 React 4 given by 80 React 7 React 10 C kt 60 s ¼ s : ð12Þ

raq Concentration, kg/m3 40 It is assumed that with the inclusion of both scales in the heap 20 processing, i.e., both at the particle and the heap levels, the total recovery will be the sum of the recoveries on both scales, or 0 0 20 40 60 80 100 120 140 160 180 200 Rt = Rs + Rh. Using Eq. (10) for each recovery, we obtain Time, d "# k q ewhheap h k kC ewhheap H tx q s s 1 ew heap raq tx q Rt ¼ R 1 ue ð1 uÞe Fig. 2. Concentration as a function of time for the central case. Reactor 1 is located at the top of the column. ð13Þ

1 1 where u ¼ Rh =R . u, kh, and ks are the adjustable parameters. hheap is the heap height at any time. R1 is calculated using the following 0.16 equation (Mellado et al., 2011): 0.14 1 p Rl ¼ b : ð14Þ Hheap þ c 0.12

Because the height and particle radius vary with time in Eq. (13), 0.1 an iterative process would be used for determining the recovery, Rt. It should be noted that the height and radius are directly relatedffiffiffiffiffiffiffiffiffiffiffiffiffi to 0.08 p3 the recovery as follows: hheap ¼ Hheapð1 aRtÞ and r ¼ R 1 Rt. 0.06 React 1 3. Performed simulations React 4 Particle diameter, m 0.04 React 7 React 10 To show the characteristics and capabilities of the models, sim- ulations were carried out for different parameter values. The values 0.02 used in these simulations are shown in Table 1. The parameters 0 chosen for these simulations are arbitrary. 0 20 40 60 80 100 120 140 160 180 200 Time, d 3.1. Well-stirred reactors in series model Fig. 3. Particle diameter as a function of time for the central case. Reactor 1 is To show the properties of the model, simulations using the located at the top of the column. parameter values for the central case (Table 1) were carried out. Fig. 2 shows the concentration as a function of time at different loca- tions in the column. For these parameters, it is observed that the in the first reactor. The trend observed for the outlet concentration soluble salts in the first and fourth reactors are depleted after at different heights is similar to that reported in Valencia et al. approximately 130 and 180 days, respectively. For times longer than (2008) for the case of nitrate. The observed differences may be due 210 days, soluble salts remain in the reactors in the lower part of the to the fact that in Valencia et al. (2008), the size of the particles in column. The same pattern is observed for the particle diameter, as the columns was approximately 1–2 cm, whereas the particle diam- shown in Fig. 3; particles disappear after approximately 130 days eter used in our simulations was 15 cm, which is closer to the sizes used in industrial heaps. This difference in particle sizes implies that the dissolution rate per bed volume is much lower in our case due to Table 1 the smaller contact area between the particles and the leaching Values used in the simulations. solution. Entity Central value Interval The relative recovery is shown in Fig. 4. For the entire column, Heap height, m 10 8–12 the simulated recovery is slightly greater than 90% after 210 days. Number of small columns 10 5–20 For the four reactors in the upper part of the column, the soluble Particle diameter, m 0.15 0.10–0.20 salts had been depleted by that time. The trend shown by the sim- 3 Solid density, kg/m 2000 ulations was similar to that of the nitrate recovery in the leaching Mass transfer coefficient, m/h 0.0001 0.00003–0.0003 Solubility, kg/m3 200 100–400 experiments by Valencia et al. (2008), which used three small col- Column porosity 0.45 umns in series. Good agreement is observed in the recovery and Water porosity in column 0.015 outlet concentration obtained in those experiments and the simu- Fraction of soluble material 0.40 lations performed using the phenomenological model. Several Water flux, m3/m2 h 0.005 0.004–0.006 experiments at the pilot scale under controlled conditions are 50 E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53

1 than 30% of the soluble salt remained in the column after 210 days, and the height of the column was approximately 7.3 m. 0.9

0.8 3.1.2. Solubility 0.7 These simulations showed that solubility has a large impact on the leaching process (Fig. 6). For example, when solubility was 0.6 React 1 increased by a factor of 2, the time for salt depletion was reduced React 4 almost 50%. In addition, for the lowest solubility (100 kg/m3), after 0.5 React 7 210 days, only approximately half of the soluble salts have been 0.4 React 10 depleted. In simulations where these two parameters were varied at the same time (data not shown), it was found that the behaviour

Relative Recovery 0.3 of the process was mainly determined by the combined effect of 0.2 these two parameters; solubility and mass transfer coefficient.

0.1 3.1.3. Dispersion – number of small reactors 0 As indicated in Section 2.1, the number of reactors used for 0 20 40 60 80 100 120 140 160 180 200 modelling the column determines the dispersion in the system. Time, d According to Eq. (1), the use of 5, 10, and 20 reactors is approxi-

Fig. 4. Relative recovery of the soluble species as a function of time for the central mately equivalent to Peclet numbers of 10, 20, and 40, respectively. case. Reactor 1 is located at the top of the column. A Peclet number of 10 corresponds to a high dispersion, whereas a Peclet number of 40 corresponds to a moderate dispersion. Peclet numbers in this interval may be expected for systems formed by planned to validate the phenomenological model. The use of re- large, non-uniform particles. The results showed that the recovery sults from industrial heap leaching is also being considered. is almost independent of the number of small reactors used for The impact of the main parameters on the recovery of saltpetre modelling the column of caliche minerals (Fig. 7). It is known that from caliche minerals was evaluated in a sensitivity study. The in systems where the reaction is important, the dispersion effect is parameters, its central values and the intervals used are shown masked by the reaction. Therefore, the simulations may be carried in Table 1. The impact of the mass transfer coefficient, solubility, out by any numbers of small reactors between 5 and 20, and sim- and number of reactors is shown in this section. The heap height, ilar results would be obtained. particle size, and irrigation rate, which may be modified to opti- mise the process, are shown and discussed in Section 3.2, where 3.2. Analytical model the predictions of the two models are compared. The results of the analytical model were compared with the 3.1.1. Impact of the mass transfer coefficient results obtained with the phenomenological model by means of The mass transfer coefficient was varied from 0.00003 to the recovery of the soluble species. Table 1 shows the data used 0.0003 m/h. As expected, the simulations showed that the recovery in the simulations. The comparison was conducted using opera- increased as the mass transfer coefficient increased (Fig. 5). How- tional parameters, i.e., parameters that can be modified in an ever, mass transfer coefficients greater than 0.0003 m/h seemed industrial process. These parameters are, for example, heap height, to have a lower effect on increasing the recovery. This is because particle diameter, and irrigation rate. The other parameters (such the recovery is controlled by salt solubility for high mass transfer as mass transfer coefficient and solubility) are important; however, coefficients. For the highest mass transfer coefficient, 0.0003 m/h, they cannot be varied in an industrial process. the salts were depleted after approximately 210 days; therefore, The analytical model’s main application is in process optimisa- the height of the heap was 6 m. For the lowest coefficient, more tion because the calculations may be performed quickly. Therefore,

1 1

0.9 k=0.00003 m/h 0.9 k=0.00010 m/h 0.8 0.8 k=0.00030 m/h 0.7 0.7

0.6 0.6

0.5 0.5

0.4 0.4 Relative recovery 0.3 Relative recovery 0.3

0.2 0.2 Cs=100 kg/m3 0.1 0.1 Cs=200 kg/m3 Cs=400 kg/m3 0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 Time, d Time, d

Fig. 5. Relative recovery of the soluble species as a function of time for different Fig. 6. Relative recovery of the soluble species as a function of time for different mass transfer coefficients, k. solubilities, Cs. E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53 51

1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5 Num react=5 H= 8 m 0.4 Recovery 0.4 Num react=10 H=10 m Num react=20 H=12 m Relative recovery 0.3 0.3

0.2 0.2

0.1 0.1

0 0 0 20 40 60 80 100 120 140 160 180 200 40 60 80 100 120 140 160 180 Time, d time, days

Fig. 7. Relative recovery of the soluble species as a function of time for different Fig. 8. Relative recovery of the soluble species as a function of time for different numbers of small reactors used for modelling the column. heap heights. The lines are the analytical model, and the markers are the simulated experimental data. the computational effort is small, even for problems requiring a large number of alternatives to be tested. 1 The properties of the analytical model were tested for different situations. In particular, the predictive capability of the model was 0.9 tested when a small amount of information is used for fitting the 0.8 model. The testing procedure for the analytical model was as follows: the phenomenological model is used to generate a set of 0.7 data, which is considered to be simulated experimental data from 0.6 an industrial leaching process. From these data (for example, the recovery of the soluble species), six times were chosen: 42, 83, 0.5 125, 146, 167, and 188 days. The analytical model is fitted using D=0.10 m

Recovery 0.4 a subset of these data, and once the parameters of the analytical D=0.15 m model have been determined, the model is then used for predicting 0.3 D=0.20 m the recovery for other cases. In these calculations, the recovery at 0.2 infinite time was assumed to be 1.0 because 100% of the soluble species are recovered after a sufficiently long time in the phenom- 0.1 enological model. 0 For the analytical model, the parameters to be adjusted are as 40 60 80 100 120 140 160 180 follows: the constants k and k in the exponentials (which charac- h s time, days terise the reaction at the column and particle scales, respectively), the dimensionless time delay, x, and the relative importance of the Fig. 9. Relative recovery of the soluble species as a function of time for different column scale in the leaching process, u. Because the dimensionless particle diameters. The lines are the analytical model, and the markers are the recovery is used for the comparisons, the error of the fitting pro- simulated experimental data. cess is calculated as follows: the differences between the simulated experimental data and the recovery calculated by the analytical model are summed, which is then divided by the number of data the model is fitted using the data points obtained with the end- points. points of the interval for each parameter, and the central value of First, the fitting capability of the analytical model was tested. the parameter is predicted. For extrapolation, the data for the cen- The simulated data was obtained using the phenomenological tral value and one endpoint value are used for fitting, and the other model for various values for the heap height, particle diameter, endpoint value (Table 2) is predicted. and irrigation rate, as shown in Table 2. The simulations were car- Several cases are considered in which the error is determined ried out for the six times indicated above (42 data points in total). only for the fitted data points (Error 1), for all 42 points including The results, shown in Figs. 8–10, indicate that the fit of the analyt- the fitted points (Error 2), and for the interpolated or extrapolated ical model to the simulated experimental data is good for the three points (Error 3). These errors are shown in Table 2 for the different cases. The average error of the fitting process is 1.8%. The results calculated cases. In Case 1, the fitting is performed using the 12 show that recovery decreases with height, and longer times are re- points corresponding to the times of 42 and 167 days for the inter- quired to obtain a high recovery. Recovery also decreases with the val endpoints (shown in Table 2) for height, particle diameter, and initial particle diameter due to the smaller surface area available irrigation rate. Then, in Case 2, the effect of height is considered, for mass transfer when the particle diameter increases. Finally, the model is fitted using 12 points for the heights of 8 and 10 m, recovery increased with irrigation rate. and an extrapolation is carried out for 12 m. Similarity in Case 3, The capability of interpolation (or extrapolation) using the ana- the effect of particle diameter was studied, the model is fitted lytical model is tested by fitting the model to a subset of data using 12 points for the diameters of 0.10 and 0.20 m, and the points and then predicting the other data points. For interpolation, recoveries for a particle diameter of 0.15 m are interpolated. 52 E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53

1 1

0.9 0.9

0.8 0.8

0.7 0.7

0.6 0.6

0.5 0.5 q=0.004 m3/m2,h H= 8 m Recovery Recovery 0.4 0.4 q=0.005 m3/m2,h H=10 m 0.3 q=0.006 m3/m2,h 0.3 H=12 m

0.2 0.2

0.1 0.1

0 0 40 60 80 100 120 140 160 180 40 60 80 100 120 140 160 180 time, days time, days

Fig. 10. Relative recovery of the soluble species as a function of time for different Fig. 11. Relative recovery of the soluble species as a function of time for different irrigation rates. The lines are the analytical model, and the markers are the heap heights. The lines are the analytical model. The simulated data for the heap simulated experimental data. heights of 8 m (dots) and 10 m (+-markers) are fitted and extrapolated to 12 m (x-markers).

Finally, the effect of irrigation rate is considered in Case 4, the approximately 92 days. In Table 2, the dimensionless time delay model is fitted using 12 points corresponding to the irrigation rates is presented, which may be converted to time in days using the of 0.004 and 0.005 m3/m2 h and an extrapolation is carried out for expression the irrigation rate of 0.006 m3/m2 h. Table 2 shows that the variations of the parameters evaluated in ewh tdelay ¼ x ¼ 11 days: each case are generally not significant. This indicates that Eq. (13) q is a good description of the heap leaching process. Almost the same From the values of u, the term corresponding to the column parameters are obtained in spite of the number of data points used scale is found to be more dominant than the term corresponding in the fitting process, which ranged from 12 to 42 points. to the particle scale. Therefore, for the set of parameters used, Using the values for the central case, the two time constants are the variation in the particle diameter is not affecting the results. calculated: However, for other sets of parameters, the particle scale in Eq. (13) may be important. khq 4 For the column scale; Kh ¼ ¼ 2:8 10 ½1=h The errors obtained in the fitting process are small. This indicates ewh that Eq. (13) describes the system well and that the model suitably captures the recovery trends in spite of the variation of the param- kskCs 4 For the particle scale; K ¼ ¼ 4:6 10 ½1=h eters. However, the most important characteristic of the model is s raq that using a limited number of data points, reasonable predictions

Kh and Ks are the dimensional time constants, [1/h], for the col- for the recovery of other parameter values may be obtained. For umn and particle scale respectively. These values indicate that the example, in case 4, the recovery data for two cases with irrigation time to reach a recovery of 0.632 (1–1/e) is approximately 160 days rates of 0.004 and 0.005 m3/m2 h were used in the fitting process and that the time for depleting 0.632 (1–1/e) of the particle is and the error was 1.5%. The largest error was obtained for the

Table 2 Errors for the different cases. Error 1: using the fitting data; Error 2: using all data points; Error 3: using the extrapolated/interpolated data in the category. The number of points is shown in parentheses.

Reference Case 1 Case 2 Case 3 Case 4 Case description Variable studied All Time Heap height Particle diameter Irrigation rate Action Fitting Inter/extra Extrapolation Interpolation Extrapolation Data points used in the fitting Number of data point 42 12 12 12 12 Time (days) 42, 83, 125, 146, 167, 188 42, 167 42, 83, 125, 146, 167, 188 42, 83, 125, 146, 167, 188 42, 83, 125, 146, 167, 188 Heap Heights (m) 8, 10, 12 8, 12 8, 10 10 10 Particle diameter (m) 0.10, 0.15, 0.20 0.10, 0.20 0.15 0.10, 0.20 0.15 Irrigation rate (m3/m2 h) 0.004, 0.005, 0.006 0.004, 0.006 0.005 0.005 0.004, 0.005 Results 3 kh 10 8.53 8.53 8.66 9.00 8.33 ks 1.39 1.44 1.55 1.14 1.38 x 9.09 7.34 5.85 8.78 7.77 u 0.80 0.82 0.62 0.78 0.84 Error 1 1.8 (42) 1.3 (12) 1.5 (12) 1.8 (12) 1.5 (12) Error 2 1.8 (42) 2.0 (42) 2.4 (42) 1.9 (42) 1.8 (42) Error 3 2.5 (24) 3.4 (6) 1.6 (6) 2.0 (6) E.D. Gálvez et al. / Minerals Engineering 33 (2012) 46–53 53

1 times. As indicated above, the main characteristic of the model is that a small number of data points may be used to predict other 0.9 parameter values. Some differences are found between the phe- 0.8 nomenological and analytical models, but they are not significant. However, the trends are clearly represented. The values used in the 0.7 simulations are arbitrary; however, this is not a significant matter because the objective of the paper is to show the characteristics 0.6 and capabilities of both models. An acceptable agreement is found between both models; how- 0.5 D=0.10 m Recovery D=0.15 m ever, as expected, some differences are also found between them, 0.4 D=0.20 m mainly due to the particular characteristics of the models. The main characteristics and advantages of the analytical model are 0.3 its simplicity and the small computational effort required. How- 0.2 ever, some difficulties are encountered in the simulations with this model when the leaching process is controlled by one or two 0.1 parameters, e.g., when the dissolution reactions are determined 40 60 80 100 120 140 160 180 200 by the salt solubility. In contrast, the phenomenological model time, days can more accurately capture the interactions between the different parameters; however, the computational time is longer. Fig. 12. Relative recovery of the soluble species as a function of time for different Therefore, the applicability of these models is different. The particle diameters. The lines are the analytical model. The simulated data for the particle diameters of 0.10 m (dots) and 0.20 m (x-markers) are fitted and interpo- analytical model is useful in the optimisation of complex systems, lated to 0.15 m (+-markers). e.g., when several heaps are simultaneously leached and in other post-modelling activities. This type of calculation requires a large number of simulations; therefore, long computing times would 1 be required for using phenomenological models. In contrast, the phenomenological models are useful in determining the influence 0.9 of different parameters on the leaching process. They are also use- 0.8 ful in the study of new processes because parameter fitting is gen- erally not required. 0.7 Acknowledgment 0.6

0.5 The authors wish to thank CONICYT for support through Project

Recovery PEL 81105010. 0.4 References 0.3 q=0.004 m3/m2,h q=0.005 m3/m2,h Bouffard, S.C., Dixon, D.G., 2001. Investigative study into the hydrodynamics of heap 0.2 leaching processes. Metallurgical and Material Transactions B 32B, 763–776. q=0.006 m3/m2,h Cariaga, E., Concha, F., Sepúlveda, M., 2005. Flow through porous media with 0.1 applications to heap leaching of copper ores. Chemical Engineering Journal 111, 40 60 80 100 120 140 160 180 200 151–165. time, days Casas, J.M., Martínez, J., Moreno, L., Vargas, T., 1998. Bioleaching model of a copper- sulfide ore bed in heap and dump configurations. Metallurgical and Material Transactions B 29, 899–909. Fig. 13. Relative recovery of the soluble species as a function of time for different Cross, M., Bennett, C.R., Croft, T.N., McBride, D., Gebhardt, J.E., 2006. Computational irrigation rates. The lines are the analytical model. The simulated data for the modeling of reactive multi-phase flows in porous media: applications to metals 3 2 3 2 irrigation rates of 0.004 m /m h (dots) and 0.005 m /m h (+-markers) are fitted extraction and environmental recovery processes. Minerals Engineering 19, 3 2 and extrapolated to 0.006 m /m h (x-markers). 1098–1108. Dixon, D.G., Hendrix, J.L., 1993. A mathematical model for heap leaching of one or more solid reactants from porous ore pellets. Metallurgical Transactions 24B, prediction of the recovery for irrigation rates of 0.006 and 0.005 m3/ 1087–1102. 2 Dokoumetzidis, A., Macheras, P., 2006. A century of dissolution research: From m h. The results for these simulations are shown in Figs. 11–13. Noyes and Whitney to the Biopharmaceutics Classification Systems. They show that, in spite of the small number of data points used International Journal of Pharmaceutics 321, 1–11. in the fitting process, the predictions at other irrigation rates and Lauterbach, A., Ober, G., 1995. In: Kirk-Othmer Encyclopedia of Chemical Technology, fourth ed. vol. 14. Wiley-Interscience, New York, pp. 709–737. even at other heap heights and particle diameters are satisfactory. Levenspiel, O., 1999. Chemical Reaction Engineering, third ed. John Wiley and Sons, New York. Mellado, M.E., Cisternas, L.A., 2008. An analytical–numerical method for solving a 4. Discussion and conclusions heap leaching problem of one or more solid reactants from porous pellets. Computers and Chemical Engineering 32, 2395–2402. Two models are presented. One is a phenomenological model, Mellado, M.E., Cisternas, L.A., Gálvez, E.D., 2009. An analytical approach to heap leaching. Hydrometallurgy 95, 33–38. which considers the decrease of the heap height when the soluble Mellado, M.E., Casanova, M.P., Cisternas, L.A., Gálvez, E.D., 2011. On scalable analytical salts are dissolved. Another is an analytical model, which uses an models for heap leaching. Computers and Chemical Engineering 35, 220–225. exponential expression for calculating the recovery. This model is Thiel, R., Smith, M.E., 2004. State of the practice review of heap leach pad design issues. Geotextiles and Geomembranes 22, 555–568. useful in an optimisation and sensitivity analysis in which an expli- Valencia, J.A., Méndez, D.A., Cueto, J.Y., Cisternas, L.A., 2008. Saltpeter extraction and cit equation is needed and/or the model is solved a large number of modelling of caliche mineral heap leaching. Hydrometallurgy 90, 103–114. APPENDIX A. PAPERS

Paper II

Seawater leaching of caliche mineral in column experiments

Hydrometallurgy 139, 79–87.

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Hydrometallurgy 139 (2013) 79–87

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Hydrometallurgy

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Seawater leaching of caliche mineral in column experiments

Javier I. Ordóñez a,⁎, Luis Moreno a,b,EdelmiraD.Gálvezc,d, Luis A. Cisternas a,c a Department of Chemical and Mineral Process Engineering, Universidad de Antofagasta, Chile b Department of Chemical Engineering and Technology, Royal Institute of Technology, Sweden c Centro de Investigación Científico y Tecnológico para la Minería, Chile d Department of Metallurgical Engineering, Universidad Católica del Norte, Antofagasta, Chile article info abstract

Article history: Caliche is a mineral that contains a high fraction of soluble minerals and that is exploited in Northern Chile Received 17 January 2013 through vat or heap leaching for the production of iodine and nitrate. In this zone, the water availability is scarce, Received in revised form 10 July 2013 being a critical issue for the mining industries and whereby the use of other leaching agents as seawater may be a Accepted 26 July 2013 viable alternative. For this reason in the present study, column-leaching experiments using seawater were Available online 8 August 2013 performed, including different irrigation rates and column heights. It is found that the highly soluble minerals such as nitrate and iodate are rapidly leached, while for other minerals like sulphate and chloride, the outlet con- Keywords: Caliche centration increased once that part of the sodium has been removed. Crystals of sodium sulphate were found at Heap leaching the column bottom, when this was dismantled. An existing phenomenological model (Gálvez et al., 2012) was Modelling used to analyse the changes of concentration of nitrate and iodine (as iodate) with a good agreement between Column experiments the experiments and the simulations. On the other hand, for sulphate and chloride a new model was developed, Seawater which takes into account the dissolution and precipitation phenomena of these ions. The model was able to cap- ture the trends observed in the experiments for the outlet concentrations of the modelled ions. © 2013 Elsevier B.V. All rights reserved.

1. Introduction Although the heaps are watered mainly with fresh water, in actual operations, mixed solutions between intermediate solutions from The caliche mineral is composed of sodium nitrate, sodium chloride, leaching downstream steps and fresh water are also used (Wheeler, sodium sulphate, potassium chloride, and minor salts. At present, iodate 2010). Due to the exploitation of this mineral done in places where is the most important component from economical point of view. Insol- the fresh water resources are scarce; the feasibility to use seawater as uble species such as quartz and other silicates are also present (Ericksen, main leaching agent in the process has been studied (Taboada et al., 1983; Pokorny and Maturana, 1997; Valencia et al., 2008). In some 2012). In a similar approach, Torres et al. (2013) studied the use of cases, the soluble fraction of the caliche can reach values up to 40% seawater in the leaching of residual salts from evaporation ponds to (Gálvez et al., 2012). Typical water-soluble species that can be found recover remaining nitrate. in caliche are listed in Table 1. In industrial operations, the caliche heaps reach heights of up to At early years, the processing of caliche was done in mobile installa- 10 m and are irrigated by aspersion with a nominal irrigation rate of tions, with stirred and heated tanks, which was applicable to high-grade 2L/h/m2. The process is divided into 3 steps: impregnation, where the caliche ores with up to 50% of nitrate minerals (Lauterbach, 2004). material is wetted; leaching, where the soluble species are dissolved When the amount of soluble minerals decreased in the caliche, new and collected as enriched solution; and washing, where the remainder techniques were developed. The Shanks technology, introduced in soluble species are removed using a leaching agent with low ion 1878 used double wall tanks heated with vapour. In 1920, the concentration. Each heap is formed by the accumulation of 600,000 to Guggenheim process was introduced, which is characterized by the 900,000 t of caliche mineral. In the leaching step, fresh water or half- grinding of the caliche and lower temperatures (Valencia et al., 2008; enriched solutions are used as leaching agents. The percolated solutions Wisniak and Garcés, 2001). Nowadays, the gradual diminishing of are transported to the iodate extraction plant, which by a reduction step caliche's grades and an increase of the costs have resulted in the imple- retrieves iodine. The resulting solution is further conducted to evapora- mentation of heap leaching, which was productively applied to this tion ponds, in which the nitrate is crystallized mainly as sodium nitrate. mineral at the beginning of 1990's, almost 20 years later than to the In a next step, sodium nitrate reacts with potassium chloride, obtained metallic minerals (Fleming, 1992; Valencia et al., 2008). from salt deposits, to produce potassium nitrate as final product, which is used as a fertilizer (Fig. 1). More details about the process can be reviewed in Pokorny and Maturana (1997). ⁎ Corresponding author. Tel.: +56 55 2657742. The needs of water resources for the mining operations are very high E-mail address: [email protected] (J.I. Ordóñez). for the arid region of Antofagasta, consuming about 60% of the fresh

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7,000,000 m3 per year, which does not consider the recirculation of Nomenclature water. In contrast to the leaching of metallic ores, where the process is Roman letters mediated by chemical reactions, the caliche treatment is governed by A Cross-sectional area, m2 simple dissolution (Valencia et al., 2008). Another important difference C Concentration, kg/m3 is that the fraction of soluble species may reach up to 40% or more. C Solubility concentration, kg/m3 s When the soluble minerals are removed by the leaching solution, the H Initial column height, m pieces of caliche mineral may collapse, reducing their size and thus k Mass transfer coefficient, m/h decreasing the heap height along the leaching. Reductions about 20% k Dissolution coefficient, 1/h r can be reached in actual operations. kp Product of solubility1 Regarding the leaching modelling, heap leaching process is a com- M Molar quantity, mol plex system that includes physical and chemical phenomena and inter- N Number of data actions between them, such as: dissolution, precipitation, chemical N Number of particles p reactions, stagnant liquid, diffusion, and convective and dispersive q Irrigation rate, m3/m2/h transport among other phenomena. There is a great interest to develop r Particle radius, m mathematical models, in order to simulate, design, optimize and under- t Time, h stand the process (McBride et al., 2012). Modelling of caliche leaching is V Volume, m3 more complicated because caliche mineral is formed by a mixture of X Molar concentration, mol/L minerals with different equilibrium constants and dissolution rates 1 The product of solubility has units of molar concentration raised to the power and a high fraction of soluble minerals that produce significant changes of the sum of the stoichiometric coefficients of the products in the equilibrium. in the heap height (Gálvez et al., 2012). Leaching is the starting point in the hydrometallurgical mining chain thus improvements in its performance may reflect global benefits. There Greek letters are different strategies of modelling that permit the representation of α Mass soluble fraction real phenomena using mathematical relations, like empirical, phenom- enological and hybrid models. εw Water porosity ρ Particle density, kg/m3 Mathematical models have been widely used in chemical processes and insofar that the computational capabilities are developing, the use of more complex models, such as phenomenological ones, including Subscripts several processes simultaneously, is becoming more common. Other types of models are the hybrid ones, which combine experimental i Output, current tank i − 1 Input, previous tank observations with theoretical knowledge giving analytical expressions for the main processes. They are useful in process optimization, where m Mineral the model is typically solved hundreds or thousands of times (Mellado et al., 2009). In spite of the importance of heap leaching of caliche, no data is water in their processes. Considering that the availability of water found in the open literature about the leaching of this mineral. There is scarce in Northern Chile, several mining industries are gradually are possibly some studies about this topic, but they are not available consuming seawater in their operations. In most of the cases, after desa- for the scientificcommunity. linization process the seawater is pumped to the mining plants, located The aim of this study is to evaluate the feasibility to use seawater in at more than thousand metres above sea level. The desalinization treat- column leaching of caliche. Therefore, leaching experiments in columns ment leads to an increase of energy costs and may cause some pollution were carried out varying the irrigation rate, the height of the column, problems when water with higher salinity is returned to the sea. Given and the leaching agent. The highly soluble minerals, such as nitrate this scenario, the direct use of seawater is being a focus of research in and iodate, are rapidly leached. The results were analysed using a the field of sustainability, especially for caliche heap leaching, where phenomenological model previously developed by Gálvez et al. (2012) leaching agents have, in many cases, concentration higher than that in with the objective to validate the model. For the other ions such as the seawater. Depending on the size of operation, the exploitations of sulphate and chloride, where the dissolution is controlled probably by caliche are between 4 and 19 million of tonnes per year, for which the the effect of the ion common, a new model was developed in order to ratio leachant/caliche is around 0.8–1.2 m3/t of heaped caliche and understand the processes occurring in the column. This model includes with global water consumption for the whole process from 800,000 to dissolution and precipitation of the ions when they are transported along the column. Sodium sulphate crystallizes at the column bottom and in the bottles used for leachate recollection. Table 1 Common water soluble species in caliche minerals. 2. Experimental procedure Extracted from Jackson and Ericksen (1994).

Ion Mineral Formula 2.1. Leaching column experiments

Nitrate Nitratine NaNO3 The experiments were performed in columns of 0.2 m in diameter. Niter KNO3

Sulphate Bloedite Na2Mg(SO4)2·4H2O The caliche was loaded in batches, distributing homogeneously the Polyhalite K2Ca2Mg(SO4)4·2H2O mineral to avoid stratification and channelling. The caliche was irrigated Glauberite CaNa2(SO4)2 during 20 days, testing different leaching agents, bed heights and irriga- Gypsum CaSO ·2H O 4 2 tion rates (Table 2). Anhydrite CaSO4 Chloride Halite NaCl The process of leaching begun with a wetting stage, where the Sylvite KCl caliche was irrigated with the leaching agent until leachate started to Iodate Lautarite Ca(IO3)2 flow out from the bottom. This point was considered as the leaching Hectorfloresite Na (IO )(SO ) 9 3 4 4 start. Upon completion of leaching, the material was downloaded and Author's personal copy

J.I. Ordóñez et al. / Hydrometallurgy 139 (2013) 79–87 81

Crushing Leaching vats Potassium chloride (from Salar) Caliche extraction Heap Crystallization Melting and Iodine plant NPT plant leaching plant Prilling plant

Prilled iodine Prilled sodium nitrate Crystallization and Drying Evaporation ponds

Prilled potassium Prilling nitrate

Fig. 1. Flowsheet of caliche processing. Adapted from Sirocco Mining (2012) and SQM (2012). solid samples were taken to determine moisture and composition. The containers. Seawater was protected from the light to avoid the prolifer- irrigation rates employed in wetting and leaching stages were equal to ation of algae. In order to approach actual heap leaching processes, values listed in Table 2. where the leaching solutions are recirculated, loaded solutions also were employed, which were prepared by stirring caliche with seawater 2.2. Sampling and chemical analysis at a solid:liquid ratio (kg:L) of 1:1 for 1 h. After a decantation for one day, the supernatant solution was separated and used as a leaching Leachate was collected at the column bottom in a plastic bottle, from solution (LX). From this rich solution another leaching solution (diluted which a 300-mL sample was taken 12 h after leaching start, and after- solution, DS) was obtained by diluting the rich solution with seawater in wards, samples every 24 h were collected. Solid samples also were a 1:1 ratio. Tap water (TW) was also used without further treatment. taken, from both initial caliche and residue, quartering dried material The chemical analysis of these leaching solutions is shown in Table 4. to choose 300 g of representative sample. The solid samples were mixed with distilled water and stirred in a relationship solid:liquid 3. Mathematical models used in the evaluation of the experiments (kg:L) 1:10 for 6 h; the mixture was then filtered and the liquid chem- ically analysed. 3.1. Model for the highly soluble species Nitrate was analysed by UV molecularabsorptionspectroscopy(UV2, Unicam UV/Vis). The sulphate content in the samples was determined by It is expected that the dissolution of the highly soluble species such gravimetry. Sodium, potassium, magnesium and calcium were measured as nitrate and iodate controls the decreasing of particle size. For both by atomic absorption spectroscopy (220FS, Varian) and chloride and io- ions, a previously developed model (Gálvez et al., 2012) was applied dine through volumetry. Perchlorate was determined with an electrode- to evaluate their outlet concentration. In this 1-D model, the column is specific method and density by pycnometry. represented as well-stirred reactors (mini-column) in series. An impor- tant characteristic in the leaching of caliche ores is the reduction of 2.3. Caliche particle size provoked by collapsing. In the model, the diminution of particle size insofar leaching progresses is based on a mass balance The mineral employed in the leaching experiments was obtained of the particle with the help of the Brunner and Tolloczko model from Northern Chile. In order to avoid a possible obstruction of the (Dokoumetzidis and Macheras, 2006). Eq. (1) shows the mass balance columns, the material was firstly screened, choosing particles with a on the particle. size above 2.36 mm in diameter. The soluble chemical composition of screened caliche is listed in Table 3. dr k i ¼ − ðÞC −C : ð1Þ A granulometric analysis of the caliche mineral used in the column dt αρ s i experiments was carried out using the Tyler sieves: 0.525″,0.371″,4, 6, and 8. From the granulometric curve, which is shown in Fig. 2,a The dissolution of the ions in terms of the concentration along the value of 6.8 mm was determined for the median. heap height, is determined by a mass balance in the column (Eq. (2)):

2.4. Leaching agents dVmCi 2 dri ¼ qAðÞ C − −C −4πr N αρ ð2Þ dt i 1 i i p dt The seawater (SW) used as leachant was extracted from the Antofagasta's coast (Chile), using a submarine outfall. The water was fil- where the left hand side term represents the accumulation, the first tered with a 0.2 μm pore diameter membrane filter and stored in plastic term on the right hand side considers the advection from a reactor to the next one, and the last term refers to the dissolution of ion. This Table 2 model was formulated to describe the dissolution of very soluble Column leaching experiments run for 20 days. species contained in the caliche minerals, such as nitrate and iodine.

Leaching agent Irrigation rate (m3/m2/h) Bed height (m)

Seawater 0.003 0.6 Table 3 Seawater 0.006 0.6 Chemical composition (%w/w) of caliche. Seawater 0.003 1.0 Tap water 0.006 1.0 Anions Cations

Rich solution 0.006 0.6 − 2− − − − 3− + + 2+ 2+ NO3 SO4 IO3 Cl ClO4 BO3 Na K Mg Ca Seawater + Rich solution 0.006 1.0 Seawater + Rich solution 0.004 0.8 3.674 9.410 0.046 4.194 0.036 0.060 5.575 0.579 0.971 0.597 Author's personal copy

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100 terms of the volume ratio (volume of leaching solution passed through

the column divided by initial bed volume, VL/VB). This is done for com- paring directly the performance of the different experiences, which 75 were performed for different irrigation rates and have different heights (volume). No significant changes were noticed after the volume ratio of 2 for all ions and experiments; hence the concentrations collected are 50 showed up to that point. The ions considered in the study were: nitrate, sulphate, iodine, sodium, potassium, magnesium, chloride, perchlorate and calcium. 25

Cumulative finer (%) finer Cumulative Fig. 3 shows the outlet concentration for a leaching column irrigated with seawater in general may be observed that the highly soluble ions 0 are removed rapidly; their concentrations reached low values for rather 2.4 4.6 6.8 9.0 11.2 13.4 low volume ratios; 0.5 for nitrate and about 0.7 for iodine and Particle size (mm) perchlorate. Final levels of most of the ions resulted similar to the concentrations Fig. 2. Experimental particle size distribution of caliche. The dashed line was drawn to fa- of the feeding, as can be compared with the data of Table 4. At the end of cilitate the view. the experiments, calcium and sulphate show concentrations higher than that at the feed. The particle radius and heap height diminution are also addressed by An interesting situation is observed for the ion sulphate, its concen- the model. Other components, as chloride or sulphate, cannot be tration increases at the beginning, reaching a peak at volume ratio of described for this model because the dissolution of these components about 0.3 and decreasing continuously afterwards. This phenomenon is probably dependent of sodium concentration. For this reason, a new occurs as a consequence of the high dissolution rate of sodium nitrate. model was developed to handle these species, which is described below. The fast dissolution of nitrate provokes an increase of free sodium levels in the column, which interacts with sulphate and resulting in a precipi- 3.2. Chemical reaction modelling tation of sodium sulphate. This situation was corroborated through the observation of crystals at the bottom of the column that appeared after The composition of the caliche is very complex, with several soluble 4–5 days of leaching. Subsequent chemical analysis of these crystals rat- minerals, which are in some cases a compound formed by several ified the composition of sodium sulphate. An important part of sodium cations. The most frequent soluble anions are nitrate, chloride, and comes from sodium nitrate dissolution; hence, the levels of sodium sulphate; while the main soluble cations are sodium, calcium, magne- decrease rapidly at initial stages due to the high solubility of sodium sium, and potassium. At the beginning of the leaching process, the nitrate. For this reason, when part of the highly soluble sodium nitrate highly soluble sodium nitrate is leached increasing strongly the concen- has been removed and the sodium concentration declines, the concen- tration of sodium. Therefore, some minerals containing sodium, such trations of sulphate and chloride (in some extent) increase. as sodium sulphate and sodium chloride may reach the saturation and The different behaviours of calcium leaching in comparison with the precipitate (Cisternas, 2009). other ions are notorious. In all the columns, the calcium concentration is A model for taking into account the effect of the common ion and its constantly increasing, this could be due to the calcium sulphate min- implication on the less soluble species was developed, which comprises erals present in caliche (as gypsum and anhydrite) have very low solu- the anions sulphate, chloride, and nitrate and the cation sodium. This bilities and the outlet concentration of calcium is controlled by the is an important simplification, since other cations and anions are sulphate levels, therefore the calcium concentration increases when also present in the soluble minerals. The modelled system is a one- sulphate concentration decreases. For magnesium and potassium, the dimensional column, located at the heap centre, which is formed by concentration patterns are similar and their dissolution rates appear well-stirred reactors (mini-column) in series. The model considers the to be controlled by their own kinetics, which showed to be slow. chemical reactions in each reactor (dissolution and precipitation) and Comparing the results of the columns irrigated with seawater and the transport of solute from a reactor to the next one. This simplified tap water, no big differences are observed. As expected, the outlet con- system comprises five well-stirred reactors in series, three sodium centrations for chloride and sodium at long time are higher for the minerals and four ions (sulphate, nitrate, chloride, and sodium). columns irrigated with seawater, because the content of these ions in Equations are detailed in Appendix A. the leaching solution (seawater) is higher (Table 4). For sulphate, the levels in SW and TW were similar and low; however the dissolution 4. Results and discussion rate using SW as a leachant is slower than TW. This behaviour is explained by the sodium concentrations in leaching agents, which in 4.1. Results of the experiences SW is higher and this ion is controlling the releasing of sulphate, there- fore, retarding its removal from the columns. The performance of the leaching experiments was evaluated by Considering all experiments, the lowest concentration levels for all using the concentration of the leachate collected at the column bottom. ions were reached by the column watered with TW, while the highest Although sampling was done every 12 h at the beginning and 24 h ones by the LX column. The key to explain this difference of behaviour afterward, in the figures the variation of the concentration is shown in that was observed clearly at long times is the composition of these

Table 4 Chemical composition (kg/m3) of leaching solutions.

Leaching solution Anions Cations

− 2− − − − 3− + + 2+ 2+ NO3 SO4 IO3 Cl ClO4 BO3 Na K Mg Ca SW 0.211 2.661 0.000 19.709 0.120 0.161 11.124 0.361 1.576 0.171 TW 0.000 0.130 0.010 0.350 0.010 0.000 0.190 0.020 0.030 0.090 DS 15.017 28.060 0.099 39.131 0.011 0.197 33.760 2.707 4.505 0.417 LX 29.300 53.716 0.198 59.879 0.012 0.384 56.274 5.023 7.697 0.465 Author's personal copy

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225 2.0 NO3 Cl I2 ClO4 SO4 K

3 180 3 Ca B Mg Na 1.5

135 1.0 90

0.5

Concentration, kg/m 45 Concentration, kg/m

0 0.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

VL/VB VL/VB

Fig. 3. Outlet concentration of major and minor ions from column leached with SW, q = 0.003 m3/m2/h and H = 0.6 m. Lines were added to facilitate the view. leaching agents. It is possible to remove almost all ions (including sul- as solubilities of controlling species, intrinsic dissolution kinetics, and phate) with relatively low water volume passed through the column mass transfer resistance. Using a solution with a higher concentration only with TW. However, small differences were observed between col- of ions than seawater and tap water, the concentration levels are higher umns irrigated with SW and TW. Other minor ions such as perchlorate because the extractive capability is less. As could be expected, LX solu- and boron do not show big differences between different leaching tion had the lowest extracting capability, because the concentration of agents. In general, the concentration levels were higher for seawater all ions was the highest, whereas for experiences leached with DS, an in- and lower for tap water. termediate behaviour between SW and LX was obtained (Fig. 4). The release of ions in the column with a higher irrigation rate is In the basis of the dissolution trend, it is possible to divide the ions in faster, reaching the steady state after a short time. However, if the irri- 3 groups depending on their behaviours: i) the most soluble ions, like gation rate is duplicated, this does not mean that the removal rate is in- nitrate, iodine and perchlorate, exhibit a rapid concentration reduction, creased in the same proportion, because other factors are involved such with the highest values at the beginning of experience, ii) intermediate

a) b) c) 225 1.8 200 SW, q=0.006 m/h, SW, q=0.006 m/h, SW, q=0.006 m/h, 3 3 H=0.6 m 3 H=0.6 m H=0.6 m TW, q=0.006 m/h, TW, q=0.006 m/h, TW, q=0.006 m/h, 180 160 H=1.0 m H=1.0 m H=1.0 m LX, q=0.006 m/h, LX, q=0.006 m/h, LX, q=0.006 m/h, H=0.6 m 1.2 H=0.6 m H=0.6 m 135 120

90 80 0.6

45 40 Iodine concentration, kg/m Nitrate concentration, kg/m Sulphate concentration, kg/m 0 0.0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0

VL/VB VL/VB VL/VB d) e) f) 200 200 30 SW, q=0.006 m/h, SW, q=0.006 m/h, SW, q=0.006 m/h, 3 3 3 H=0.6 m H=0.6 m H=0.6 m TW, q=0.006 m/h, TW, q=0.006 m/h, TW, q=0.006 m/h, 160 160 24 H=1.0 m H=1.0 m H=1.0 m LX, q=0.006 m/h, LX, q=0.006 m/h, LX, q=0.006 m/h, H=0.6 m H=0.6 m H=0.6 m 120 120 18

80 80 12

40 40 6 Sodium concentration, kg/m Chloride concentration, kg/m 0 0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0Magnesium concentration, kg/m 0.0 0.5 1.0 1.5 2.0

VL/VB VL/VB VL/VB

Fig. 4. Experimental dissolution of selected ions in columns irrigated with seawater, tap water and charged solution. Lines were added to facilitate the visualization. Author's personal copy

84 J.I. Ordóñez et al. / Hydrometallurgy 139 (2013) 79–87 ions, such as sodium, potassium and magnesium, where the diminution Table 6 of concentration started with certain delay depending on the concentra- Mass transfer coefficient, k, of nitrate and iodine using phenomenological model for each experience. tion of other ions, and iii) the less soluble species as sulphate and chlo- ride, which reach the saturation and start to precipitate within the Leaching Irrigation rate Column height Nitrate Iodine agent (q), m3/m2/h (H), m column due possibly to the high sodium concentration existent in the k,m/h RSD,% k,m/h RSD,% column in the initial period; when the sodium concentration decreases SW 0.003 0.6 1.61E−5 4.5 0.60E−52.5 these ions start to dissolve. SW 0.006 0.6 2.95E−5 2.4 1.13E−51.0 In these column experiments a small particle size was used (particle SW 0.003 1.0 1.34E−5 8.0 0.47E−56.7 diameter of 6.3 mm). Therefore, it is expected that the influence of the TW 0.006 1.0 1.99E−5 3.9 0.90E−52.3 particle was small and the dissolution of the different ions in a large ex- LX 0.006 0.6 3.36E−5 3.0 0.94E−52.9 DS 0.006 1.0 3.14E−5 3.1 0.97E−53.7 tent is controlled by the solubility limitations and dissolution rate. DS 0.004 0.8 1.19E−5 3.9 0.52E−54.9

4.2. Evaluation using the phenomenological model bed or retention of leaching solution. However these small variations 4.2.1. Fitting of mathematical model are acceptable, considering the normal fluctuations observed in column A previously developed model (Gálvez et al., 2012) was evaluated leaching experiments. using the experimental data collected in the present work. Nitrate and iodine species were chosen, since both are highly soluble ions and 4.2.2. Effect of operational variables on mass transfer coefficient therefore its dissolution rate is less dependent of the concentration of Operational variables such as irrigation rate, column height, and other species forming caliche. Table 5 presents the parameter values type of leaching solution were studied in the column experiments. used as input data for the modelling. Within the data listed, water Particle diameter was not studied, since all the columns were loaded porosity and porosity are estimated from experimental observations. with the same material size. The coefficient of mass transfer is predom- The nitrate and iodine fractions were determined as the average of the inantly determined by the irrigation rate, since a larger rate implies that respective fractions for the caliches is loaded in the seven columns. the resistance to mass transfer is reduced. Therefore, it is expected that In the phenomenological model, the mass transfer coefficient (k) the mass transfer coefficient for experiments performed with of highest was fitted independently for each experiment and each ion (nitrate irrigation rate was the largest, which is physically consistent due to the and iodine) by using the least square method. The function to minimise higher rates provoking a thinning of liquid layer overlying particles. On is, in this case, the square sum of the difference between the experimen- the other hand, the effect of the other variables would be small, since tal and model calculated concentration values. The k values obtained in the leaching solution is taken into account in the particle balance the fitting process are listed in Table 6. (Eq. (1)) and the column height by the mass balance of the bed The importance of k is that it describes the rate at which the soluble (Eq. (2)). ions are dissolved. Higher values of k indicate that the ion solubilisation The obtained mass transfer coefficients proved to be highly depen- is faster. The results show that the mass transfer coefficient for nitrate dent of irrigation rate; the lowest values for the coefficient were found is around three times greater than for iodine in all experiences. The for the experiments with an irrigation rate of 0.003 m3/m2/h and the concentration at column bottom for both ions is initially very high, fall- highest values for irrigation rate of 0.006 m3/m2/h. The mass transfer ing drastically when VL/VB is about 0.25 for nitrate and about 0.50 for coefficient as a function of the irrigation rate is shown in Fig. 6 for nitrate iodine. It is clearly observed that among the seven experiences for and iodine. In both cases the trend lines are very similar. An increase of each ion those columns with a high irrigation rate show higher mass the irrigation rate by a factor 2 increases the mass transfer coefficient by transfer coefficients (Fig. 5). the same factor. The quality of the fitting process is determined by using the relative When similar plots were done for studying the effect of leaching standard deviation (RSD), which is calculated in terms of difference agents, it was found that no correlation exists between the mass trans- between experimental and modelled concentrations. In order to fer coefficient and the type of leaching solution. The same conclusion compare these values between ions (nitrate and iodine) the standard was obtained when the impact of the initial height of the column on deviation was divided by the solubility concentration for each of these the mass transfer coefficient was studied; no correlation was observed. ions, Cs. This is shown in Eq. (3). According to the above studies, the model was validated in terms of vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi that the values of the mass transfer coefficient obtained for the seven uX  2 experiences correspond with the trends that could be expected from u exp− mod 100 t C C RSD ¼ : ð3Þ the theory. Cs N 4.3. Modelling of ionic interaction through chemical reaction model AscanbeseeninTable 6, the level of fitting obtained between the modelled and experimental concentrations for both nitrate and iodine Outlet concentration for sulphate and chloride presents different was, in general, good with most of the relative standard deviations behaviours to that shown by nitrate and iodine. In the initial period about 3.5% for nitrate and about 3% for iodine. The highest deviations the concentration of sulphate and chloride is increased when the con- could be attributed to experimental issues such as channelling in the centration of the sodium and nitrate decreases. This type of behaviour cannot be described by the phenomenological model used for the Table 5 nitrate and iodine. Due to the different trends of dissolution between Values employed in the simulation. the ions nitrate and iodine for a side and sulphate and chloride for the other side, a new model was developed for the last group, considering Parameter Value the chemical reactions that are occurring in the column. These interac- Particle diameter, m 0.006 tions include the dissolution of minerals and precipitation of a part of Mineral density, kg/m3 1900 Water porosity in column 0.08 them when the solubility product is exceeded. Porosity 0.45 The objective of this simplified modelling is to reproduce the trends Nitrate fraction in caliche 0.037 observed in the column experiments, overcoming phenomena related Iodine fraction in caliche 0.00046 with chemical interaction between ions that share common ion, Number of well-stirred reactors in the model. 4 which in this case is sodium. Sodium is associated to nitrate, sulphate Author's personal copy

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a) 225 a) 3.6E-05 SW, q=0.006 m/h,

3 H=0.6 m 3.0E-05 180 TW, q=0.006 m/h, H=1.0 m LX, q=0.006 m/h, H=0.6 m 2.4E-05 135

1.8E-05 90 1.2E-05

45

Nitrate concentration, kg/m 6.0E-06 Mass transfer coefficient, m/h 0 0.0 0.5 1.0 1.5 2.0 0.0E+00 0.0025 0.0035 0.0045 0.0055 0.0065 VL/VB Irrigation rate, m3/m2/h b) 1.5 SW, q=0.006 m/h, b) 1.2E-05

3 H=0.6 m TW, q=0.006 m/h, H=1.0 m LX, q=0.006 m/h, 1.0E-05 1.0 H=0.6 m 8.0E-06

6.0E-06 0.5

4.0E-06 Iodine concentration, kg/m

0.0 2.0E-06 0.0 0.5 1.0 1.5 2.0 Mass transfer coefficient, m/h

VL/VB 0.0E+00 0.0025 0.0035 0.0045 0.0055 0.0065 Fig. 5. Concentration of a) nitrate and b) iodine in experiments irrigated with poorer solu- Irrigation rate, m3/m2/h tions. Markers are experimental data and lines are phenomenological model fitted (dotted: SW, solid: TW and dashed: LX). Fig. 6. Effect of irrigation rate on the mass transfer coefficient. a) Nitrate and b) iodine.

and chloride; since the solubility of sodium nitrate is high (around The dissolution constants for the sulphate, nitrate, and chloride sodi- 3 478 kg/m as a compound pure) compared with sodium sulphate um minerals (kr1, kr2 and kr3) in the model (see Appendix A) were fitted (205 kg/m3) and sodium chloride (320 kg/m3), it is expected that the with the experimental data using the least square method. In the seven solubility product for this mineral was reached at the initial period, cases, the model was able to reproduce the trends observed in the outlet when the concentration of sodium is very high in the leacheate. In concentration with time. Some fitting results are shown in Fig. 7 for order to keep the model very simple, it is assumed that the caliche is column experiments leached with SW, TW and LX (operational details formed by three soluble minerals (sodium nitrate, sodium sulphate, are set forth in the caption of Fig. 7). The model reproduces the more im- and sodium chloride) and only four ions (sodium, nitrate, sulphate, portant characteristics of the experimental data; the increase of the and chloride). It is assumed that the column is formed by five well- sulphate and chloride concentration at the beginning, once that part stirred reactors in series, for each reactor, four mass balance equations important of the sodium nitrate has been dissolved and removed from are required, one for each ion. In addition three dissolution/precipitation the column. equations, one for each mineral, are needed. These results are encouraging, in order to develop a model that The amount of soluble minerals was determined by analysis of the may describe the outlet concentration from heap leaching with time. solid samples. It was assumed that nitrates and chlorides form minerals However, the modelling requires a lot of information, which are not only with sodium, for the soluble sulphate only a fraction is considered; available, at least, in the public technical literature. Mineralogy of the sodium sulphate. Calcium sulphate is also found in the caliche in large caliche, solubility products of these minerals, and dissolution rates are amounts, but this mineral starts to be dissolved in the last part of the some of the information that is fundamental for this kind of chemical leaching process. The solubility constants were determined using the simulation. Due to that the solutions having a large ionic strength, concentrations existent in the leachate at the beginning of the leaching which varies with time, the determination of the activity coefficients process, when it is expected that the leaching solution is saturated with is also very important. respect to sodium sulphate and sodium chloride. In the simulations, it is In these simulations, due to the rather small particle size used, it was assumed that the solubility constant keeps the same value along all the assumed that the soluble minerals were directly accessible to the leaching process, in spite, it is probable that the value of the solubility leaching agents from the beginning. In the practical operations of heap constant changes along the process, when the activities change due to leaching the size of the particles may be of the order of 1 m or more. the decreasing ionic strength of the solution. It is also assumed that Therefore, in a rigorous modelling these factors have to be considered. the dissolution of the sodium nitrate is not limited by its solubility, But these results show that this type of modelling is necessary in due to its high value. order to understand the leaching of caliche and its complexity. Author's personal copy

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a) 4 b) 4 c) 4 NO3 NO3 NO3 Cl Cl Cl SO4 SO4 SO4 3 3 3

2 2 2

1 1 1 Concentration, mol/L Concentration, mol/L Concentration, mol/L

0 0 0 0 200 400 02004000 200 400 Time, h Time, h Time, h

Fig. 7. Experimental (markers) and simulated outlet concentration (lines) using a chemical reaction model for columns: a) SW, q = 0.006 m3/m2/h, H = 0.6 m, b) TW, q = 0.006 m3/m2/h, H = 1.0 m and c) LX, 0.006 m3/m2/h, H = 0.6 m.

5. Conclusions in the equations i is the reactor. The mass balance for the ions in each re- actor is: Column leaching experiments were done, which showed the differ- ences of dissolution behaviours of the distinct species forming caliche. Ion sulphate Nitrate and iodine leave the column quickly, regardless the operational  dX dM conditions employed. The dissolution of potassium and magnesium is 1;i ¼ 1 − − 1;i : ð Þ ε qA X1;i−1 X1;i A1 apparently controlled by their solubilities. Perchlorate compounds dt V w dt have the highest solubilities and for this its concentration decreases abruptly. Ion nitrate Variation of outlet concentration of nitrate and iodine was analysed  dX dM using a previously developed phenomenological model. The results 2;i ¼ 1 − − 2;i : ð Þ ε qA X2;i−1 X2;i A2 show that the model may describe adequately the behaviour for these dt V w dt ions in the leaching process, fitting only the mass transfer coefficient (k) for each column, and demonstrating that this parameter is indepen- Ion chloride dent of the leaching agent and column height, nevertheless a correlation  dX dM of irrigation rate and the mass transfer coefficient was observed, which 3;i ¼ 1 − − 3;i : ð Þ ε qA X3;i−1 X3;i A3 follows the theoretical behaviour that k increases as the irrigation is dt V w dt higher. On other hand, the experiments show that precipitation of sodium Ion sodium fi sulphate occurred in the initial stages of leaching. This reaf rms the con-  dX dM dM dM cept that within a heap, there is a dynamical dissolution/precipitation 4;i ¼ 1 − − 1;i − 2;i − 3;i : ð Þ ε qA X4;i−1 X4;i 2 A4 process during leaching, controlled by the different solubilities of min- dt V w dt dt dt erals that are forming caliche. In order to contribute to the understand- ing of this phenomenon, a new model was developed and tested, with For the sodium minerals the dissolution equations are: good levels of agreement. The model was applied to the minerals fi containing sodium in the caliche, simpli ed to 3 species: sodium nitrate, Sodium sulphate sulphate, and chloride. It includes dissolution and precipitation of these ! minerals. dM X2 X 1;i ¼ − − 4;i 1;i : ð Þ The results of experiments show that it is possible to use seawater, kr1M1;i 1 A5 dt Kp1 without desalination, directly in the leaching of caliche minerals. No important differences are found in the recovery of most of the ions in the caliche; in particular for nitrate and iodine that are the most Sodium nitrate important products. However the effect of seawater on the materials  dM2;i X4;iX2;i (pumps and piping) would be studied in detail. In future work, it is ¼ −k M ; 1− : ðA6Þ dt r2 2 i Kp planned to improve the chemical model for including the mineralogy 2 of the soluble species in the caliche, the activity coefficients and applied the model for large particles, which are used in the industrial heap Sodium chloride leaching (Run of Mine, ROM).  dM ; X ; X ; 3 i ¼ −k M 1− 4 i 3 i : ðA7Þ dt r3 3;i Kp Acknowledgements 3

The authors wish to thank CONICYT for supporting through the pro- ject MEL 81105010, J.I.O. thanks CONICYT for the PhD scholarship. References Cisternas, L.A., 2009. Diagramas de fases y su aplicación, 1st edition. Reverté, Barcelona. Appendix A Dokoumetzidis, A., Macheras, P., 2006. A century of dissolution research: From Noyes and Whitney to the Biopharmaceutics Classification Systems. Int. J. Pharm. 321, 1–11. Ericksen, G.E., 1983. The Chilean nitrate deposits. Am. Sci. 71, 366–374. The system is then formed by 3 sodium minerals, M (amount in Fleming, C.A., 1992. Hydrometallurgy of precious metals recovery. Hydrometallurgy 30, molesineachreactor)and4ions,X (concentration in moles per litre), 127–162. Author's personal copy

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Gálvez, E.D., Moreno, L., Mellado, M.E., Ordóñez, J.I., Cisternas, L.A., 2012. Heap leaching of Sirocco Mining web page, 2012. Accessed at December 21 http://www.siroccomining.com. Caliche minerals: phenomenological and analytical models — some comparisons. SQM web page, 2012. Accessed at August 3 http://www.sqm.com. Miner. Eng. 33, 46–53. Taboada, M.E., Hernández, P.C., Galleguillos, H.R., Flores, E.K., Graber, T.A., 2012. Behavior Jackson, J.C., Ericksen, G.E., 1994. An X-ray diffraction method for semiquantitative miner- of sodium nitrate and Caliche mineral in seawater: solubility and physicochemical alogical analysis of Chilean nitrate ore. U.S. Geological Survey, Open-file Report properties at different temperatures and concentrations. Hydrometallurgy 113–114, 94–240, pp. 1–28. 160–166. Lauterbach, A., 2004. Reduction of perchlorate levels of sodium and potassium nitrates Torres, M.A., Meruane, G.E., Graber, T.A., Gutiérrez, P.C., Taboada, M.E., 2013. Recovery of derived from natural caliche ore. ACS Sym. Ser. 872, 45–57. nitrates from leaching solutions using seawater. Hydrometallurgy 133, 100–105. McBride, D., Gebhardt, J.E., Cross, M., 2012. A comprehensive gold oxide heap leach Valencia, J.A., Méndez, D.A., Cueto, J.Y., Cisternas, L.A., 2008. Saltpeter extraction and model: Development and validation. Hydrometallurgy 113–114, 98–108. modelling of caliche mineral heap leaching. Hydrometallurgy 90, 103–114. Mellado, M.E., Cisternas, L.A., Gálvez, E.D., 2009. An analytical approach to heap leaching. Wheeler, A., 2010. Technical report on the Aguas Blancas property, Chile. Internal Report, Hydrometallurgy 95, 33–38. pp. 1–57. Pokorny, L., Maturana, I., 1997. Sodium nitrate, fourth edition. Kirk-Othmer ECT Encyclo- Wisniak, J., Garcés, I., 2001. The rise and fall of the salitre (sodium nitrate) industry. Ind. pedia of Chemical Technology, 22 427–438. J. Chem. Technol. 8, 427–438. APPENDIX A. PAPERS

Paper III

Modeling validation of caliche ore leaching using seawater

International Journal of Mineral Processing. In Press.

87 Manuscript to be published in International Journal of Mineral Processing, November 2013.

MODELING VALIDATION OF CALICHE ORE LEACHING USING SEAWATER

Javier I. Ordóñeza*, Luis Morenoa,b Mario E. Melladoc and Luis A. Cisternasa,c a Department of Chemical and Mineral Process Engineering, Universidad de Antofagasta, Chile b Department of Chemical Engineering and Technology, Royal Institute of Technology, Sweden c Centro de Investigación Científico y Tecnológico para la Minería, Chile

ABSTRACT

Leaching column experiments of caliche were performed using seawater as the leaching agent because the caliche deposits are located in Northern Chile where water resources are scarce. The use of seawater without desalination is an attractive alternative for mining operations. The experimental recoveries of different ions were modeled using a hybrid model, which uses empirical information and fundamental principles. The following ions were considered: nitrate, iodine, sulfate, chloride, sodium, potassium and magnesium. The model explicitly considers different column heights, irrigation rates, and leaching agents. A sensitivity analysis showed that parameters associated with the particle level predominantly determined the calculated recoveries. The predictive capability was also tested, and the results were generally good, except for the sulfate ion, the dissolution of which was controlled by the presence of other ions.

Keywords: Caliche, heap leaching, modeling, column experiments, seawater, model validation.

* Corresponding author. Tel.: +56 55 2657742

E-mail address: [email protected] (J.I.Ordóñez)

1 1 INTRODUCTION

Caliche, also termed nitrate deposit, is a mineral composed of a high proportion of water soluble salts, of which nitrate, sulfate, and chloride are the main anions and sodium, magnesium, potassium, and calcium are the main cations. Nitrate and chloride are mainly found as sodium nitrate (nitratine) and sodium chloride (halite), respectively. Sulfate is frequently associated with a wide range of cations, the most relevant being the following: calcium, sodium, magnesium, and potassium. It is commonly found in complex salts, such as bloedite (Na2Mg(SO4)2·4H2O), polyhalite (K2Ca2Mg(SO4)4·2H2O), and glauberite CaNa2(SO4)2. The largest sources of calcium are sulfates in the form of gypsum and anhydrite. Magnesium and potassium are associated with sulfate complex salts, such as bloedite and polyhalite. Sodium is present as chloride, nitrate, and sulfate. Another component, which occurs in lower proportions but has a high economic value, is iodine, which is found as lautarite (Ca(IO3)2) and hectorfloresite (Na9(IO3)(SO4)4) (Ericksen, 1983; Jackson and Ericksen, 1994; Pokorny et al., 1997). Quartz and other silicates compose the insoluble fraction.

The caliche mineral is exploited by both vat and heap leaching; the latter has increased its importance due to the gradual diminution of grades (Wisniak and Garcés, 2001; Lauterbach, 2004). The heaps are irrigated with water or a mix of water and intermediate solutions drawn from downstream stages of the process (Wheeler, 2010). Currently, the feasibility of using seawater as the leaching agent has been discussed because caliche processing is performed in locations where fresh water resources are scarce. The use of seawater in metallic mining in these areas is also under consideration (Taboada et al., 2012; Cochilco, 2012).

In contrast to the leaching of metallic ores, where the dissolution process is mediated by chemical reactions, caliche treatment is governed by simple dissolution (Gálvez et al., 2012; Valencia et al., 2008; Wadsworth, 1987). This difference leads to distinct operational conditions. Moreover, due to the high content of soluble species in the caliche, when the particles are dissolved, they decrease in size and thus, the heap height also decreases with time. Height reductions exceeding 20% can be achieved in actual operation.

Frequently, heap leaching is the first stage of mineral hydrometallurgical processing; therefore, a better understanding of the involved phenomena in this stage may help to improve the process in its totality, and optimal conditions of operation could be reached. Heap leaching is a complex system due to the simultaneous interaction of physical and chemical phenomena, such as simple dissolution of the mineral species, chemical interactions of the ions present in the leaching solution, presence of zones with stagnant solution in the heap, convective, diffusive, and dispersive transport for liquids and gases, heat generation and transport (Havlík, 2008; McBride et al., 2012).

2 For a better understanding of a process and its management or optimization, modeling is a useful tool by which a phenomenon or process can be studied. Models may be phenomenological or empirical and its selection depends on the objective to reach. Phenomenological models are appropriate when the interest is centered on the understanding of processes. Conversely, empirical models may be suitable when the focus is on optimization or for operations where the model must be solved hundreds or thousands of times. However, the small amount of information that can typically be obtained from this type of model is a limitation that has motivated the development of another family of expressions named hybrid models. The hybrid models, also named empirical knowledge-based models, combine relations obtained from experimental data with expressions based on fundamental principles. For this reason, a hybrid system gives more information than empirical models but may be solved a large number of times in a reasonable time because such systems are sufficiently simple. Therefore, in industrial operations, it is advantageous to employ hybrid models for tasks such as design and optimization (Trujillo, et al., 2013).

Although heap leaching is widely employed in both metallic and non-metallic mining, for the latter, modeling studies are currently emerging and are focused on understanding the dissolution phenomena and concentration variations of the major ions. Mellado et al. (2009) presented a hybrid model for the heap leaching of copper ores that captures the exponential trend of the recovery using a Bernoulli-type equation. The model was compared with other more complex models and achieved good levels of representation with less computational effort. Recently, Mellado et al. (2011b) proposed three analytical hybrid models that are sufficiently accurate for use in applications such as stochastic analysis and the planning of leaching operations.

The modeling of heap leaching has been widely developed for the processing of metallic ores; however, for the exploitation of water soluble minerals, such as caliche, the availability of information is limited. The first antecedent regarding the modeling of caliche leaching is the research of Valencia et al. (2008), which formulated empirical kinetic expressions to determine the recovery of mineral species of nitrate and magnesium and compared it with column experiment results. This article was the first approximation of the modeling of caliche in columns. An important approach to caliche heap leaching modeling was achieved by Gálvez et al. (2012), who developed two models, one of which is a hybrid model that was modified from Mellado et al. (2009), which was adapted for the dissolution of soluble particles. The other model is a phenomenological expression based on the model developed previously by Valencia et al. (2008), which considers particle size reduction using the model of dissolution proposed by Brunner and Tolloczko (Dokoumetzidis and Macheras, 2006). In more recent efforts, Ordóñez et al. (2013) collected empirical data from pilot column leaching experiments and used them to validate the phenomenological model proposed by Gálvez et al. (2012). Moreover, important observations about the dynamics of dissolution were noted, such as sodium sulfate crystallization during the caliche leaching.

3 This article aims to validate the hybrid model obtained in Gálvez et al. (2012) using the experimental data collected by Ordóñez et al. (2013). This validation is performed by adjusting some parameters and includes a sensitivity and predictability analysis. The parameters are adjusted using couples of experiments, and the obtained parameters are used to predict other experiments to demonstrate the applicability of this model in design and optimization tasks.

2 EXPERIMENTAL PROCEDURE

2.1 Leaching column experiments

Columns with diameter of 0.2 m were used in the leaching experiments. To avoid stratification and channeling, the loading of caliche mineral was performed in small batches for every column. The leaching agents, initial bed heights and nominal irrigation rates used in each experiment are given in Table 1. Initially, each column was irrigated with the leaching agent at a rate of 6 L/h/m2 until the leachate started to flow out from the bottom. Subsequently, the wetted caliche was irrigated at the nominal rate for 20 days.

Table 1. Treatments performed in caliche column leaching Experiment Leaching agent Irrigation rate (m3/m2/h) Bed height (m) SW3S Seawater 0.003 0.6 SW6S Seawater 0.006 0.6 SW3L Seawater 0.003 1.0 TW6L Tap water 0.006 1.0 RS6S Rich solution 0.006 0.6 DS6L Seawater + Rich solution 0.006 1.0 DS4M Seawater + Rich solution 0.004 0.8

The nomenclature of the experiments involves 4 characters; the first two are related to the leaching agent used: seawater (SW), tap water (TW), rich solution (RS) and diluted solution (DS). The third component of the abbreviation is the irrigation rate: 0.003 (3), 0.006 (6) and 0.004 (4) m3/m2/h. Finally, the last letter of the nomenclature is linked to the initial bed height: 0.6 (S-small), 0.8 (M-medium) and 1.0 m (L-large).

Leachate samples were collected from the column bottom 12 hours after leaching began, and afterwards, samples were collected every 24 hours, which were posteriorly analyzed. Solid samples were taken from the initial caliche and the residue. These samples were mixed with distilled water at a solid:liquid (kg:L) ratio of 1:10 and stirred for 6 hours. The mixture was then filtered, and the liquid was chemically analyzed. Using a material balance, the experimental recoveries were calculated for each experiment for the most abundant ions of the caliche: nitrate, sulfate, chloride, iodate, sodium,

4 potassium, and magnesium. The total recoveries for each ion consider the sum of the extracted fraction and the fraction remaining in the residue.

2.2 Caliche and leaching agents

The material was screened, and particles exceeding 2.4 mm in diameter were used to avoid possible obstructions in the columns. From a granulometric analysis, the average particle size was estimated at 6.8 mm. The mineral employed in the leaching experiments was obtained from Northern Chile, and the composition of the soluble species is shown Table 2.

Table 2. Chemical composition of the caliche Ion Concentration (%) Analytical method 2- SO4 9.41 Gravimetry Na+ 5.58 Atomic absorption spectroscopy Cl- 4.19 Volumetry - NO3 3.67 UV molecular absorption spectroscopy Mg2+ 0.97 Atomic absorption spectroscopy K+ 0.58 Atomic absorption spectroscopy - IO3 0.05 Volumetry

The mineralogical composition of the caliche was determined by X-ray diffraction using a D5000 diffractometer (Siemens). This analysis provides general information about the most abundant species. The caliche used in this work had a high fraction of soluble species (approximately 45%). Nitrate and potassium had unique mineral sources, that is, nitratine and polyhalite, respectively. Chloride was predominantly present as halite (the main soluble component). All of these minerals are very soluble. Sodium, calcium, magnesium, and sulfate were found in a wide variety of minerals, whereas sources of iodine were not observed in the diffractogram because of its relatively low abundance. The insoluble species were present as silicates (quartz and albite). Anhydrite is partially insoluble. The complete list of minerals detected by XRD is given in Table 3.

5 Table 3. Mineral composition of the caliche ore Specie Formula %

Albite NaAlSi3O8 26.3 Quartz SiO2 19.9 Halite NaCl 19.7 Nitratine NaNO3 9.5 Glauberite Na2Ca(SO4)2 9.1 Anhydrite CaSO4 7.3 Bloedite Na2Mg(SO4)2·4H2O 3.3 Loeweite Na12Mg7(SO4)13·15H2O 1.9 Polyhalite K2Ca2Mg(SO4)4·2H2O 1.6 Hydrochlorborite Ca2B4O4(OH)7Cl·7H2O 1.4

Regarding the leaching agents, SW was extracted from the Antofagasta coast using a submarine outfall and filtered through a membrane filter with a 0.2 μm pore diameter. The water was stored in plastic containers and protected from the light to prevent algae growth. Because solutions are recirculated in heap leaching processes; a loaded solution was prepared by stirring caliche with seawater at a solid:liquid ratio (kg:L) of 1:1 for 1 hour. After decantation for one day, the supernatant was separated and used as the leaching solution, RS. DS was obtained by diluting the rich solution with seawater in a 1:1 ratio. TW was also used for comparison. The chemical analyses of these leaching solutions are given in Table 4.

3 Table 4. Chemical composition (kg/m ) of the leaching solutions (Ci ) Ion TW SW DS RS - NO3 0.00 0.21 15.02 29.30 2- SO4 0.13 2.66 28.06 53.72 - IO3 0.01 0.00 0.10 0.20 Cl- 0.35 19.71 39.13 59.88 Na+ 0.19 11.12 33.76 56.27 K+ 0.02 0.36 2.71 5.02 Mg2+ 0.03 1.58 4.51 7.70

3 THE HYBRID MODEL

A hybrid model was developed for copper ore leaching that addresses the metal recovery over time (Mellado et al., 2009). This model is classified as a hybrid model because its equation links the empirical exponential trend of recovery with the phenomenological description of the dimensionless times. In Gálvez et al. (2012), further modifications of this model were made to adapt the expression to the heap leaching of caliche ores. The main concept was maintained: leaching is a multiscale

6 phenomenon that has two scales of size and time, with time constant K for heap scale and Ki for the particle scale:

q Csiki K  Ki  (1a) εwH rtαi ρ

The dimensionless times are then expressed as:

  Kt i  Kit (1b)

Where the time constant K pertains to the operational parameters related to heap level, i.e., irrigation rate ( q ), the initial heap height ( H ) and the volume fraction of solution ( w ). The time constants Ki consider characteristics inherent to the particle level, such as the radius ( rt ), particle density (  ), the ion mass fraction ( i ), solubility ( Csi ) and mass transfer coefficient ( ki ). For a reaction of order 1, the kinetic constants of each scale, k and k , were introduced in the global recovery Ri,t :

q   wH  Csi ki   wH   k  t   k  t      wht  q  rt i   q  Ri,t  Ri 1i e  1i e  (2)  

 corresponds to the dimensionless delay associated with the heap scale. In this work, the initial time was defined when the leachate reached the bottom of the column, and therefore  was considered to be zero. Because two levels are handled, the i parameter, which takes into account the heap-scale recovery on the overall recovery, is defined; the term (1i ) is the contribution of the particle scale to the overall recovery. The recovery model is given by a Bernoulli type function, with an asymptotic trend  that reaches a limit recovery Ri , which corresponds to the recovery obtained at prolonged times for  each ion. Although conceptually i and Ri are variables that may differ for each ion, in this paper, single values were assumed for all ions to simplify the model by increasing the stability of the solution and the velocity of calculation. The use of a simple value for the recoveries at long times was motivated by the fact that recoveries in the column experiments were similar for all ions.

Some of the variables involved were taken directly from the operational conditions, such as the irrigation rate, heap height and ion mass fraction. Others were determined in the laboratory or directly

7 from the literature, including the mineral density and the water retained fraction in the column.

However, other parameters, such as k , k , and ki , needed to be determined by fitting.

The fitted parameters can be grouped in 2 adjustable constants: K1 and K 2,i :

K1  k (3)

K2,i  kki (4)

The dimensionless constant K1 is related to the heap level and, for this reason, is equal for all the experiments and ions. K2,i involves parameter k for the particle level and the mass transfer coefficient ki , which is ion specific. Because different solutions were used as the leaching solution, the solubility of the ions is replaced by the difference between the operational solubility Csi and the composition of the respective ion in the leaching agent, Ci . Finally, the following expression is generated:

K q K (Cs C )  1 t 2,i i i t   εw ht rt αi ρ Ri,t  R 1 e  1e  (5)  

The model considers the variation of the particle radius and the height of the heap; these values are reduced as a result of the collapse of particles during mineral dissolution. Moreover, the model uses a constant porosity value in the column. Because the leaching experiments employed very small particles, the effect of the radius shrinking is not significant; for that reason and to keep the model simple, the particle size ( rt ) is considered constant. If model validation is performed for industrial heap leaching operations, the reduction of the particle size should be considered, due to the use of larger particles. The height diminution was linked to the mass of material removed from the heap, assuming constant porosity. This parameter was calculated using the following equation:

mout  min h  H  t t (6) t A

The fitting was performed using the least squares method considering the differences between the modeled and experimental recoveries at different times for each ion and column experiment listed in

Table 1. , K2,i and  were the adjustable parameters.

8 4 RESULTS AND DISCUSSION

4.1 Experimental leaching tests

The recoveries of the column leaching experiments for each ion were calculated by determining the mass extracted at a certain time as a fraction of the total extractable mass, as indicated in Section 2.1. Figures 1, 2 and 3 show the recoveries for SW3L, TW6L and RS6S, respectively. In general, the highly soluble nitrate was removed rapidly, resulting in high recoveries in a short time. The recoveries of nitrate and iodate for the experiments leached with seawater were similar to the results of the tap water experiment; nevertheless, the remaining ions resulted in higher recoveries for the least concentrated leachant, tap water. For the experiments leached with the loaded solutions (RS and DS), the recoveries were lower than for the diluted solutions. This was expected because the extraction capability decreases when the concentration of the leaching solution is higher. Iodate dissolution was somewhat slower than that of nitrate in all of the cases.

1.0 1.0

0.8 0.8

0.6 0.6

0.4 NO3 0.4

Recovery Recovery K SO4

0.2 Cl 0.2 Mg

IO3 Na 0.0 0.0 0 100 200 300 400 0 100 200 300 400 Time, h Time, h

Figure 1. Experimental recovery for the SW3S experiment (seawater, 0.003 m3/m2/h and 0.6 m).

9 1.0 1.0

0.8 0.8

0.6 0.6

0.4 NO3 0.4

Recovery Recovery K SO4

0.2 Cl 0.2 Mg

IO3 Na 0.0 0.0 0 100 200 300 400 0 100 200 300 400 Time, h Time, h

Figure 2. Experimental recovery for the TW6L experiment (tap water, 0.006 m3/m2/h and 1 m).

1.0 1.0

0.8 0.8

0.6 0.6

0.4 NO3 0.4

Recovery Recovery K SO4

0.2 Cl 0.2 Mg

IO3 Na 0.0 0.0 0 100 200 300 400 0 100 200 300 400 Time, h Time, h

Figure 3. Experimental recovery for the RS6S experiment (rich solution, 0.006 m3/m2/h and 0.6 m).

For all of the ions, the response matched the expected results, where the highest recoveries were achieved for the leachants, irrigation rates and column heights in the following order: TW>SW>DS>RS, 0.006>0.004>0.003 m3/m2/h and 0.6>0.8>1.0 m. From this analysis and by observing the recovery curves, the leaching agent appears to be the most relevant factor in the recovery responses.

The sulfate recovery was the lowest in all of the leaching tests, possibly because the dissolution of this ion was initially controlled by the presence of other ions, such as sodium and calcium. At this point, the leachate was saturated in sodium sulfate; this finding was supported by the presence of crystals of sodium sulfate at the column bottom (Ordóñez et al., 2013). Sodium is an important ion in the dissolution process of many species because it is shared between several minerals, whereas the

10 dissolution of potassium and magnesium is controlled by the solubilities of these species. The release of ions from the columns with higher irrigation rates was faster, and the steady state was reached after a short time; conversely, the experiments with low irrigation rates required prolonged times. The taller columns showed slower kinetics of recovery for all ions, but at the final time, the recovery was the same.

For all of the experiments, the particles used had small sizes (average particle diameter of 6.8 mm); therefore, it is expected that the influence of the particle size was small and that the dissolution of the different ions, to a large extent, was controlled by solubility limitations and the dissolution rate.

4.2 Evaluation of the column leaching experiments using the model

As discussed in the model presentation (section 3), K1 , K2,i , and  need to be adjusted by comparing the experimental recoveries with those calculated using Equation 5. and  were common for all column experiments and ions, whereas K2,i had a particular value for each ion. The other values were taken from the experimental conditions. H is the initial column height, and q is the irrigation rate; both are shown in Table 1. Csi is the operational solubility of the respective ion and was obtained from the maximum concentration reached during the column leaching tests (Table 5). The difference between the solubility and the concentration of the leaching solution was used as the driving force.

Table 5. Values of operational solubility ( Csi ) Ion Operational solubility (kg/m3) - NO3 250 2- SO4 140 - IO3 1.8 Cl- 140 Na+ 150 K+ 12 Mg2+ 25

For the most loaded leaching agent, RS, the difference between the concentration in the leachant and the operational solubilities for the most soluble species, such as nitrate and iodate, was large (approximately 9 times), whereas for the other ions, the ratios were smaller (by 2-4 times). This finding confirms that the differences between these concentrations have a direct effect on the leaching behavior.

The parameters used in the simulations are shown in Table 6. The fractions of the different soluble species in the caliche mineral  i were obtained from chemical analysis (Table 2) as the relative amount of each ion in the total mass of the solid.

11

Table 6. Values employed in the simulation Parameter Symbol Value

Particle radius, m rt 0.003 Mineral density, kg/m3  1900

Fraction of retained solution  w 0.08 Limit recovery R 0.99

The recoveries of the seven column experiments were adjusted for several ions (nitrate, iodate, sodium, potassium, magnesium, chloride, and sulfate). The fitted heap-related parameters K1 and  were 0.21 and 0.70, respectively. For each ion, the particle-related parameter K2,i is listed in Table 7. The magnitude of  reveals that the column scale had a slightly larger effect on the recovery, possibly because the average particle size was smaller than 7 mm; therefore, the most important resistances were located on the column side.

Table 7. Values of fitted K2,i , considering the recoveries of all experiments and ions

Ion K2,i (m/h) - -4 NO3 2.10*10 2- -6 SO4 1.30*10 - -4 IO3 1.20*10 Cl- 6.40*10-6 Na+ 7.70*10-6 K+ 5.50*10-6 Mg2+ 6.70*10-6

Regarding the values of K2,i , which is the parameter for the particle scale, the differences between them are mainly determined by the dissolution constant, ki . The largest values are for nitrate and iodate, species that are dissolved rapidly. Sulfate had the smallest value because the dissolution of this ion is controlled by the presence of other species, such as sodium. The presence of sodium also influences the dissolution of chloride; therefore, chloride and sodium also exhibited small values of this parameter. In addition, small values were obtained for potassium and magnesium because these ions were dissolved slowly. The outlet concentration for these ions decreased slowly and was apparently controlled by their solubilities (Ordóñez et al., 2013).

In general, an exponential trend of recovery was captured by the model, and when the fitting quality was analyzed separately, the agreement between the experimental recoveries with the calculated recoveries had different grades of accuracy: high accuracy for the seawater leaching experiments

12 SW3S (Figure 4) and SW3L and medium accuracy for the experiments irrigated with loaded and partially loaded solutions RS6S (Figure 6) and the DS6L. The agreement was intermediate for the experiment that used tap water, TW6L (Figure 5), and was insufficient for SW6L and DS4M. A possible cause for these discrepancies could be the formation of preferential paths through which the solution flowed. For this reason, these experiments were not considered in the predictability analysis because the responses were expected to be low quality.

1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6

Rm,Na

0.4 0.4 0.4 Rx,Na

Recovery Recovery Recovery Rm,Cl Rm,NO3 Rm,K Rx,Cl 0.2 Rx,NO3 0.2 0.2 Rx,K Rm,IO3 Rm,SO4 Rm,Mg Rx,IO3 Rx,SO4 Rx,Mg 0.0 0.0 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time, h Time, h Time, h

Figure 4. Experimental (markers) and modeled (lines) recoveries for the SW3S experiment.

1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6 Rm,Na

0.4 0.4 0.4 Rx,Na

Recovery Recovery Recovery Rm,NO3 Rm,Cl Rm,K Rx,NO3 Rx,Cl Rx,K 0.2 0.2 0.2 Rm,IO3 Rm,SO4 Rm,Mg Rx,IO3 Rx,SO4 Rx,Mg 0.0 0.0 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time, h Time, h Time, h

Figure 5. Experimental (markers) and modeled (lines) recoveries for the TW6L experiment.

13 1.0 1.0 1.0

0.8 0.8 0.8

0.6 0.6 0.6 Rm,Na

0.4 0.4 0.4 Rx,Na

Recovery Recovery Rm,NO3 Recovery Rm,Cl Rm,K Rx,NO3 Rx,Cl Rx,K 0.2 0.2 0.2 Rm,IO3 Rm,SO4 Rm,Mg Rx,IO3 Rx,SO4 Rx,Mg 0.0 0.0 0.0 0 100 200 300 400 0 100 200 300 400 0 100 200 300 400 Time, h Time, h Time, h

Figure 6. Experimental (markers) and modeled (lines) recoveries for the RS6S experiment.

Deficiencies in some of the fittings can be attributed to the model not accounting for collateral phenomena that occur during the leaching of caliche, as the precipitation of specific ions. As a result, certain conditions of the modeled recoveries were below or above the experimental values.

In the presented model, the dissolution of each ion was considered independently. Although the model included the term Csi  Ci , the representation of the experiments appears insufficient because the dissolution of various ions (specially the less soluble) depends not only on its solubility but also on the influence of other species, as was corroborated by Ordóñez et al. (2013), who observed sodium sulfate precipitates after brief times.

4.3 Sensitivity analysis

To determine which parameters were the most important in the recovery, a sensitivity analysis was performed. In this case, caliche-specific properties ( K2,i and Csi ) and operational parameters ( H and q ) were included. For the analysis, 3 values of each parameter were considered independently, and the remaining studied variables were set to the central values given in Table 8.

Table 8. Parameter values used in the sensitivity analysis Parameter Units Values -5 -4 -4 K2,i m/h 3*10 1*10 4*10 kg/m3 20 80 200 H M 0.4 1.0 1.6 q m3/m2/h 0.002 0.004 0.006

Figure 7a shows the recoveries as a function of the K2,i -parameter, which is determined by the content of the ion in the caliche and the dissolution rate, ki . For a high value of the K2,i -parameter,

14 the recovery reaches its maximum value after a short time. The opposite occurs for a low value of this parameter. For species with high solubilities, high recoveries were obtained after relatively short times because the solubility concentration acts as a component of the driving force for the dissolution. Very long times were required to reach high recoveries for species with low solubilities (Figure 7b). Simulations using different column heights showed that, for a short column, higher recoveries are obtained for a given time than for a long column (Figure 7c). Larger recoveries were obtained at higher irrigation rates, as shown in Figure 7d. However, increasing the irrigation rate has less impact on the recoveries, possibly because at a high irrigation rate, the dissolution is controlled by the dissolution kinetics ( K2,i -parameter). This result was corroborated by Mellado et al. (2011a); for copper mineral leaching that demonstrated that the q has an important role at the beginning and becomes less important in later stages.

From these observations, it is apparent that the recovery calculated by the model is strongly influenced by the intrinsic characteristics of the material (such as K2,i and Csi ) and not as much by the operating conditions. Over short times, the differences in recovery are high, although as the leaching progresses, these differences become smaller.

15 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4 Recovery Recovery K2i = 3E-5 m/h Csi = 20 kg/m3

0.2 K2i = 1E-4 m/h 0.2 Csi = 80 kg/m3 K2i = 4E-4 m/h Csi = 200 kg/m3 0.0 0.0 0 100 200 300 400 500 0 100 200 300 400 500 Time, h Time, h a) b) 1.0 1.0

0.8 0.8

0.6 0.6

0.4 0.4 Recovery Recovery H = 0.4 m q = 0.002 m3/m2/h

0.2 H = 1.0 m 0.2 q = 0.004 m3/m2/h H = 1.6 m q = 0.006 m3/m2/h 0.0 0.0 0 100 200 300 400 500 0 100 200 300 400 500 Time, h Time, h c) d)

Figure 7. Sensitivity analysis for the model for several parameters: a) K2,i -parameter, b) solubility, c) initial column height, and d) irrigation rate.

4.4 Predictive capabilities of the model

To prove the versatility of the model, predictions were performed. The parameters K1 , K2,i and  were obtained by fitting the recoveries obtained in the model and those from the experiments. These fitted parameters were used in other experiments that were conducted under different operational parameters ( q , H and Ci ); all ion recoveries were predicted. The determination coefficient between the experimental and predicted recovery was calculated as an indicator of the quality of the prediction. Three different cases were considered using distinct experiments in the fitting and prediction; these experiments are detailed in Table 9. In each case, two column experiments were fitted using 40 data points, and predictions were performed for 2-3 other experiments.

16 Table 9. Strategy of predictability tests

Cases Fitted experiments Predicted experiments R2 Case 1 SW3S - SW3L RS6S 0.92 DS6L 0.96 Case 2 SW3L - TW6L SW3S 0.97 RS6S 0.85 Case 3 TW6L - RS6S SW3S 0.97 SW3L 0.93 DS6L 0.94

When the predicted recoveries were plotted against the experimental recoveries, a large quantity of data was located in the upper part of the graph, which corresponds to the highly soluble species because these species reach high recoveries early. In contrast, less soluble ions, such as sulfate, show a more homogeneous distribution along the different recoveries because the release of these ions gradually increased during leaching.

In the experiment RS6S (Figure 8a), the simulated recoveries for the sodium, chloride and sulfate ions at the early times were higher than the experimental values, whereas at longer times, the trend was the opposite. This phenomenon can be explained from the observations made by Ordóñez et al. (2013), who reported that the dissolution of these species was controlled by the presence of the common ion sodium, which caused the precipitation of sodium sulfate in some situations. These dynamic aspects are not addressed in the hybrid model; this precipitation results in experimental recoveries less than the predicted recoveries. At long timepoints, the behavior is contrary because a significant amount of the sodium has been removed and the dissolution is not limited by the effect of the common ion. When using a more diluted leaching agent (Figure 8b), the determination coefficient was very accurate, and most of the predicted recoveries were close to the experimental results. The effect of precipitation of the common ion was less evident because the concentration of sodium in the leaching agent was lower.

17 1.0 1.0 R2 = 0.92 R2 = 0.96 0.8 0.8

0.6 0.6

0.4 NO3 IO3 0.4 NO3 IO3 Na K Na K

Mg Cl Mg Cl Predicted Predicted recovery Predicted Predicted recovery 0.2 0.2 SO4 SO4 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 a) Experimental recovery b) Experimental recovery

Figure 8. Predictability analysis (Case 1) a) RS6S and b) DS6L.

When the analysis was used to predict the results of experiments with different initial column heights (or, indirectly, the mass of loaded caliche), the quality was less satisfactory (case 2). Further analysis showed that this lower R2 resulted because one of the fitted tests exhibited feed flow fluctuations.

The model showed to be a useful tool in the prediction of pilot experiments, even when the operating parameters were changed; the determination coefficients of a majority of the experiments were greater than 90%.

5 CONCLUSIONS

The contribution of this work is the validation of the analytical hybrid model for the heap leaching of caliche ores (Gálvez et al., 2012). Leaching column experiments conducted at different operational conditions, such as different irrigation rates, heap heights, and leaching agents, were used in the validation of the model. In general, the fitting of the recoveries exhibited acceptable agreement considering the simplifications and assumptions that were used in the model. Its strength is that the values obtained for the particle-related constants ( K2,i ) are coherent with the values expected considering the dissolution kinetics of the different ions.

To study the importance of these parameters, a sensitivity analysis was performed. It was found that the most important parameters were those related to the particle, such as the operational solubility Csi and the mass transfer coefficient ki . The applicability of the model was tested under different leaching conditions. Three cases were considered, where for each case, the parameters K1 , K2,i and  were determined by fitting the recoveries to two column experiments. Using these values for the parameters, other column experiments carried out under different operation conditions were predicted. The predictions showed, in most cases, good agreement. Using the overall trend, it is possible to infer that from a couple of

18 experiments, the responses that would be obtained in other tests with different experimental conditions can be determined.

Some of the challenges for future work are focused on the measurement of physical properties of the caliche ores, such as the porosity, permeability, and capillary suction. Another important aspect to consider is the particle size; therefore, experiments using larger particles are planned.

6 ACKNOWLEDGMENTS

The authors wish to thank CONICYT for support through the project MEL 81105010. J.I.O. thanks CONICYT for the PhD scholarship.

7 NOMENCLATURE

A Cross-sectional area of column (m2) q Irrigation rate (m3/m2/h)

3 Ci Concentration of ion i in leachant (kg/m ) rt Particle radius at time t (m) 3 Csi Solubility of ion i (kg/m ) Ri,t Relative recovery of ion i at time t  H Initial heap height (m) Ri Relative recovery of ion t at infinite time ht Heap height at time t (m) t Time (h)

K1 Adjustable parameter  i Mass fraction of ion i in caliche

K2,i Adjustable parameter (m/h)  w Volumetric solution fraction ki Mass transfer coefficient of ion i (m/h) i Importance of heap leaching scale of ion i 3 k Kinetic constant of heap scale  Mineral density (kg/m ) k Kinetic constant of particle scale  Dimensionless time related to heap scale m Mass added in feeding at time t (kg)  Dimensionless time related to particle scale for ion i int i m Mass extracted from leaching at time t (kg)  Dimensionless delay time outt

8 REFERENCES

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