Copper Overview: From the Ore to the Applications – A Case Study of the Application of Concentrated Solar Energy to the Treatment of Copper Metallurgy Slags

*Daniel Fernández-González and Luis Felipe Verdeja González*

### **Abstract**

Copper is a metal that is widely used in different applications mainly due to its thermal and electrical conductivities, together with its corrosion resistance, particularly when it is alloyed. This chapter intends to be a summary of the copper metallurgy: from the historical aspects and mineral deposits or statistics to the different technologies used to produce metallic copper together with the distinct applications (of copper and copper alloys). Environmental issues are deeply rooted in industrial policies to improve the recovery of the metal as well as to minimize the residues generated in the process, which are a problem from the environmental point of view but also from the economic standpoint. Therefore, this document concludes with a research work carried out with the aim of treating copper slags with concentrated solar energy to recover valuable elements from these slags, as iron and copper. Results from this investigation suggest that solar energy could have an enormous potential in the copper metallurgy.

**Keywords:** copper slag cleaning, copper metallurgy, electrowinning, flash smelting, copper applications

### **1. Introduction**

Copper has been associated to the human history from the moment when it was discovered in native state. It was the first metal used by humans and the second most used after iron through the ages. The name "copper" derives from the Latin word "cuprum", and this word comes from the Roman name of the island Cyprus, where copper was extracted in that period. Nevertheless, there is a historic period known as the Chalcolithic or Copper Age, also termed as the Eneolithic or Aeneolithic, now

regarded as part of the broader Neolithic, where copper was used for utensils, ornaments, tools, and weapons before the Roman Empire appearance. In the Chalcolithic period, copper predominated in metalworking technology and can be defined as a transitional period between the Neolithic and the Bronze Age, where humans discovered that by adding tin to copper, it was possible to create bronze, a metal alloy harder and stronger than either component. Anyway, the utilization of copper significantly increased in the nineteenth and twentieth centuries with the spread of the electricity utilization. Nowadays, approximately 50% of the copper production is employed in the electric power industry and around 25% in construction. The main copper alloys are: brass (Cu-Zn), bronze (Cu-Sn), and cupronickels (Cu-Ni) or aluminum bronze (Cu-Al), widely used in the naval industry and in several piping applications due to its corrosion resistance [1].

The chemical element copper is a reddish metal at the head of group IB in the periodic table, with oxidation states +1 and + 2. Its symbol is Cu; atomic number, 29; and atomic weight, 63.546. The physical properties of the copper depend on the purity as well as on the ore and on the process used to obtain it. This way, impurities in solid solution or segregated phases at the grain boundaries due to the treatment of the metal can have a relevant influence on the properties of the metal. Dislocations or substitutional solid solutions have a significant influence on the thermal and electrical conductivities of the copper, on the plastic behavior as well as on the corrosion resistance. This way, high-purity copper is very ductile; although work hardening increases the hardness and the resistance while the annealing reduces the hardening (elements in substitutional solid solution play the same role). Pure copper can be hot worked, without brittleness, but the resistance at high temperature is poor. Several impurities produce this deterioration of the resistance: S, Bi, Sb, Pb, and Se. The electrical conductivity of copper is the highest among the metals after silver (0.6% of the electrical conductivity of this metal). Cu (2+) is the most stable state but above 800°C, Cu (1+) is more important, which is relevant in pyrometallurgical processes. Copper is a relatively noble element as it can be deduced from its high potential of standard reduction. It gets covered with a thin layer of cuprous oxide under dry air at room temperature. At high temperature (under air), cuprous oxide is first formed but cupric oxide appears later [1]. In the ambient atmosphere, copper surface oxidizes with the years and forms a thin layer, decorative and protective, of green color, mainly formed by basic carbonates and sulfates of copper, which is quite typical from the roofs of historical buildings in central Europe (**Figure 1**).

Copper in a dry atmosphere resists the attack of aggressive products although it exhibits great affinity for the halogen elements and sulfur. Non-oxidizing acids (sulfuric, hydrochloric, and other diluted organic) badly attack the copper. Copper is soluble in oxidizing acids such as nitric and chromic, and in non-oxidizing (sulfuric) having an oxidizing agent (such as oxygen or hydrogen peroxide). Pure water does not corrode copper, but sea water produces a moderate attack. Sulfides are attacked in hydrometallurgy using solutions of ferric salts. Regarding alkaline solutions, there is passivation and the attack at acid pH requires great potential. Oxygen solubility in liquid copper has certain importance. SO2 dissolves in liquid copper and forms sulfides. Hydrogen is soluble in liquid copper and also remains dissolved after the solidification, being the quantity controlled by reaction with the oxygen (forms water vapor that evaporates and generates residual porosity). Hydrocarbons do not, in general, react with the copper except acetylene. **Table 1** collects the values of several important physical and chemical properties of the copper [1].

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

### **Figure 1.**

*Greenish roofs made of copper and covered with a layer of basic carbonates and sulfates of copper.*


### **Table 1.**

*Physical and chemical properties of the copper.*

### **2. Deposits, minerals, and trends**

First copper utensils, ornaments, tools, and weapons were manufactured with casted native copper, but soon other techniques were applied to use other copper sources. In this line, around 80% of the copper that is mined nowadays comes from low-grade ores containing 2% or less of Cu. In this way, even when the copper sulfides metallurgy is relatively recent, it is possible that a few centuries BC metallic copper was obtained from a matte by means of repeated roasting and smelting cycles. This method was applied for centuries, and it was not until the 19th century when the reductant capacity of sulfur was considered. Anyway, before starting with the copper metallurgy, it is convenient to introduce the main copper minerals because they define the process that is nowadays used to produce metallic copper. In fact, copper content in the Earth's crust reaches 70 ppm. This way, more than 160 minerals that contain copper are known but only two main families have importance: oxidized ore (cuprite, Cu2O; tenorite, CuO) and mainly sulfide ores (chalcopyrite, CuFeS2; bornite, Cu5FeS4; chalcocite, Cu2S). Deposits are mined when the ores contain 0.5% Cu in open-pit mining and 0.7–6% Cu in underground mining. However, significant research is appearing in the field of complex copper ores due to the increasing demand and the potential depletion and decline of good copper ore grades. Low-grade sulfide ores are subjected to concentration operations, which include flotation, to obtain dry concentrates of around 30% of copper with 10–200 μm of grain size [1]. Within this context, it is possible to mention Velásquez-Yévenes and Lasnibat's research [2] about the simultaneous recovery of copper and manganese from "exotic-Cu" deposits in Chile, characterized by the refractoriness to dissolution under acidic and oxidative conditions, or the research of Godirilwe and collaborators about the extraction of copper from complex carbonaceous sulfide ore, characterized by their mineralogical complexity and impurities of organic carbon and carbonates [3]. Other research in this line that can be mentioned is that of Corin and coauthors about complex copper ore (sulfide, oxide, and mixed) in Zambia [4], or Liu and researchers that reported the beneficiation of complex copper oxide ores rich in malachite [5] or the research of Hu et al. about low-grade copper ores with high contents of oxide ore and carbonate gangue (malachite, chrysocolla, chalcopyrite, and chalcocite with gangue minerals as quartz, limonite, calcite, and dolomite) from Yunnan province in China [6].

Porphyry copper deposits are currently the largest source of copper ore. The copper reserves are estimated in 2021 in 880 Mt. (Million tons) according to the United States Geological Survey. Half of these reserves are concentrated in five countries: Chile (200 Mt), Australia (93 Mt), Peru (77 Mt), the USA (48 Mt), and China (26 Mt). Regarding the production/demand of copper, this has grown since the eighteenth century, particularly in the last decades: 10000 tons in 1700, 18,000 tons in 1800, 450,000 tons in 1900, 2.5 Mt. in 1950, 4.5 Mt. in 1960, 7.3 Mt. in 1970, 9.3 Mt. in 1980, 10.9 Mt. in 1990, 15.1 Mt. in 2000, 19.1 Mt. in 2010, 23.1 Mt. in 2015, and 25.3 Mt. in 2020 (year with production significantly affected by the COVID-19 pandemic situation; the estimation for 2021 was 26 Mt). These values refer to the total consumption/production of copper, but it is important to make a distinction between copper mine production and refined copper. This way, approximately 80% of the copper produced worldwide comes from copper extracted from mining operations. Regarding the principal mine copper producers, the main countries are (2021): Chile, 5.6 Mt.; Peru, 2.2 Mt.; China, 1.8 Mt.; USA, 1.2 Mt.; Australia, 0.9 Mt. Regarding the main refinery copper producers of copper, it is possible to indicate (2021): China, 10 Mt.; Chile, 2.2 Mt.; Japan, 1.5 Mt.; the USA, 1 Mt.; Germany, 0.63 Mt.; Australia, 0.45

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

Mt.; Peru, 0.35 Mt. With respect to the price, the minimum price in 10 years was reached in December 2015 (4577 \$/ton) and March, 2020 (4789 \$/ton, coincident with the quarantine period resulted from COVID-19), while the maximum price in 10 years was reached in March 7, 2022 (10,729 \$/ton, after the Russian invasion of Ukraine).

Aligned with the above-mentioned questions, the equilibrium between the supply and the demand of raw materials or semifinished and finished products is almost unattainable. The reasons of this disequilibrium can be explained by an irrational gathering of raw materials, a sanitary problem (i.e., COVID-19), or military reasons (i.e., Russian invasion of Ukraine). Basic resources (materials, energy, and food) are the first resources in being affected in one or other manner by the distortions of the markets, and this has a significant impact on the development of the poorest countries and regions, in the growth of emerging countries and regions and in the sustainability of developed countries and regions. In this line, countries are identifying strategical minerals or elements whose scarcity would have a significant impact on the chain value. Copper is one of these elements. This metal has still enormous importance in the market despite of its utilization for hundreds of years. In fact, it has gained significant interest in the last centuries due to the electricity market and, it will probably attract more interest with the development of both the sustainable methods of producing electricity and the electric vehicles. In this context, considering the data of the National Renewable Energy Laboratory (NREL) of the USA, 0.7–1.8 tons of copper and 110 tons of steel are required for each MW of installed wind energy [7].

In general, it is important for the beneficiation of the basic resources, particularly copper, to study the evolution of the price of the raw materials in a period of time comparable to the proposed duration of the project (development, exploitation, and conclusion). For this reason, it is realistic to analyze the copper market from 1980 [8]. The copper price in 1980, which approximately coincided with the end of the second oil crisis, was 2400 \$/ton, while in 1995 it was not far from the price in 1980: 2976 \$/ ton. However, the irrational development of the real-estate market in the period 1995– 2010 made the copper price to grow 2.2 times, while in the period 1980–1995, the growth was only 0.24 times. After the real-estate bubble, the price descended to a minimum of 4553 \$/ton in 2015 and started to progressively grow up to an average value around 6000 \$/ton before another minimum coincident with the COVID-19 lockdown in March 2020 in 4789 \$/ton. The copper price has sharply grown since that minimum until reaching values never seen before, after the Russian invasion of Ukraine (>10,000\$/ton). It is possible to think, as it is indicated by Brinded [9], that the copper market is mad. Maybe this term is not the most adequate because it sounds better to say that the copper market is in crisis. There is not a single reason to justify this situation, but it is necessary to consider several variables in the implementation of a mining project: the price of the metal in the London Metal Exchange, the tons of proven metal reserves in the deposit, and the grade-concentration of the metal in the proven reserves. Therefore, it seems not reasonable to start a mining project considering only the highest prices in the market but an average value over a long period (and different scenarios) together with the other variables indicated in this paragraph, as otherwise, for instance, projects started under the current copper prices could lead the mining project to fail whether the prices descend. Moreover, the project should consider its complete duration (from the early stages of reserves estimation to the land rehabilitation after the end of the project). Therefore, economic resources obtained from the sale of the metal in the market are approximately distributed as follows: 14% for the exploration, 44% for the mining-exploitation-concentration operations and environmental conservation, 23% for the extractive metallurgy, 6% for general costs

and management of the project, and 13% of economic profit, for successful project implementation, based on previous works within this field and considering the economic evaluation of mine implementation projects [10, 11].

### **3. Copper metallurgy and refining**

### **3.1 Introduction**

The primary source of Cu is porphyry deposits. The treatment of primary copper ores by the pyrometallurgical process is responsible for about 80% of the world's copper production [12]. However, the production of copper taking advantage of copper sulfides' characteristics is relatively recent. The production of copper in the Middle Age (as it is collected in *De Re Metallica* of Georgius Agricola) was based on the Mansfeld process, which involved seven operations of roasting and melting. First, the slagged gangue was separated from the matte with low metallic content, and then, this was enriched by concentrating smelting, carrying to the slag, by oxidation, the iron content. The enriched matte was dead roasted to obtain an oxide that was treated by reducing smelting to obtain black copper, which was later refined. It was in 1700 when the Welsh process was introduced, which significantly modified the method of obtaining copper. It consisted of 10 operations at the beginning, although it involved 6 or 7 stages in 1830. The main difference was the extensive utilization of the roasting process or double decomposition process, where sulfur was used as reductant reagent. At the beginning of the Modern Age, Germany was the leader in copper production, but in 1800 England became the biggest copper producer. Chile became the first copper producer in 1859 and, from that moment, this country is the biggest copper producer in the world. Even when, as we have already seen, copper has been produced for several centuries, the greatest developments in technique are from the last centuries: the application of air/oxygen blowing as in the Bessemer converter, the development in Finland of the flash smelting process after the World War II, industrial electrowinning in the second half of the nineteenth century or the discovery of the differential flotation of sulfides also in the second half of the nineteenth century. These developments, as well as the applications of copper in construction and electricity, have made this metal one of the five most produced worldwide [13].

### **3.2 Principles of the process used to obtain the matte**

Pyrometallurgical copper smelting processes are based on the principle of partial oxidation of sulfide concentrates [1]. The methods based on the total oxidation of sulfides with posterior reduction of the metal oxide, without formation of a copper matter, are generally not used due to both the high consumption of combustible, the formation of copper-rich slags and the obtaining of crude copper with high level of impurities. This way, the smelting of sulfide concentrates, partially roasted or without roasting, with the addition of impurities, produces two immiscible phases: one heavy containing most of sulfides that is known as matte; other oxidized and ferrous is known as slag. The reactions of oxidation of the sulfur of sulfides and iron, both exothermic, produce the matte with adequate composition and it is possible to use the heat of the reaction if the suitable technology is used. The formation of the slag, by reaction of the iron (II) oxide with the silica, which is used as a flux to form fayalite

(main component of the slag) and separate the iron from the matte, is also exothermic. The reactions involved in the formation of the matte are described as follows:

$$4\text{CuSFeS(s)} + 5\text{O}\_2(\text{g}) \leftrightarrow 2(\text{Cu}\_2\text{S} \cdot \text{FeS})(\text{dis;} \text{matte}) + 2\text{FeO}(\text{s}) + 4\text{SO}\_2(\text{g})\tag{1}$$

that is an exothermic reaction, as the next one:

$$\text{2FeO}(\text{s}) + \text{SiO}\_2(\text{s}) \leftrightarrow \text{2FeO} \cdot \text{SiO}\_2(\text{dis}; \text{slag}) \tag{2}$$

The most important equilibrium, between the phases (matte and slag), is the following one, which is displaced to the right side of the equation:

$$\text{Cu}\_2\text{O}(\text{dis};\text{slag}) + \text{FeS}(\text{dis};\text{matte}) \leftrightarrow \text{Cu}\_2\text{S}(\text{dis};\text{matte}) + \text{FeO}(\text{dis};\text{slag}) \tag{3}$$

The presence in the matte of liquid iron sulfide reduces the iron (III) oxide to iron (II) oxide:

$$\rm{3Fe\_3O\_4(s) + FeS(s) \leftrightarrow 10FeO(s) + SO\_2(g)}\tag{4}$$

The previous reaction can be used to eliminate part of the magnetite, with the presence of silica because the magnetite is detrimental for the operations in the furnace due to its high melting point (>1500°C), which increases the viscosity of the slag and increases the quantity of copper in the slag.

Therefore, the process used to obtain the matte is a copper concentration process in this phase. There are several elements that accompany the copper that are essentially reduced. Thus, calcium, magnesium, and aluminum go directly to the slag, while precious metals go to the matte. The other metals, Ni, Co, Pb, Zn, As, Sb, Bi, etc., distribute between both phases or, separate with the gases of the furnace. The matte is fundamentally a mixture of sulfides in the pseudo binary Cu2S-FeS system. The density of the matte is in the range of 4.9–5.3 g/cm3 depending on the state (liquid or solid) and the copper content. On the contrary, the slag has a density 1 g/cm<sup>3</sup> lower and comprises a 30–40% of iron as oxides and 25–40% of silica, mainly as iron silicate (fayalite). The smelting process involves an almost complete separation of the matte and slag due to the different densities and the different nature of the chemical bonding (covalent in the matte and ionic in the slag). Some technologies of fusion (reverberatory furnace) produce slags with 0.6% of copper and others, as the flash smelting Outokumpu (introduced by this Finnish company) [1], produce slags with 1.2% of copper that must be treated by either reduction in an electric furnace with additions of carbon and pyrite or flotation after milling.

### **3.3 Traditional smelting of copper sulfides**

The most traditional form of obtaining copper in the fifties of the twentieth century consisted in roasting the concentrates of sulfides and melting the products in reverberatory furnaces, sometimes in electric furnaces and less frequently in shaft furnaces. A matte was obtained, which was later subjected to oxidation in Pierce-Smith converters. The main advantage of this technology is the production of slags that can be directly sent to controlled landfill. Within this group of technologies, it is also possible to mention the Noranda and Teniente processes [1], which in fact are big converters adapted for the smelting to obtain the matte. In these technologies, the

concentrate is mixed and flows in a turbulent bath matte/slag; additionally, the Fe and S of the concentrate oxidize to form a rich matte, a slag that cannot be disregarded, and a gas with high SO2 content. The matte (70–75% Cu) is sent to the converter to obtain blister copper. In the particular case of the Noranda process, it was set at the beginning as a continuous process to directly produce blister copper, but it failed. The idea/objective of obtaining copper in a single stage was one of the industrial research objectives for years, as we are going to see later. Returning to the Noranda process, the system involved the simultaneous presence of three phases (slag, matte, and metal) and, it was not possible to achieve a good recovery of copper from the slag. The metal was obtained with great contamination and, therefore, several problems arose during the electrowinning.

### **3.4 Flash smelting**

The flash smelting is the dominant technology in the market. It can be autogenous or not, but the main characteristic is the rapidness of the smelting process resulting from the utilization of a burner with preheated air, enriched with oxygen, or with industrial oxygen. The process will be autogenous if the following condition is accomplished: the partial oxidation of sulphides generates enough heat to melt the matte and the slag and have them as separated phases in the furnace (due to density difference). Heat is usually provided to ensure the reactions matte-slag and the separation of both phases. In flash smelting, the stages of roasting and oxidizing smelting happen simultaneously taking advantage of the heat generated in the process. The only autogenous technology is the INCO process that uses industrial oxygen and a design of the furnace that allows copper slag with 0.7% Cu. The other technologies have the disadvantage of high copper content in the slag due to the high oxidizing environment of the process and the high quantities of magnetite in these conditions (which is in solid state when it is in excess), which makes it almost impossible to empty the slag from copper using the Eqs. (3) and (4).

The Outokumpu process of flash smelting is the most important technology to produce copper (8 of 20 biggest copper smelters according to the ICSG Directory of Copper Mines and Plants use this technology). This process was developed in Finland

**Figure 2.** *Scheme of the Outokumpu smelting process (*source: *Wikicommons).*

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

in the fifties of the last century and has great productivity and easy control. The scheme of the process appears in **Figure 2**.

The furnace can be divided into three sections [1]: tower, for the partial roasting and smelting of the dry concentrate in suspension; horizontal zone, where the matte and the slag are separated; and, chimney, for the exit of gases that end in the acid plant after pretreatments to use the heat and remove the particulate matter. The process in the tower is almost autogenous but the heat for the separation of the matte and the slag is provided by gas or fuel. The copper content in the slag is around 2% of copper, which involves a posterior treatment in an electric furnace with pyrite and carbon to reduce the copper content in the slag (the slag can be sold as abrasive or material for roads). The hot gases collected in the process are used in a boiler and the powders that they contain are collected with mechanical separators or electrostatic filters. These powders (5–10%) are recycled again in the furnace or treated depending on the concentration of volatile elements.

Other technologies of flash smelting are the INCO process, cyclonic smelting KIVCET, Isasmelt process, Vanyukov process, and Contop process.

### **3.5 Conversion**

Conversion is the process where the matte generated in the smelting process, which is in molten state, is treated by injecting oxygen to the melt, mainly in Peirce-Smith converters. The process consists of two stages:

• The first is known as "slagging stage" and a phase formed essentially by copper sulfides, white metal, where there are less than 1% of iron sulfides, is obtained. The converter is filled again with copper matte to obtain more white metal by oxygen injection. The process is repeated several times (5 or 6 [1]) until the moment when the converter is filled with copper sulfide. The main reaction of this first stage is:

$$2\text{FeS}(\text{dis};\text{matte}) + \text{\textdegree O}\_2(\text{g}) \leftrightarrow 2\text{FeO}(\text{dis};\text{slag}) + 2\text{SO}\_2(\text{g})\tag{5}$$

The ferrous slag of the first stage is separated, normally, by addition of silica (fayalite) as in the Eq. (2).

• The second stage allows obtaining blister copper by oxygen injection to the white metal. The reactions in this stage are:

$$2\text{Cu}\_2\text{S}(\text{dis}) + 3\text{O}\_2(\text{g}) \leftrightarrow 2\text{Cu}\_2\text{O}(\text{dis}) + 2\text{SO}\_2(\text{g})\tag{6}$$

$$2\text{Cu}\_2\text{O}(\text{dis}) + \text{Cu}\_2\text{S}(\text{dis}) \leftrightarrow \text{6Cu}(\text{l}) + \text{SO}\_2(\text{g})\tag{7}$$

Even when there is 1% of FeS at the end of the first stage [1], it is impossible to avoid the formation of magnetite due to the high oxidizing potential inside of the converter and the inefficiency of the reaction indicated in Eq. (4) to destroy the magnetite. For that reason, the excess of magnetite crystals (with high melting point) produces a viscous slag that involves the pass of significant quantities of copper oxide to the slag (15% Cu). This way, converter slag must be recycled.

The conversion stage is used, apart from to eliminate sulfur and iron, to refine the content in metallic elements. Nobler metals as nickel and cobalt remain in the blister

copper. On the contrary, the slag enriches in zinc, although part volatilizes during the process. As, Sb and part of the Sn, Pb, and Bi can be found in the particulate matter collected before the chimneys (the rest remains in the slag, and only very small quantities in the metal, mainly the bismuth). Finally, blister copper contains 1% S, 0.5–0.6% O and traces of the above-mentioned metals. The conversion process is highly exothermic, making the process autogenous, which allows the charge in the converter of scraps, cemented copper or even concentrates to control the temperature of the process. Therefore, recent investigations in this line are focused on the application of mathematical modeling to minimize copper losses [14] and to increase the energy efficiency of the process [15].

### **3.6 Flash smelting to produce copper**

We have already pointed out that one of the objectives in the copper industry has been to obtain blister copper in a single step. The process required to use air highly enriched with oxygen, which resulted in installations with low capacity of operation because of the rapid deterioration of the tuyeres. Different technologies were proposed in this line, as the Noranda process as it was already pointed out, or the Mitsubishi, which is not based in a single step, among others. Mitsubishi process consists of three interconnected furnaces (smelting furnace to produce the matte, furnace to recover copper from slags and converter furnace) and is installed at least in Birla Copper (Dahej) in India according to the ICSG Directory of Copper Mines and Plants. Further information about the Mitsubishi process can be found in Ref. [16].

### **3.7 Copper hydrometallurgy**

This route of production of primary copper accounts for approximately 15% of the total world production. This route is particularly useful for low-grade ores or lowgrade sulfide residues. This is because oxide ores are very limited worldwide. The copper hydrometallurgy is very extensive. Here we present a summary of the most common techniques (further details about copper hydrometallurgy can be found in the reference [17]). Lixiviation can be applied: in situ to low-grade ores, in spoil tips for piled-up material, in boxes by percolation for fine-grained material, or in stirred reactor with or without pressure or temperature for fine-grained material. As leaching agents, it is usual to employ diluted sulfuric acid (for copper oxide ores, carbonates, basic sulfates, and silicates), iron (III) salts solutions prepared or formed *in situ* in presence of oxygen during the lixiviation process from iron (III) sulfate (these solutions, the same as chlorides, are oxidizing and are adequate for copper sulfides), chloride solutions with an oxidizing agent (which are adequate for copper sulfides) and ammonia solutions with ammonia salts, as the ammonium carbonate, for oxidized ores as well as for native copper in presence of carbonate gangue. Rich solutions obtained in the lixiviation process are filtered and sometimes purified to remove polluting dissolved elements. Finally, copper is obtained by cementation, electrolysis, or precipitation of compounds. Cemented copper is melted and fire-refined and subjected to electrowinning. The electrodeposit is sold or melted in ingots because it has its own market (99.9% Cu), or it is subjected to electrowinning. The application of hydrometallurgy in the recovery of wastes is gaining interest, particularly to treat waste that is generated in large quantities in the copper pyrometallurgy as the copper slag. Within this context, Mussapyrova and colleagues [18] reported the copper

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

selective leaching from mechanically activated copper smelter slag with copper recovery of 87.3% and maximum copper selectivity of 97.9%.

### **3.8 Fire refining and electrowinning**

The refining traditionally involves two stages: fire refining and electrowinning. The product obtained at the end of the first stage usually has 99.9% Cu, which can be insufficient for most applications and electrowinning is required to achieve a purity of 99.995% [1], required for electrical applications. It is possible to obtain a purity of 99.9999% Cu by repeated electrowinning processes or zone melting. This quality is used in research or electronics.

Fire refining (applied in the case of blister copper or in the products of the hydrometallurgical route) consists in eliminating the sulfur (to thousandths of percentage point) and reducing the oxygen content below 0.1%, by reduction, until having a free flat surface of metal resulted from the compensation of the volume of the pores by release of water vapor and gases retained in the metal. The equilibrium sulfur-oxygen in the blister copper can be expressed as follows:

$$\text{SO(dis;metal)} + \text{2O}(\text{dis;metal}) \leftrightarrow \text{SO}\_2(\text{g})\tag{8}$$

with an equilibrium constant of:

$$\mathbf{k}\_{\text{eq(Eq.8)}} = \frac{\left[\text{SO}\_2\right]}{\left[\text{O}\right]^2 \cdot \left[\text{S}\right]} \tag{9}$$

The value of this constant between 1200 and 1300°C is 25, which for a pressure of SO2 of 0.1 atm gives ½ � **<sup>O</sup> <sup>2</sup>** � ½ �¼ **<sup>S</sup> <sup>4</sup>** � **<sup>10</sup>**�**<sup>3</sup>** . This implies that for a sulfur content of 0.02%, the oxygen content would be around 0.5%, and in the case of 2 ppm of sulfur, copper would admit oxygen content above 1%. However, the part of the copper oxidizes to copper (I) oxide during the blowing stage, being dissolved in the metal, and this phase is a selective oxidizing agent as it is expressed in the following equation:

$$\text{S(dis;metal)} + 2\text{ Cu}\_2\text{O(s)} \leftrightarrow 4\text{Cu(l)} + \text{SO}\_2(\text{g})\tag{10}$$

**Figure 3.** *Copper anodes for the electrowinning process (source: Wikicommons).*

The fire refining process is carried out in modern cylindrical furnaces (and sometimes in reverberatory furnaces) and at the end of the process high copper content slags are obtained, which are recycled, and the metal with very low sulfur and oxygen content, which is casted in anodes for the electrowinning process (**Figure 3**).

More than 80% of the world**'**s copper production is refined by electrowinning, which yields high electrical conductivity copper and the separation of the impurities (the precious metals can be recovered at this stage). The process is carried out in cells with 50 g/l of copper in sulfuric medium at temperatures of around 60°C [1]. Periodic purges of the electrolyte are required to eliminate the metals that could compete with the copper in the electrolysis process (As, Sb, Bi, Ni, Co, and Fe). Nobler metals than the copper end in the anodic lodes. The contamination with silver is controlled with small additions of chloride. Sulfur, selenium, and tellurium fall to the anodic lodes, the same as the lead and tin because of not being soluble in sulfate medium. The purification of the electrolyte is carried out by crystallization of the copper pentahydrate sulfate salt and posterior precipitation of the metals by pH control or by means of additives (it is also possible to precipitate the competing metals in an impure cathode that is later recycled in previous stages). The copper cathodes have a purity of >99.99% Cu, which is the electric quality as we will describe later. Anodic slime represents a quantity <1% in weight but they contain precious metals, so they are periodically collected from the bottom of the cells. They are later filtered and dried and subjected to treatments to recover the valuable metals: initial treatments allow to solubilize the copper, later selenium and tellurium are recovered and precious metals finally are melted in an alloy that is known as bullion or doré. Further details about the anode slime are available in Ref. [19].

### **3.9 Copper foundry**

Copper cathodes can be sold as produced but it is quite common to melt the metal to obtain semifinished products. This way, cathodes are melted in furnaces where the metal is cleaned, and alloying elements are added to finally cast the metal. There are different processes of casting: semicontinuous casting, continuous casting, or casting in ingot molds. Different types of furnaces are used for this purpose, but combustibles must be free of sulfur to avoid the contamination of the copper with this element [1], with a maximum of 10 ppm of sulfur because greater contents have a noticeable influence in the mechanical properties of the copper. Semifinished copper products include wires, strips, and rods, among others, and for some specific applications, copper powders are gaining interest. Powders are manufactured from aqueous solutions by cementation or precipitation with hydrogen at high pressure, or also by atomization or by electrolytic method. Finally, three different copper qualities are defined [20]: Refined copper or electrically refined cathode (Electrolytic-tough Pitch Copper, ETP): 99.99% Cu with 0.03 0.01% Cu2O, which can be easily worked and has high electrical conductivity (100% IACS) but poor weldability (80% of the world copper production is from this quality).

• Phosphorus deoxidized copper: almost free of oxygen and is produced by the addition of reductant reagents. It can be welded. The electrical resistivity can be increased due to the presence of phosphorus, being this copper (0.04% P) used in applications where electrical conductivity is not required.

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

• Copper free of oxygen (Oxygen-free copper [OFC], or oxygen-free high thermal conductivity [OFHC]): obtained whether molten copper is kept under an inert or reductant atmosphere. This allows an oxygen content <0.001%. It is used in electronics due to the high electrical conductivity.

Finally, there is another quality of copper obtained by electrical recovery: 99.9%, with poor applications, maybe in some alloys. Research in this line is gaining interest in order to minimize the waste. For instance, the recovery of copper from electric cable waste is derived from the automotive industry by corona-electrostatic separation (99.8% Cu) [21] or waste printed circuit boards utilizing recycling of leachate (99.9% in electrowinning) [22].

### **4. Applications of copper**

Copper, and copper phases, has many different applications due to the excellent properties. Here we present a summary of the main traditional uses of copper. In this line, 50% of the copper is employed because of its excellent electrical conductivity, particularly in low-voltage applications (electric machines, including engines or transformers, among others). Another important application of copper is in semiconductor interconnects in integrated circuits [23].

Copper also exhibits high thermal conductivity and, therefore, it is used for vessels and heat exchange tubes. Other of the main applications of copper is in chemistry or feeding industries, as well as in automotive or naval industries due to the corrosion resistance, particularly when it is alloyed as brass (Cu-Zn), bronze (Cu-Sn), and cupronickels (Cu-Ni) or aluminum bronze (Cu-Al).

Copper is also used in the construction industry for conductions and coatings, and also in appliances, ornamental, and coins. It is also applied in antifriction bearings and several parts of powder metallurgy, and also in the manufacture of ammunition. Copper salts, mainly sulfates and oxides of copper, represent 1% of the world's production. Copper sulfate pentahydrate is used in agriculture to avoid fungi in fruit trees and vegetables due to the efficiency and low toxicity. Soluble copper is also added to feed and food, and also other copper compounds are used as insecticides and preservatives. Metallic copper and some of the copper compounds are used as catalyzers in numerous organic reactions, or as pigments for glass, ceramics, or enameling. Certain copper compounds have applications in the petroleum industry.

We mention here some novel potential applications of copper, copper alloys, or copper phases, as, for instance, complex copper alloys for extreme conditions applications (novel CuCrZrFeTiY alloy for fusion reactor [24]) or bulk metallic glasses [25]. It is also gaining interest due to the bactericidal activity against important human pathogens [26].

### **5. Environmental issues**

Regarding environmental issues, the most relevant points to be considered for action are: control of emissions to the atmosphere, and protection of water and disposal of solid residues. We might indicate here the growing importance of obtaining copper from secondary materials or scraps, as it was already mentioned, in order to reduce the volume of residues and the energy consumption (which is smaller in the case of recycling copper). In this line, apart from the practice carried out in other metallurgical industries with respect to environmental issues, two points have special relevance: SO2 emissions and copper slags. In the case of SO2, this is unavoidably formed in the production of copper during the smelting and conversion, but the final application of this gas is the manufacture of sulfuric acid. The production of sulfuric acid implies cleaning and drying the gases of the furnace followed by the catalytic oxidation of SO2 to SO3 and the absorption of the resulting SO3 by the water to generate H2SO4 with 98% concentration. This process is autogenous when we start from gases with 4 vol. % of SO2 or greater content, bigger contents involve specific treatments. Modern plants of double absorption can even recover 99.5% of the SO2 at the entrance. The manuscript of Alexander and colleagues about the environmental performance of modern copper smelting technologies is an interesting review about the environmental issues in copper metallurgy [27].

Copper slags are a problem in copper metallurgy due to the large quantity that is generated of this by-product: 2.2–3.0 tons slag for every ton of copper produced [28]. The applications of this residue are very limited since the researchers have still not found a massive utilization for this material [29]. Copper slags have been used as abrasives (polishing and cleaning) for metallic structures [30, 31] and mainly in the building industry: concrete manufactured with copper slag [32]; copper slags as fine particles in concrete manufacturing [33]; copper slag as a replacement for the sand in cement [34]; copper slag as a filler in glass–epoxy composites [35]; and copper slag as a construction material in bituminous pavements [36]. However, due to the high iron and copper contents (>40 wt. % and 1–2 wt. %, respectively), copper slags could become a secondary source for metal recovery [37, 38]. A total of 20 Mt. of primary copper is produced worldwide, and this involves 45 Mt. of slag generated in the process (2.2–3 tons of slag/ton copper [28]), which would represent >20 Mt. Fe and 0.5–1 Mt. Cu yearly sent to controlled landfills. Therefore, copper slag represents an environmental impact [39]: risks of heavy metals lixiviation, a visual impact, and sometimes occupation of cultivable areas. Moreover, research has also focused on the recovery of iron from the slag due to the high iron content in the copper slags: by using coke as a reductant of the copper oxide and the magnetite [40]; by modifying the molten slag with the purpose of promoting the mineralization of recoverable mineral phases and inducing the growth of the mineral phases [41]; by using a method based on coal, Direct Reduction Iron (DRI), and magnetic separation [42]; by means of a process based on aluminothermic reduction [43]; by reduction in an electric furnace with the objective of obtaining a Cu-Pb-Fe alloy [44]; by carbothermal reduction to transform the copper slag into pig iron and glassy material [45]; by irradiation with a microwave as a support of the carbothermal method [46]; or by reduction with coke powders and magnetic separation [47]. In the following section, we present a study about the application of concentrated solar energy to recover valuable metals from copper slags.

### **6. Case study: Application of concentrated solar energy to the treatment of copper metallurgy slags**

### **6.1 Introduction**

The term solar energy is often associated with the generation of heat or electric power. Nevertheless, solar energy, when it is adequately concentrated offers

### *Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

enormous possibilities in the field of materials science and metallurgy, including the recycling of residues from these industries, because of the high temperatures that can be reached by using this technology (up to 3500 K [48]). In this context, solar energy has been used in metallurgy and materials science for centuries [48]. The legend tells that Archimedes destroyed the Roman army during the Syracuse Siege using mirrors (213–212 BC), although the most traditional application of solar energy in the field of materials was the drying of adobe bricks for the construction of houses. More technical applications appeared during the early Modern period (17th century), when a German mathematician, Ehrenfried Walter Von Tschirnhaus, designed, constructed, and worked with lenses and mirrors to concentrate solar energy [48] and melted iron and obtained ceramics (porcelain). Other researchers worked with concentrated solar energy during the Modern period as Cassini (seventeenth century), who designed a lens with 1 meter in diameter to reach temperatures of around 1000°C and melted iron and silver, or Lavoisier (eighteenth century), who melted iron and approached the melting point of platinum, and also treated metals under special atmosphere such as nitrogen [48]. Anyway, it was after World War II when the investigation in the field of solar energy applications definitely emerged with the construction of the first solar furnace in Mont-Louis (France) in 1949, which was the precursor of the Odeillo solar furnace (Font-Romeu-Odeillo-Via, France; construction from 1962 to 1968; start of operations in 1969, **Figure 4**) under the figure of Felix Trombe, who demonstrated how to employ solar energy to melt high melting point refractory ceramics (alumina, chromium oxide, zirconia, hafnia, and thoria) [48]. Nowadays, there are several installations where it is possible to research within this topic: PSA-CIEMAT (Plataforma Solar de Almería, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas, in Spain), PROMES-CNRS (Procédés, Matériaux et Énergie Solaire, Centre National de la Recherche Scientifique, in France), Solar Laboratory at the Paul Scherrer Institute (in Switzerland), Weizmann Institute of Science (in Israel), or National Solar Thermal Test Facility and National Renewable Energy Laboratory (in USA), among others, which have made significant contributions to the development of solar-based metallurgical processes. From these original researchers of Von Tschirnhaus, many other researchers have made significant contributions to the progress in the field of concentrated solar energy applications in the field of metallurgy and materials science. These researchers can be read in the extended review published in 2018 in the journal *Solar Energy* with the title *Concentrated solar energy applications in materials science* by Fernández-González and collaborators [48].

**Figure 4.** *Odeillo solar furnace (font-Roméu-Odeillo-via, France).*

Focusing on our research group, the investigation has focused on the: synthesis of calcium aluminates [49], iron metallurgy [50, 51], the treatment of Basic Oxygen Furnace (BOF) slag [52], the production of silicomanganese [53], and transformations in the Ca-Si-O system [54]. The objective of the present Case Study is to present an application of concentrated solar energy in the copper metallurgy: potential recovery of copper and iron from copper slag using solar energy as heat supply for the process.

### **6.2 Materials and methods**

As raw material for experiments, original copper slag from the cleaning furnace was used. It consisted of (wt. %): Fe, 42.82; O, 36.15; Si, 10.36; Al, 3.24; Cu, 1.84; Ca, 1.76; Na, 0.99; S, 0.52; others, 2.32, determined by X-ray fluorescence. X-ray diffraction technique was employed to determine the form in which the crystalline phases of the above indicated elements were: fayalite (Fe2SiO4), 85.80 1.30% in the quantitative analysis; other important crystalline phases were magnetite (Fe3O4) and copper– iron oxide (cuprospinel, CuFe2O4, with Cu2+ and Fe3+), 7.90 1.60% and 6.20 1.80%, respectively, in the quantitative analysis [37].

Tests were performed in a vertical axis 1.5 kW solar furnace located in Font Romeu-Odeillo-Via. The functioning of the solar furnace consists of making solar radiation converge on a small surface (12–15 mm in diameter), called the focal point (where the experimental device is located), using a parabolic concentrator (2.0 m in diameter) and a heliostat that directs sun radiation to the parabolic concentrator. A scheme of the process is represented in **Figure 5**. Several experiments were carried out. They lasted between 15 and 30 minutes, with values of power from 563 to 1409 W.

**Figure 5.** *Scheme of the equipment used for the experiments [37].*

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

### **6.3 Results and discussion**

From visual macroscopic analyses of the samples, it was possible to check that the sample became magnetic after the treatment of the slag with concentrated solar energy. Moreover, occluded matte (copper sulfides) decomposed at the temperatures of the treatment as it is deduced from the investigation carried out by Winkel (metallic copper, iron sulfide, and elemental sulfur can be obtained after the treatment of copper concentrates at a high temperature under an inert atmosphere) [55]. This was corroborated by the fact that there was sulfur in the opposite face to the solar beam, which was the result of the decomposition, according to the above indicated mechanism, of the occluded matte under an ambient in this zone characterized by the low oxygen content.

Samples were subjected to Scanning Electron Microscope (SEM) observations, which confirmed the partial transformation of the copper (as sulfides or oxide) into rich nodules of copper (60–85 wt. % Cu), and also the partial transformation of the fayalite (FeSiO4) into magnetite (iron spinel). SEM images can be observed in **Figure 6**.

The average composition of the copper nodules (as those in **Figure 6**) was 65–85 wt. % Cu; 5–10 wt. % Fe; 2–10 wt. % O; <3 wt. % S, while the size was between 5 and 10 μm, although nodules with a larger size were detected in some samples (between 20 and 35 μm).

Samples were subjected to crushing and grinding down to 40 μm. Then, they were separated into two fractions: magnetic and non-magnetic. The ratio of magnetic to non-magnetic was >80 (average value: 83.3625, in weight). Each fraction was analyzed by X-ray diffraction and X-ray fluorescence. The copper concentrated in the non-magnetic phase 3–6.5 times with respect to the initial slag (1.84 wt. % Cu), nonmagnetic fraction contained >7 wt. % Cu. The grade in mining is an important factor about how much a deposit is worth, as it was mentioned at the beginning of this manuscript. The average grade of copper ores in the 21st century is below 0.6% Cu for outside mining operations. This would mean that copper slags might become a potential secondary source of copper, particularly if copper could be concentrated using solar energy. Further information can be read in *Recovery of Copper and Magnetite from Copper Slag Using Concentrated Solar Power (CSP)* [37].

**Figure 6.** *SEM images of the copper slag treated with concentrated solar energy.*

### **7. Conclusions**

This chapter includes a brief review of all the processes used in copper production. The document begins with the introduction of the properties of copper as well as the correlation of the applications with the properties, where it is important to mention the application of copper in electrical and mechanical applications due to its excellent values of thermal and electrical conductivities. The chapter continues with a brief description of the main copper ores, the copper sulfides, which define the subsequent processes that are employed to obtain the metal. The main copper producers are highlighted later. Here it is possible to see the importance of porphyry copper deposits in Latin American countries (as Chile and Peru). However, refined copper is mainly produced in China, Chile, and Japan. Regarding the price of copper, it has significantly increased since the end of the COVID-19 restrictions and has reached the maximum just after the Russian invasion of Ukraine, although this situation could be transitory and copper prices for projects should be based on a long period not in a short period, combined other variables as the proven reserves or the copper grade in the deposit. The process of copper production, including all existing technologies, is described later, from the principles of the matte production to the different qualities of copper that are obtained at the end of the process. The manuscript concludes with a case study about the utilization of concentrated solar energy to treat copper slags in attempts to recover copper and iron from these slags. This document should be seen as an overview of the copper production process.

### **Author details**

Daniel Fernández-González<sup>1</sup> \* and Luis Felipe Verdeja González<sup>2</sup>

1 Center for Research in Nanomaterials and Nanotechnology-Spanish National Research Council (CINN-CSIC), El Entrego, Asturias, Spain

2 University of Oviedo, Oviedo-Uviéu, Asturias, Spain

\*Address all correspondence to: d.fernandez@cinn.es

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Copper Overview: From the Ore to the Applications – A Case Study of the Application… DOI: http://dx.doi.org/10.5772/intechopen.113741*

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[50] Mochón J, Ruiz-Bustinza Í, Vázquez A, Fernández D, Ayala JM, Barbés MF, et al. Transformations in the iron-manganese-oxygen-carbon system resulted from treatment of solar energy with high concentration. Steel Research International. 2014;**85**:1469-1476. DOI: 10.1002/srin.201300377

[51] Fernández-González D, Prazuch J, Ruiz-Bustinza I, González-Gasca C, Piñuela-Noval J, Verdeja LF. Iron metallurgy via concentrated solar energy. Metals-Basel. 2018;**8**:873. DOI: 10.3390/met8110873

[52] Fernández-González D, Prazuch J, Ruiz-Bustinza I, González-Gasca C, Piñuela-Noval J, Verdeja LF. The treatment of basic oxygen furnace (BOF) slag with concentrated solar energy. Solar Energy. 2019;**180**:372-382. DOI: 10.1016/j.solener.2019.01.055

[53] Fernández-González D, Prazuch J, Ruiz-Bustinza I, González-Gasca C, Piñuela-Noval J, Verdeja LF. Transformations in the Mn-O-Si system using concentrated solar energy. Solar Energy. 2019;**184**:148-152. DOI: 10.1016/ j.solener.2019.04.004

[54] Fernández-González D, Prazuch J, Ruiz-Bustinza I, González-Gasca C, Piñuela-Noval J, Verdeja LF. Transformations in the Si-O-Ca system: Silicon-calcium via solar energy. Solar Energy. 2019;**181**:414-423. DOI: 10.1016/ j.solener.2019.02.026

[55] Winkel HE. Thermal decomposition of copper sulfides under concentrated irradiation [PhD thesis] Swiss Federal Institute of Technology Zurich, Zurich, Switzerland. 2006

### **Chapter 2**

## Electroosmotic Drainage Applied to Mining Waste

*Leonardo Romero, Manuel Cánovas and Juan Sanchez-Perez*

### **Abstract**

One factor affecting the stability of mining stockpiles is the moisture defined mainly by copper solution trapped in the porous by capillary. This moisture is not easy to remove if conventional methods are applied which use pressure or gravity as driving force. In the case of saturated or partially saturated soils with water, containing a large fraction of fine material, electroosmosis not only allows to reduce the humidity but also changes the structure, giving a higher strength and stability to the soils. Since the movement of the water, due to the electric gradient, is from the anode toward the cathode, the soil water content will decrease at the anode and will increase at the cathode. Water accumulated at the cathode then can be discharged by providing a drainage system at the cathode. This chapter presents theoretical and experimental aspects on electroosmotic drainage technique, based in works realized by the authors of this chapter. To explain the water flow through a mining residue containing a certain fraction of fine material and that in addition presents a high humidity, a model for the fluid flow in porous media is described here, taking into consideration two driving forces, defined by hydraulic and electric potentials.

**Keywords:** electroosmosis, electroosmotic, drainage, electroosmotic flux, driving force

### **1. Introduction**

Mine waste represents one of the critical aspects of mining activity due to the environmental and social impacts that could generated not only in the period of extraction and processing of mineral but also in the post-closure period of the mining activity. Whether extraction and processing are stages that generate large quantities of waste that are stored above ground where they may constitute a potential risk of groundwater contamination or they may present structural stabilization problems by its humidity.

In waste from copper leaching, the remaining humidity is due to the solution trapped in the capillary interstices of the solid matrix. To avoid structural stabilization problems, it is necessary to reduce the moisture of the waste. One possibility is to let the humidity reduce naturally, by letting the water drain gravitationally. The action of this technique is limited, since gravity has no action on capillary trapped water. Thus, to reduce the remaining moisture content of the solid material and accelerate the

drainage process, electroosmotic drainage technique is proposed. Electroosmotic drainage consists of applying a low electric potential to dewater a porous medium, in this case the solid mining waste. This technique was employed in the 50 years to consolidated clay soils as a simple and efficient way to accelerate the dewatering process in soils with low hydraulic conductivity [1, 2]. Since then, electroosmotic drainage has been successfully applied mainly to the drying process of sediments, and remediation of contaminated soils with heavy metals [3–10]. Applications of this technique in mining activities are still under development. In a previous work, through the realization of mining waste drainage experiments, at laboratory and bench scale, the conceptual validation of the technique was demonstrated [7, 10, 11]. Electroosmotic drainage is more efficient than conventional drainage techniques such as vacuum filtering, belt filter pressing and centrifuging in terms of collected solution, time of drained solution, and energy consumption [12]. Water in a porous material can be divided into four types: free water, interstitial or capillary water, surface or vicinal water and intracellular water [13]. While conventional drainage techniques, which are based on mechanical pressure, are effective at removing free water, electroosmotic drainage can be applied to remove free, interstitial, and vicinal water [14].

The establishment of an electric field, in a porous medium with high humidity, in addition to the removing of the capillary trapped water, causes the ionic species present in solution to migrate toward the oppositely charged electrode (anode or cathode), and this ion migration is called electromigration, while the mechanism that govern the movement of the water toward the positively charged electrode (cathode) is called electroosmosis. In this chapter, the theoretical basis, complemented with experimental data at laboratory and bench scale, is established, describing conceptual and mathematically; in addition to the gravitational drainage, the electroosmotic flow as a transport mechanism allows an additional drainage of solution in a process of heap pile copper leaching. The importance of the application of this mechanism is that it allows a larger volume of solution to be drained than that could be drained naturally, in which the gravity is the only driving force acting on the medium. Keeping in mind that with the application of an electric field to the medium, the electroosmotic mechanism acts mainly on that fraction of solution trapped capillary, and this occurs in the fine solid fraction.

### **2. Flow of fluid in porous media**

Flow of water in porous media is a relevant subject in applications such as hydrogeology and in multiple branches of engineering. At large physical scales, Darcy's law is used, which provides a macroscopic description of flow in porous media. At smaller physical scales, flow and transport are simulated using more detailed descriptions such as Hagen-Poiseuille or Navier-Stokes flow. In the past decades, the topic of multiphase flow in porous media has received widespread attention. There are numerous pore-scale simulation and experimental studies on single-phase and multiphase flow and transport in porous media. However, very few studies of flow and transport in charged porous media have been reported [15–17]. When the porous medium and the fluids present in the pore space are exposed to an electric field, a number of electrokinetic and electro-hydrodynamic effects or mechanisms can take place, such as electromigration, electrophoresis, and electroosmosis. These phenomena have been used in applications, such as electrophoretic migration of contaminants in soils [4], microfluidics [18], or enhanced oil recovery [19].

### **2.1 Conceptualization of the electroosmotic waterflow**

Electroosmosis is the flow of water induced by the application of an electric field [20, 21]. This waterflow, named electroosmotic flow, is generated by the electrical interaction between the surface of the solid particles and the fluid, which leads to charge separation at a "double layer" interface. The volumetric flow of water is dependent of the double-layer properties, the chemical composition of the porous material, the type of fluid in the pores, the geometry and size of the pores, the saturated condition of the medium, and the intensity of the applied electric potential [22]. Fluid flow usually occurs in the same direction as the applied electric potential, from anode to cathode [23, 24].

One of the earliest and most widely used theoretical models of the electroosmosis process is based on a model introduced by Helmholtz in 1879 and refined by Smoluchowski in 1914 [25]. Thus, to estimate the electroosmotic flow of water per unit of area (qeo) in a saturated porous media, the Helmholtz-Smoluchowski model (H-S model) is used [22]. This flux of water (qeo), expressed in units of water volume per unit of area and unit of time is formulated as:

$$q\_{ev} = -\frac{\varepsilon\_p \varepsilon\_w \tilde{\zeta}}{\eta} \frac{\Delta \mathcal{Q}}{\Delta L} \tag{1}$$

where ε<sup>p</sup> is the soil porosity, ε<sup>w</sup> is the electrical permittivity of the soil, ζ is the zetapotential, η is the dynamic viscosity of the fluid, Δϕ is the applied electric voltage difference between electrodes, and ΔL is the separation distances between electrodes.

The direction of the electroosmotic flow, relative to the electric potential, is solely determined by whether the zeta-potential is positive or negative. Most soils and porous ceramics exhibit a negative zeta-potential causing the direction of the electroosmotic flux to be from the anode toward the cathode. As the zeta-potential (ζ) is a parameter dependent of the pH value, the movement of the water may be in one direction, toward the cathode, or toward the anode, [23–25]. The electroosmotic flow can be expressed in terms of the electric gradient and the electroosmotic permeability of the porous media (keo), which is a measure of the fluid flux per unit area of the porous media. The value of keo is assumed to be a function of the zeta-potential of the soil-pore fluid interface, the viscosity of the pore fluid, the porosity, and electrical permittivity of the soil:

$$k\_{eo} = \frac{\varepsilon\_p \varepsilon\_w \zeta}{\eta} \tag{2}$$

The electroosmotic permeability is pH-dependent as the z-potential (ζ) do it. Taken as reference the Kaolinite, an increase of the pH from 0 to 14 makes the electroosmotic permeability increases in the rage of (3 to 8) � <sup>10</sup>�<sup>9</sup> (m<sup>2</sup> /V/s) [26].

### **2.2 Flux of water for the case of saturated medium**

The fluid flux is the consequence of three gradients: hydraulic gradient ∇(�h) (Darcy's law), electrical gradient ∇(�ϕ), and a chemical gradient. The latter, chemical gradient, is significant only in the presence of large molecular chains and in very active clay deposits. Assuming that the chemical gradient is not significant [27, 28], the porous fluid mass flux (Jw), expressed in mass flow of water per unit of area, is thus estimated by two contributions:

$$J\_W = J\_h + J\_{e\bullet} \tag{3}$$

where Jh, and Jeo (kg/m<sup>2</sup> /s) are the hydraulic and electroosmotic mass flux of water, respectively. Both fluxes, Jh y Jeo, are defined by a driven force times the conductivity coefficient (K) that describes the ease with which a fluid (water) can move through pore spaces. Thus, rewriting the mass flux in terms of the volumetric flux (q) gives:

$$J\_W = f\_h + f\_{eo} = \rho\_w (q\_h + q\_{eo}) = \rho\_w [K\_h \nabla(-H) + K\_{oo} \nabla(-\mathcal{Q})] \tag{4}$$

where ρ<sup>w</sup> (kg/m<sup>3</sup> ) is water density, qh and qeo (m3 /m<sup>2</sup> /s) are hydraulic and electroosmotic flow velocity, respectively, H is hydraulic head (m), and ϕ is the applied electric potential (V). The Kh (m/s) and Keo (m<sup>2</sup> /V/s) are the hydraulic and electroosmotic conductivity, respectively. The negative sign indicates that flow of water occurs from large to small hydraulic head, for the hydraulic flow, and from anode to cathode, opposite to the electric gradient, for the electroosmotic flow. The hydraulic head, H, in length units, at any point in the soil is defined as the summa of the elevation head, z, and the pressure head ð Þ Ψ :

$$H = \frac{p\_c}{\rho\_w \mathbf{g}} + \mathbf{z} = \Psi + \mathbf{z} \tag{5}$$

where pc is the pore water pressure, ρ<sup>w</sup> is the density of the fluid (solution), and g is the gravitational acceleration. Then, the equation for the mass flux, Eq. (4), may be rewritten as:

$$J\_W = f\_h + f\_{co} = \rho\_w (q\_h + q\_{co}) = -\rho\_w [\mathbf{K}\_h \nabla(\Psi + \mathbf{z}) + \mathbf{K}\_{co} \nabla(\mathcal{Q})] \tag{6}$$

The relative importance of the hydraulic and electroosmotic contributions, to the flow of water, is determined by the ratio of the electroosmotic to the hydraulic conductivity, expressed as Keo/Kh. This ratio is affected by the soil type, microstructure, and pore fluid conditions. In coarse-grained soil, the ratio is very low, due to the almost nonexistent electroosmotic flow and relatively high hydraulic conductivity (>10�<sup>3</sup> cm/s) of such soils. In soft, fine-grained soils, the ratio is significant as Keo is usually on the order of 10�<sup>5</sup> cm<sup>2</sup> V�<sup>1</sup> s �1 , while Kh varies between 10�<sup>5</sup> cm/s for fine sand and 10�<sup>9</sup> cm/s for bentonite [27–29]. Therefore, for moving liquid through finegrained soils, the electrical gradient is more effective than the hydraulic gradient.

The hydraulic conductivity value (Kh) is always positive, and therefore, the hydraulic gradient always determines the direction of the hydraulic flow. In contrast, the Keo can be either positive or negative resulting in flow with or against the electric potential. On the other hand, the magnitude of the Kh is dependent of the pore size distribution. However, Keo is independent of pore size (**Figure 1**). In low-permeability zones such as clay, particle size smaller than 0.002 mm in diameter, the electroosmotic flow is easier to achieve than hydraulic flow (pressure-driven) (see **Figure 1**).

When water is trapped between fine solid particles, the electroosmotic technique is more efficient than the technique driven by pressure [29], because electroosmotic flow is based on the surface and colloidal characteristics of particles in suspension and is independent of pore size, unlike conventional hydraulic flow, which falls off significantly with pore size [30]. For copper mining waste, as a reference, tailing material from mineral processing, finely ground waste with particle size range 0.06–0.002 mm (similar to fine

*Electroosmotic Drainage Applied to Mining Waste DOI: http://dx.doi.org/10.5772/intechopen.106363*

**Figure 1.**

*a) Electro osmotic (Keo) and hydraulic (Kh) conductivity for selected sediments; b) Comparison of hydraulic (qh) and electro osmotic (qeo) flow rates [24].*

sand/coarse silt), the hydraulic conductivity is 1.65 <sup>10</sup><sup>7</sup> m/s [31]. Since pressure dewatering is a popular technique to reduce the water content of solid waste, some works have combined electroosmotic drainage and pressure dewatering [32, 33].

### **3. Humidity and fraction of fine material on the drained solution**

The total fluid flowing in a porous material under the effects of an electrical potential and the gravitational force is mainly caused by two gradients: the hydraulic gradient (Darcy's law) and the electrical gradient (electroosmosis). The contributions of each of the gradients are affected by soil type, soil microstructure, and pore fluid conditions [28]. For example, in coarse-grained soils, the ratio of electroosmotic to hydraulic flow is very low, and it means that the electroosmotic flow is almost nonexistent, while in fine-grained soils the ratio is high [34]. Therefore, a large electrical gradient is more effective than a hydraulic gradient for moving liquid through fine-grained soils.

Experimental tests have been carried out, at laboratory scale, to evaluate the effect of the initial moisture degree and the fraction of fine material contained in the mining residues, over the volume of solution drained out from the electroosmotic cell containing the residues [35]. All the tests were done in 20-liter electroosmotic cells as shown in **Figure 2**, using a linear configuration of stainless steel electrodes, 24 V of constant applied voltage between electrodes, and an operating time of 48 hours. The tests followed a 3<sup>2</sup> factorial design experiment with and without replication,

**Figure 2.** *(a) electroosmotic drainage cell; and (b) gravitational drainage cell [35].*


### **Table 1.**

*Distribution of the particle size fraction of the solid matrix [35].*

considering two factors with three levels each. The factors were the fraction of fine material and the moisture of the sample, and the levels of them were 10, 15, and 20% for fine material and 10, 20, and 30% for the moisture. The volume of drained solution was defined as the response variable.

The solid matrix is made up of two materials: coarse material made up of solid particles of different granulometric sizes (gravel, coarse, and fine sand) and fine material made up of clay material (**Table 1**).

The highest percentage of fine material (FP) was that established by slope safety regulations, while the other two were chosen to study the influence of lower levels of fine material content. The initial moisture (IM) levels of 10, 20, and 30% were defined based on mining applications. The first value of 10% is typical in leaching residues, while 30% is the typical level in tailings.

Two series of experimental test were run, differencing them only in the applying of an electrical field. In both tests act the gravity as one of the forces responsible of the volume of solution drained. In the first one test (**Figure 2a**), a voltage of 24 [V] between stainless electrodes was applied, following a lineal configuration of electrodes with a separation distance of 20 cm. In the other one test (**Figure 2b**), no voltage was applied, acting only the gravity as the force responsible of the drained volume of solution.


### **Table 2.**

*Data series collected from carried out run with electroosmotic and gravitational drainage, following a 3<sup>2</sup> -factorial design [35].*


### **Table 3.**

*Data series collected from carried-out tests run with electroosmotic and gravitational drainage, following a 3<sup>2</sup> factorial design with replica [35].*


### **Table 4.**

*ANOVA, using the data series as shown in Table 2 and the software Statgraphics, for the experimental run applying electrical field [35].*

An operating time of 48 hours was determined for each of the tests carried out, whose results are summarized in **Tables 2** and **3**.

For the data series in **Table 2**, an ANOVA was applied based on the proposed 32 factorial design test to identify the influence of the relevant factors and their interaction (**Table 4**). Subsequently, a nonlinear regression was applied to obtain a mathematical model.

The analysis of variance for the quadratic model, with a confidence interval of 95%, showed that four p-values are less than 0.05 (see **Table 4**), which means that the null hypothesis (zero contribution to the final moisture) is rejected by the four effects (A, B, AB, and BB), while the effect AA on the final moisture is not significant. The resulting statistic model is formulated by Eq. (7) and is graphically shown in **Figure 3**:

$$\text{FinalMoisture} \left( \text{\(\%\)} = -6.093 + 0.177(A) + 1.942(B) - 0.017(A\*B) - 0.034(B)^2 \right) \tag{7}$$

If the contribution of electroosmotic drainage on the final moisture level is analyzed, the analysis of variance for the quadratic model, with a confidence of 95%, showed that the three p-values are less than 0.05, which means that three null hypothesis is rejected for the effects A, B, and AB. The effects AA and BB did not significantly affect the final moisture level. The model describing the contribution of electroosmotic drainage, Ceod, to the final moisture is:

**Figure 3.** *Final moisture affected by the % of fine material and the % of initial moisture when an electric potential is applied [35].*

**Figure 4.** *Contribution of the electroosmotic drainage technique on final moisture [35].*

$$\mathbf{C}\_{end} = \mathbf{9.55} - \mathbf{0.47}(\mathbf{A}) - \mathbf{1.56}(\mathbf{B}) + \mathbf{0.12}(\mathbf{A} \times \mathbf{B}) \tag{8}$$

**Figure 4** represents the contribution of electroosmotic drainage on the final moisture level of the sample. The results show that the higher the initial moisture, the greater the reduction of moisture when an electric field is induced. As can be seen, the tests with natural drainage were less efficient. This electroosmotic contribution is greater as the % fine particles of the solid matrix increases.

### **3.1 Model describing the volume of drained solution from the solid matrix**

A 3<sup>2</sup> factorial design test with replication was used to determine the effect of the factors (fraction of fine particles (FP) = B and initial moisture (IM) = A, notation in **Table 2**), and their interaction against the drained volume as response variable. **Table 3** summarizes data series collected from the carried-out tests.

According to the realized ANOVA, four p-values were less than 0.05, which means that the null hypothesis (zero contribution to the final moisture) is rejected for the effects A, B, AB, and BB on the drained volume, while the effect AA results to be not Significative (see **Table 4**). The equation representing the electroosmotic model is:

### **Figure 5.**

*Representation of the model for the volume of drained solution from the sample by applying the electroosmotic technique [35].*

$$W\_{drained} = 2.876 - 0.567(A) - 0.921(B) + 0.063(AB) + 0.054(B)^2 \tag{9}$$

where Vdrained is the drained volume of the solution in cubic centimeter. **Figure 5** graphically represents the electroosmotic drainage model.

### **3.2 Comparison in the drained solution by the two techniques**

The dewatering experimental tests realized to compare the electroosmotic technique with the conventional technique (gravitational dewatering) were done in the 20-liter electroosmotic cells at laboratory scale as those shown in **Figure 2**. The results plotted in **Figure 6** shows that the volume of collected solution using the electroosmotic technique may reach three times more than the collected by the gravitational technique (0.32 over

### **Figure 6.**

*Solution collected by electroosmotic and gravitational drainage technique in cells containing 7 kg of dried material with an induced humidity of 15% [35].*

0.1 L, respectively). This difference of 0.22 L may be explained for the high fraction of fine particles contained in the sample material. The capacity of drained solution, defined as the volume of collected solution per mass of sample material, is estimated in 0.046 L/ kg, value that varies depending of the fine solid fraction which is directly related to the high volume of water trapped by capillary. Thus, the larger the fraction of fine material in the mining waste, the larger the volume of drained solution by electroosmotic flow.

### **4. Flux of water for the case of unsaturated medium**

For the case of a saturated medium, the conductivity (K), associated to the fluid properties, density and viscosity, and of the soil, intrinsic permeability (k), is constant. But when the medium is partially saturated it is not, because the permeability (k) varies with the saturation degree (Se). In the case of an unsaturated medium, as the pore space is occupied by two fluids (in this study water and air), the conductivity coefficient (K) is redefined by an effective permeability coefficient (Ke) related to one fluid. The subscript "e" to the coefficient K indicates that the conductivity is not necessarily that of a medium occupied by only one fluid. Usually, the effective conductivity (Ke) will be smaller than the conductivity (K) when only one fluid occupies the totality of the porous medium cavities, at saturated conditions. Then, the ratio Ke/Ksat is defined as the relative permeability (kr) which reaches its maximum value of 1 at saturation (the cavities or the porous of the soil are fully with water). Then, rewriting the mass flux Eq. (6) for the effective conductivity (Ke) in terms of the relative permeability (krel) and the conductivity at saturated conditions (Ksat) gives

$$J\_w = \rho\_w \left( q\_w^h + q\_w^{co} \right) = -\rho\_w \left[ K\_{\rm sat}^h k\_{rel}^h \nabla(\Psi + \mathbf{z}) + K\_{\rm sat}^{co} k\_{rel}^{co} \nabla(\mathcal{Q}) \right] \tag{10}$$

where *K<sup>h</sup> sat and k<sup>h</sup> rel* are the saturated conductivity and the relative hydraulic permeability of the soil, respectively, and *Keo sat an keo rel* are the electroosmotic saturated conductivity and the relative electroosmotic permeability of the soil, respectively. Then, both hydraulic and electroosmotic conductivities are defined as products of a permeability, depending on the microstructural properties of the porous medium, and a nondimensional relative permeability coefficient, which accounts for the effects of partial saturation on soil.

Relative permeabilities are functions of the saturation degree (Se), and the estimates of them are especially difficult to obtain, partly and mainly because of its extensive variability in the field. Models have been used for calculating the unsaturated conductivity from the more easily measured soil-water retention curve, and analytical expressions have also been developed [36, 37]. To simplify the analysis of the present work, the model formulated by Eqs. (11) and (12), defined by the power law of the effective saturation, is adopted for the relative hydraulic and electroosmotic permeabilities, respectively [38]:

$$k\_{\rm rel}^h = \mathfrak{a}\_h \left( \mathbb{S}\_\varepsilon \right)^{b\_h} \tag{11}$$

$$k\_{rel}^{eo} = \mathfrak{a}\_{eo} (\mathbb{S}\_{\epsilon})^{b\_{o}} \tag{12}$$

where ah, aeo, bh and beo are numerical curve fitting parameters. For a wide variety of soils, proposed values of bh, for hydraulic flow, vary between 3 and 3.5 [34, 38–40]. For the case of compacted clay material, a value of bh = 5 was suggested [41].

*Electroosmotic Drainage Applied to Mining Waste DOI: http://dx.doi.org/10.5772/intechopen.106363*

**Figure 7.**

*Relative electro-osmotic permeability vs. saturation. The data adjusts well to the model expressed by eq. (12), with a value of 1 for aeo, and a value of 3.2 for beo [38, 42, 43].*

For the case of electroosmotic flow, the dependence of the saturation degree on the electroosmotic permeability was experimentally investigated in electrokinetic filtration tests [43]. The experimental results compare well with the results reported in **Figure 7** [43].

Rewriting Eq. (10) for the total mass flux, by inserting Eqs. (11) and (12) gives

$$J\_w = -\rho\_w \left[ K\_{\rm sat}^h (\mathbb{S}\_\epsilon)^{b\_h} \nabla (\Psi + \mathbf{z}) + K\_{\rm sat}^{eo} (\mathbb{S}\_\epsilon)^{b\_w} \nabla (\mathcal{Q}) \right] \tag{13}$$

### **4.1 Governing equations of electroosmotic flow in a porous media partially saturated**

Unsaturated flow conditions in porous media correspond to a particular case of two-phase flow. Generally, the "non-wetting" phase, which in this case corresponds to the gas phase, is such that its pressure is constant, thus, this phase is considered as a stagnant or inactive phase.

### *4.1.1 Balance of the drained water mass flux*

For the case of a porous media under the application of an electrical potential, the balance of the mass of water per unit volume in a porous medium is given by the expression:

$$\frac{\partial m\_w}{\partial t} = \nabla f\_w \tag{14}$$

where Jw is the total mass flux of water (kg m�<sup>2</sup> s �1 ), defined by two contributions, hydraulic and electroosmotic flow. The mass of water, mw, per unit of total volume (kg m�<sup>3</sup> ) is defined as:

$$m\_w = \varepsilon\_p \mathbb{S}\_\ell \rho\_w \tag{15}$$

where ε<sup>p</sup> is the porosity of the soil, ρ<sup>w</sup> is the water density, and Se is the effective saturation. Se is defined as the fraction of the total pore space occupied by the wetting phase, fraction dependent of the pressure head, and that can vary from point to point within the medium. The Se is defined as:

$$\mathcal{S}\_{\varepsilon} = \frac{(\theta - \theta\_r)}{(\theta\_{\varepsilon} - \theta\_r)} \tag{16}$$

with θ as the volumetric water content, defined as the volume of water per unit volume of soil (m<sup>3</sup> /m<sup>3</sup> ), θ<sup>s</sup> as the water content at saturation, and θ<sup>r</sup> as the residual water content. By inserting Eq. (13), for the total mass flux, and Eq. (15), for the mass of water in the porous, into Eq. (14), the following equation is obtained:

$$\frac{\partial \left( \varepsilon\_p \mathbb{S}\_\epsilon \right)}{\partial t} + \nabla \left[ K\_{\text{sat}}^h (\mathbb{S}\_\epsilon)^{b\_h} \nabla (\Psi + \mathbf{z}) + K\_{\text{sat}}^{\text{co}} (\mathbb{S}\_\epsilon)^{b\_{\text{co}}} \nabla (\mathcal{Q}) \right] = \mathbf{0} \tag{17}$$

The conductivity coefficient, Ksat, is constant and determined at saturation conditions. The saturation degree, Se, is dependent of the pressure head, ψ, and to solve this equation it is necessary also to solve the continuity equation for the current density (Je) that is obtained by doing a charge electric balance.

### *4.1.2 Balance of electric charge*

In the presence of an external electric field, the balance of electric charge equation is expressed as:

$$\nabla \cdot J\_{\epsilon} + \frac{\partial Q\_{\epsilon}}{\partial t} = \mathbf{0} \tag{18}$$

where Je is the electric current density and Qe is the charge density per unit volume. Neglecting the soil electric capacitance, the source term in Eq. (18) vanishes and the equation reduces to:

$$\nabla \cdot f\_{\varepsilon} = \mathbf{0} \tag{19}$$

Neglecting the contribution of streaming currents produced by liquid flow, the equation for the electric current density, Je, is provided by the Ohm's law for the porous medium:

$$J\_{\mathfrak{e}} = -k\_{\mathfrak{e}} \nabla \mathfrak{Q} \tag{20}$$

where ke is the effective electric conductivity of the unsaturated porous medium that can be expressed as the sum of two terms [44]:

$$k\_{\varepsilon} = k\_{es} + k\_{esat}k\_{erl} \tag{21}$$

where kes is the apparent electric conductivity of the solid and generally assumed negligible, kesat is the apparent electric conductivity of bulk pore water under saturated conditions, and kerel is the relative electrical conductivity, accounting for the effects of partial saturation. The following power law has been assumed in this work [44, 45]:

$$\mathcal{A}\_{\text{erel}} = \mathcal{a}\_{\text{e}} (\mathbb{S}\_{\text{e}})^{b\_{\text{e}}} \tag{22}$$

where ae and be are fitting parameters, with ae = 1 and be = 2, as suggested by literature experimental data [45, 46]. Then, by inserting Eqs. (20)–(22) into Eq. (19), the following equation is obtained:

*Electroosmotic Drainage Applied to Mining Waste DOI: http://dx.doi.org/10.5772/intechopen.106363*

$$\nabla \cdot k\_{\text{ext}} \left( \mathbf{S}\_{\epsilon} \right)^{b\_{\epsilon}} \nabla \mathcal{Q} = \mathbf{0} \tag{23}$$

### *4.1.3 Approach of the effective Saturation*

Then, to solve the system of Eqs. (17) and (23), it is necessary to find some mathematical model that correlates the dependence of Se with the pressure head. In scientific literature, numerous models of soil-water retention curve and permeability have been reported, showing that dependence [36, 46]. Then the effective saturation, Se, could be estimated using van Genuchten's retention curve model formulated as:

$$\mathcal{S}\_{\varepsilon} = \left[\frac{1}{1 + (\boldsymbol{\alpha} \cdot \boldsymbol{\Psi})^{\boldsymbol{\eta}}}\right]^{m} \tag{24}$$

where "α", "n", and "m" are fitting parameters, and "ψ" is the matric suction defined by the pressure difference at the interface between the gas (air) and liquid (water) and named as pressure head. Combining Eqs. (16) and (24), the following equation is obtained:

$$\theta = \theta\_r + \frac{(\theta\_s - \theta\_r)}{[1 + (a \,\Psi)^n]^m} \tag{25}$$

where, the pressure head, ψ, is positive, and the parameters "m" and "n" are correlated by Mualem's model [45] as:

$$m = 1 - \frac{1}{n} \tag{26}$$

Eq. (25) contains four independent parameters (θr, θs, α, and n), which must be estimated from observed soil-water retention data. A graphical methodology may be found in a paper written by Van Genuchten (1980) [45].

The functional relationship of Se, Eq. (24), used to estimate the relative permeability of the unsaturated porous media, has not a unique value because it is affected by hysteresis. The value of krel is different if Se is obtained by starting with a dry medium and increasing the liquid saturation than if Se is obtained by removing liquid from an initially vacuum-saturated medium. Hereby, as this paper is concerned with the drainage of liquid, by the moment, the hysteresis problem will be not considered, only as a way of simplifying the estimate of krel.

### **5. Application of the electroosmotic flow model**

Once the copper is extracted from the ore through a heap leaching process, an acidwetted solid waste is left with a 15–18% moisture. At the beginning of the leaching cycle, the agglomerated mineral has a good permeability, approximately 10�<sup>4</sup> cm/s, but at the end, because of the drag of fine material (mainly clay or some precipitate generated during the leaching cycle) by the leaching solution, the permeability at the bottom of the heap become lower, making not easy the drainage of solution by gravity. The application of the electroosmotic model will be done to a copper leaching heap in its last stage of the leaching process, in the drainage step before to dispose the waste material left after the copper extraction.

The drainage electroosmotic model formulated by Eqs. (14)–(26) describes the partial saturated heap with a volumetric water content, θ, varying with height of the heap, showing larger water content at the bottom than at the top of the heap, *at t* ¼ 0, *H* ¼ �ð Þ *y* þ 2 , where (H) is the hydraulic head and (y) is the independent variable of position related to the y-axis. The hydraulic head H is related to the water volumetric content θ by developing Eqs. (5) and (25). The initial electric field is assumed to be zero everywhere: *at t* ¼ 0, *V* ¼ 0. The boundary conditions (BCs) are no flow across the boundary top and through the right vertical side of the heap pile. At the left wall, a symmetry boundary is assumed (**Figure 8** shows the sketch of the 2D pile). At the bottom, the boundary condition is open and free draining. For the electric BC, the voltages are maintained at the top and bottom, whereas all other boundaries are assumed to be isolated to the electric current. The parameters required by the model are listed in **Table 5**.

The results of the simulation, including hydraulic and electroosmotic flow, are represented in **Figure 8** for the volumetric water content θ at initial time and after 480 minutes. These results are only demonstrative, because the data used in the simulation are only slightly approximated to the studied case. In addition to the volumetric water content, **Figure 8** shows the schematic view of the 2D pile to be simulated (8 meters wide and 2 meters high). The anode and cathode bars, represented by circles, locate at the top and bottom, respectively.

The simulation results represented in **Figure 8** show the dewatering evolution of the heap leaching in a situation where the mineral bed presents a very low hydraulic permeability and high electroosmotic conductivity (see **Table 5**). This means that the relevant driving force, responsible of the drainage process, is the electroosmotic force. This situation may be realistic only if during the leaching process, it exists a great drag of fine material toward the bottom of the pile that could difficult the drainage of solution from the pile. Due to the lack of field data, (permeability, porosity, volumetric water content, and soil-water characteristic curve (SWCC)) for the studied case, it is not possible to make a comparison with results obtained from an experimental pilot test of one cubic meter of acid mining waste, realized and documented previously [11].

### **Figure 8.**

*Volumetric water content, in cm<sup>3</sup> of water per cm<sup>3</sup> of soil, varying between 0 and 1, of the leaching pile in 2D, at (a) initial time; and (b) time of 480 minutes. (Software Comsol Multiphysics).*

*Electroosmotic Drainage Applied to Mining Waste DOI: http://dx.doi.org/10.5772/intechopen.106363*


**Table 5.**

*Parameters utilized in the simulations for the case of a heap leaching.*

### **6. Conclusion**

The two-phase fluid flow in porous media may be used to explain the drainage from a residue with high humidity, taking into consideration two driving forces, defined by the hydraulic and electric potentials. Electroosmotic flow is significative only when water is trapped capillary, as in those samples where the fraction of fine material is considerable. In an electroosmotic process, the movement of the water is from the anode toward the cathode; thus, the soil water content will decrease at the anode and will increase at the cathode. Thus, to discharge the water, a drainage system has to be provided at the cathode proximity.

To apply the electroosmotic model in the dewatering process of mining waste, it is necessary to know beforehand some hydraulic and electrical parameters such as permeability, porosity, volumetric water content, and the soil-water characteristic curve.

### **Acknowledgements**

The authors thank RMV Ltda. and the UCN (Universidad Católica del Norte) for supporting this work, funded by a CONICYT Fondecyt Initiation Grant No. 11180329—Phenomenological aspects of electroosmotic drainage technique: application to copper leaching.

## **Conflict of interest**

The authors declare no conflict of interest.

## **Author details**

Leonardo Romero<sup>1</sup> \*, Manuel Cánovas<sup>2</sup> and Juan Sanchez-Perez<sup>3</sup>

1 Department of Chemical Eng., Universidad Católica del Norte, Antofagasta, Chile

2 Department of Metallurgy and Mines, Universidad Católica del Norte, Antofagasta, Chile

3 Department of Applied Physics and Naval Technology, Universidad Politécnica de Cartagena, Spain

\*Address all correspondence to: leon@ucn.cl

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Electroosmotic Drainage Applied to Mining Waste DOI: http://dx.doi.org/10.5772/intechopen.106363*

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### **Chapter 3**
