Reducing CO2 emissions in the copper smelting process by using high-temperature solar heat: Tecno-economic assessment

Applied Thermal Engineering 226 (2023) 120270 Available online 24 February 2023 1359-4311/© 2023 Elsevier Ltd. All rights reserved. Research Paper Reducing CO 2 emissions in the copper smelting process by using high-temperature solar heat: Tecno-economic assessment Irving Cruz-Robles a , * , Jorge M. Islas-Samperio a , Elisa Alonso b , Alfonso J. V´ azquez-Vaamonde c , Carlos A. P´ erez-R´ abago a , Claudio A. Estrada a a Institute of Renewable Energy – National Autonomous University of Mexico (IER-UNAM), Priv. Xochicalco, Azteca, 62588 Temixco, Morelos, Mexico b Universidad Polit´ ecnica de Madrid, Madrid, Spain c National Center of Metallurgical Research, Madrid, Spain ARTICLE INFO Keywords: Solar mining Copper smelting process Industrial heat process CSP th Central Tower technology ABSTRACT The work explores the idea of using high-temperature solar heat in the copper smelting process; a Hybrid Central Tower system is analyzed to supply the high-temperature air for this process. The methodology was built based on the equilibrium of the smelting reactions; therefore, this analysis only account for the reactions’ energy demand. Two process schemes (process with/without using high-temperature air) and five off-gas scenarios were evaluated. Using Hybrid Central Tower systems with 13 h of Thermal Energy Storage leads to significant reductions in the annual equivalent energy consumption of the reactions (up to 22.61 %) and in the CO 2 emissions of the smelting process (up to 61.4 %). The scheme that doesn’t use high-temperature air is the lower-cost option; however, with a 15 % reduction in the capital expenditure and using a discount rate of 5 %, the scheme that uses Hybrid Central Tower systems with 13 h of Thermal Energy Storage shows the similar present value costs. If a carbon price of 25 USD/tCO 2 e is included, the latter scheme represents the lower-cost option and the most costeffective solution to avoid CO 2 emissions. 1. Introduction Copper is an important metal for the global development. Owing its chemical, thermal, electrical, and mechanical properties, copper is widely used for electrical and electronic equipment, construction, infrastructure, industrial processes, and transport [1]. To fulfill the worlds copper demand, copper production by mining has been growing from 15.9 million tons in 2010 to an estimated 20 million tons in 2020 [2]; this represents a growth rate of nearly 3 % per year. However, as much as copper is needed for a wide range of applications, copper has its downsides: producing copper leaves a significant footprint on the environment in the form of atmospheric emissions, and both solid and waterborne wastes [3,4]. Copper is produced by two main routes: the pyrometallurgical and the hydrometallurgical route [5]. The pyrometallurgical route accounts for about 80 % of the primary copper production [6]. Norgate et al. [7] calculated with a Life Cycle Assessment (cradle to gate) that every kilogram of refined copper (kg-Cu) requires around 33 MJ and generates about 3.3 kg-CO 2 if processed by the pyrometallurgical route. Using this data for a rough estimation, in 2020, the pyrometallurgical route was accountable for about 52.8 million tons of CO 2 emissions. However, CO 2 emissions are related to energy consumption [8] and the energy consumption is highly influenced by the ore grade [4], which is decreasing progressively. Lower ore grades demand more energy for the mining and beneficiation processes. For example: in Chile, the energy demand of the copper mining industry grew by 63 % from 2001 to 2012, whereas the copper production increased just 15 % [9]. In order to sustain the growth rate of copper production while part of the environmental damage is avoided, copper production requires a large-scale decarbonization. In this sense, some studies propose to use solar energy to address the energy requirements of this industry. One of the main and potential topics is the substitution of electricity from the grid (or changing the current generation mix) by using either Photovoltaic (PV) systems or Concentrating Solar Power (CSP) systems [10–12]. Another common topic is the use of low-temperature solar heat for processes such as leaching, froth flotation, electrowinning, and electrorefining [9,13–15]. In other level of development, the use of solar fuels has been mentioned for processes that require fuel consumption * Corresponding author. E-mail addresses: [email protected] (I. Cruz-Robles), [email protected] (C.A. Estrada). Contents lists available at ScienceDirect Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng https://doi.org/10.1016/j.applthermaleng.2023.120270 Received 16 October 2022; Received in revised form 17 January 2023; Accepted 17 February 2023 Applied Thermal Engineering 226 (2023) 120270 2 on-site [16]; also, at an innovative level, direct solar irradiation has been studied for new processes of copper production [17,18]. As it can be seen, there are already some feasible alternatives for the use of solar energy in this industry; however, there are other options that have not been studied, such as using high-temperature solar heat for the hightemperature processes. At the current commercial state, the CSP Central Tower technology produces high-temperature heat and can be scaled in the order of megawatts. Besides, this technology provides a high-reliable energy supply if combined with Fuel-Based systems: this combination is known as CSP Hybrid systems [19]. It should be noted that “CSP” refers to electric power generation; for this work, the term “CSP th ” was introduced to refer to Concentrating Solar Thermal Power. Nowadays, just few works evaluate the use of a CSP th Hybrid Central Tower system (CSP th Hybrid-CT system) for industrial process heat; for example, Schr¨ oders and Allelein [20] studied this technology for the ammonia production process. However, no work has analyzed the use of this technology for copper production. In this sense, this work explores the effects of using high-temperature solar heat in the copper smelting process. The work proposes to use a CSP th Hybrid-CT system to produce the high-temperature solar heat. The entire analysis is based on the equilibrium of the chemical transformations of the reactants. Several process scenarios were analyzed: for each scenario, a CSP th Hybrid-CT system was designed and evaluated. The CSP th Hybrid-CT systems were designed using two solar multiples, 1 and 2.5; for the solar multiple of 2.5, a Thermal Energy Storage system was integrated in the analysis. The paper also presents an estimation of the avoided CO 2 emissions and an economic analysis. Section 2 gives a short description of the copper smelting process, Section 3 describes the methodology, Section 4 presents results and discussions, and Section 5 summarize the main conclusions of this work. 2. The copper smelting processes Copper is mainly presented in the form of copper sulfide minerals, such as chalcopyrite (CuFeS 2 ), chalcocite (Cu 2 S) and bornite (Cu 5 FeS 4 ). In the book Extractive Metallurgy of Copper, Schlesinger et al. [5] describe the two routes for processing copper minerals; the best option to treat sulfide minerals is the pyrometallurgical route (Fig. 1). Because the ore grade in copper minerals goes from 0.5 % for open-pit mines to 2 % for underground mines, the ore passes through comminution and beneficiation processes to produce copper concentrates, which contain between 20 % and 30 % of copper. The concentrates are dried to eliminate humidity; in some cases, a roasting process is carried out to eliminate impurities. Copper concentrates are sent to the smelting process, which produces matte, slag, and off-gas. The converting process transforms the matte into copper blister, which then is converted into copper anodes in a thermal refining process. These anodes are electrorefined to produce high-purity copper cathodes (99.99 % Cu). The smelting, converting, and thermal refining processes operate at temperatures around 1,250 ◦C. Although smelting and converting involves exothermic reactions, a significant amount of fuel is combusted in these processes [22,23]. Fuel consumption depends on the furnace technology, which is diverse; Moskalyk and Alfantazi [24] provide a review of the smelting technologies. Particularly, the reverberatory and flash-smelting furnaces account for about 25 % and 50 % of the world’s copper smelting capacity, respectively [25]. The smelting process is a complex sequence of concatenated chemical reactions [26]. However, the process can be illustrated with a general simplification [27]; Fig. 2 shows the control volume and the mass flows involve in the flash-smelting process. The input flows are copper concentrates, fossil fuel, air, industrial oxygen, silica flux, and recovery dust. The chemical reactions produce matte, slag, and off-gas; matte and slag are separated in the settler shaft, while the off-gas is Fig. 1. Pyrometallurgical route for copper production. Information sources: [5,21]. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 3 extracted by the off-gas taker. The smelting process is exothermic because of the sulfur oxidation; this heat is used by the reactions. However, fossil fuel is combusted for four purposes: to complement the energy requirements, to raise the process temperature, to avoid cold spots, and for temperature control. Energy leaves the furnace through the products and part of the energy is lost through the furnace walls. One goal during the smelting process is to maintain the composition of the products; this goal might be affected by a variation in the feed material [28]. Usually, the control of the process involves models that combine input parameters and feedback data, such as the products’ quality. An important quality parameter is the copper grade in matte; this parameter is obtained after testing matte samples. Given the delay between the continuous process and the feedback data, variations in input parameters might complicate the furnace operation. In this sense, some authors have proposed alternatives to predict and control the smelting process [29–34]. However, a classical methodology to model the chemical reactions of the smelting process is the mass and energy balance. This methodology does not consider the reactions’ kinetics and fluid dynamics, but it is of high relevance because it provides the thermodynamic equilibrium of the smelting process. The mass and energy balance is a useful tool to simulate the smelting process [27]. The results can be used to compare with industrial data and to find improvement opportunities [35]. 3. Methodology One important input for the smelting process is air (Fig. 2). Air introduces oxygen that is used for the combustion of hydrocarbons and sulfur. The nitrogen in the air does not react; however, it consumes energy from the reaction to increase its temperature. Preheating the air avoids the cooling effect of nitrogen and provides energy for the chemical reactions; in consequence, the smelting process requires less industrial oxygen and less fossil fuel. In this sense, the paper proposes to use a CSP th Hybrid-CT system to supply high-temperature air to the smelting process. The methodology in this paper consists of three models: one for the smelting process, one for the CSP th Hybrid-CT system, and one for the economic evaluation. The input rate of preheated air and its temperature were obtained from the equilibrium of the chemical reactions; therefore, the smelting process was solved using a steady-state mass and energy balance. For the CSP th Hybrid-CT system, the CSP th Central Tower was designed and evaluated using SolarPILOT and an energy balance was performed to estimate the energy required from the backup system. Data and results were analyzed and processed using Wolfram Mathematica. The geographic site chosen for the analysis corresponds to the Region of Antofagasta, Chile; this site has a high solar resource (annual DNI 3,454 kWh/m 2 ) [36]; besides, Chile is the biggest producer of copper concentrates [37]. 3.1. Definition of the CSP th Hybrid-CT system The most practical way of preheating air with the CSP th Central Tower technology is to use air as a heat transfer fluid. If air acts as a heat transfer fluid, the CSP th Central Tower technology can preheat it at temperatures up to 800 ◦C [38–40]. However, this scheme presents one significant drawback for the purpose of this work: there isn’t a commercial Thermal Energy Storage (TES) system for air preheating. Nowadays, the commercial technology of CSP th Central Tower with TES system uses molten salt as a heat transfer fluid. A typical molten salt called “solar salt” is a blend composed of sodium nitrate (60 %) and potassium nitrate (40 %), this salt can operate at temperatures up to 574 ◦C [41]; however, a single nitrate component can operate at a temperature around 600 ◦C, whereas carbonate-based salts or chloride-based salts can operate at around 650 ◦C [42]. In this sense, this work proposes to use a heat exchanger to transfer heat from a hot molten salt to the air. Fig. 3 shows a general scheme for the CSP th Hybrid-CT system. The figure shows the plant configuration and the major components of the system. The heliostat field reflects the solar irradiation towards the receiver device. The receiver absorbs irradiation and transforms it into thermal energy. Then, molten salt removes heat from the receiver and goes to the TES system. High-temperature air is produced by using a heat exchanger between molten salt and air. A backup system (auxiliary boiler) operates if there isn’t enough energy from the solar source; as explained further in the text, the backup system could heat the cold molten salt and send it to the hot tank. Finally, the high-temperature air is sent to the flash smelting furnace. General assumptions for the CSP th Hybrid-CT system: •For this work, just the major components of the CSP th Hybrid system were considered. •The system’s performance was evaluated throughout the year, using time steps of 1 h. •The system was considered to operate in steady-state at each time step. •The solar energy production was weighted with an annual degradation factor of 0.2 % [43]. •Pressure drops were neglected. •The electrical parasitics of the CSP th Central Tower, which usually accounts for about 10 % of the electricity output in power generating systems [44], were not considered. •The backup system was considered to operate with natural gas. •The system’s lifespan was considered to be 30 years. Fig. 2. Flash smelting process. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 4 3.2. Smelting process model The smelting process was modeled using steady-state mass and energy balances. The mass balance equations were built based on every element entering and leaving the flash furnace, whereas the energy balance equation was built based on the first law of thermodynamics. This set of equations were solved using linear algebra. Finally, a parametric analysis was conducted for the solutions, and the amount of energy for air preheating was obtained. The molar weights and enthalpies used in this model were obtained from the FactSage-Education software. For this work, the copper concentrate was considered to be chalcopyrite (CuFeS 2 ) and pyrite (FeS 2 ). Two sources of oxygen were considered: industrial oxygen and air; air also introduces nitrogen to the process. Natural gas was selected as fossil fuel. The analysis also considered recovery dust. The off-gas carries dust in the form of Cu 2 O, Fe 3 O 4 , and SiO 2 ; this dust contains a significant amount of copper. After cooling the off-gas, the dust is recovered and sent to the furnace in the form of CuSO 4 , Fe 2 (SO 4 ) 3 , and SiO 2 . Using a method similar to that used by Davenport and Partelpoeg [27], the following unbalanced stoichiometric equation condenses the smelting process studied in this paper. CuFeS2+FeS2+O2+N2+SiO2+ [SiO2+CuSO4+Fe2(SO4)3]InputDust +CxHy→Cu2SMatte +FeSMatte +FeOSlag +SiO2Slag + [SiO2+Cu2O+Fe3O4]OutputDust +SO2Off−Gas +N2Off−Gas +CO2Off−Gas +H2OOff−Gas (1) Two kind of mass balance equations were used to define the smelting process: equations for single elements and complementary equations. Equation (2) describes the general form of the mass balance equations for single elements. MEi=∑ n j=1 βCj Ei*mCjReactants =∑ n j=1 βCj Ei*mCjProducts (2) M Ei : Mass of element “i” (elements: Cu, Fe, S, O, N, SiO 2 , C, H). C Ji : Compound “j” (Reactants: CuFeS 2 , FeS 2 , O 2 , N 2 , SiO 2 , Dust input , C x H y ; Products: Cu 2 S, FeS, FeO, SiO 2 , Dust output , SO 2 , N 2 , CO 2 , and H 2 O). B Ei Cj : Concentration of element “i” in compound “j”. m Cj : mass of compound “j”. SiO 2 is an inert chemical specie in the smelting reaction [35]; therefore, it was treated as it were a single element. Eight balance equations and sixteen variables were generated using equation (2). These mass balance equations were complemented with other seven equations. Equation (3) specifies the slag composition. Equation (4) specifies the matte grade, but it introduces a new variable which is defined with equation (5). Equations (6) and (7) specify the rate of input and output dust. Since the fossil fuel (natural gas) contains a significant amount of nitrogen, other two variables and two equations were included, equations (9) and (10). mSiO2Slag =mFeO*(mSiO2 mFeO )Slag (3) 0=βCu2S Cu *mCu2S+βMatte Cu *mMatte (4) mMatte =mCu2S+mFeS (5) mInputDust =d*(mSO2+mN2+mCO2+mH2O)(6) mOutputDust =0.5*mInputDust (7) mInput N2Fuel =βFuel N2*mFuel (8) mOutput N2Fuel =mInput N2Fuel (9) d: rate between the mass of input dust and the mass of off-gas. The energy that enters and leaves the flash furnace was calculated based on the compounds’ enthalpy, energy inputs, and energy losses. The chemical transformations that take place in the furnace’s reaction shaft are carried out at constant pressure with no other work than the work performed by the volume change against pressure. Under these conditions, the net heat exchange during the reactions is an exact differential, independent of the path or the transformation steps. This heat can be calculated using the compounds’ enthalpy (Hess’s Law). Because the enthalpy is a thermodynamic property, the net heat exchange depends only on the nature and condition of the initial reactants and final products. For the energy balance equation, the energy inputs must be equal to the energy outputs. A new variable was added to the energy inputs, the energy for air preheating “E AP ”; also, the variable energy losses “E L ” was added to the energy outputs. The energy losses correspond to the conductive, convective, and radiative thermal losses in the flash furnace. Fig. 3. Scheme of the CPS Hybrid-CT system adapted for the smelting process. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 5 ∑ n j=1(ΔHo f)Vj *mVjReactants +EAP =∑ n j=1(ΔHo f)Vj *mVjProducts +EL(10) ΔH f ◦ VJ : enthalpy of formation per unit of mass of variable j. m VJ : mass of variable j. The enthalpy of the fossil fuel (natural gas) was calculated from its composition and the enthalpies of its compounds. This set of mass and energy balance equations is a linear system of 16 equations with 21 variables. In order to solve the system, a numerical value has to be specified for the variables m CuFeS2 , m FeS2 , m Fuel , E AP , and E L . The system was solved for a fixed rate and composition of copper concentrates (m CuFeS2 , m FeS2 ) and for a fixed rate of energy losses (E L ); on the other hand, the system was evaluated for several increments of both fuel consumption (m Fuel ) and energy for air preheating (E AP ). For every solution, the mass of industrial oxygen “m IO ” was calculated. mIO =mO2−(0.23 0.77)Air mN2(11) Every solution provides information on the smelting process: industrial oxygen consumption, fuel consumption, energy for air preheating, mass of air, mass and composition of the off-gas. These parameters were plotted in 2-D space and were characterized using linear equations (see Appendix A). The general form of equation (12) defines all the parameters as function of two of them: the energy for air preheating and the industrial oxygen consumption. P(EAP,OI) = aP(EAP) + bPOI= (a1P+a2PEAP) + bPOI(12) P: Parameter: off-gas, total energy consumption, mass of air, sulfur dioxide, carbon dioxide, and steam. a P and b P : coefficients of the linear equations. O I : industrial oxygen consumption. For the copper smelting process, the off-gas production is a key parameter because of two reasons: 1) the off-gas handling systems impose a technical limit in the rate of smelting, and 2) the off-gas production establishes a correlation between industrial oxygen consumption, fuel consumption, and energy for air preheating. Considering these reasons, the off-gas parameter was used to establish five off-gas scenarios (see Appendix B) where theoretical baseline cases that doesnt use high-temperature air are compared to theoretical scenarios that use high-temperature air. Appendix B also shows the procedure to calculate the thermal power required for air preheating, which is further used to generate the layouts of the CSP th Hybrid Central Tower systems. In order to evaluate the benefits of replacing fuel or industrial oxygen by high-temperature air, the mass of these inputs was converted to equivalent energy. The general assumptions that were considered for the smelting process model are the following: •Copper concentrates composition: 80 % chalcopyrite (CuFeS 2 ) and 20 % pyrite (FeS 2 ). 1 •Input dust’s composition: 40 % CuSO 4 , 50 % Fe 2 (SO 4 ) 3 , and 10 % SiO 2 . 1 •Output dust’s composition: 40 % Cu 2 O, 40 % Fe 3 O 4 , and 20 % SiO 2 . 1 •Rate of smelting: 50 ton of copper concentrates per hour. 2 •Matte grade: 60 %. •Off-gas scenarios: 1328, 1528, 1728, 1928, and 2128 kg/ton of copper concentrates. 3 •Furnaces energy loss: 25,000 MJ/hour. •Energy equivalent of 1 kg of industrial oxygen: 4.38 MJ. 4 •Gross heat of combustion of natural gas: 51.04 MJ/kg. 5 1 Data from Davenport and Partelpoeg [27] was used for the input and output dust compositions. 2 This value corresponds to a large-size smelting installation that can process about 500,000 tons of copper concentrates per year. 3 Appendix B. 4 The thermal energy equivalent of 1 kg of industrial oxygen was calculated assuming an electric consumption of 0.574 kWh per normal m 3 of oxygen [45] and a thermal to electric efficiency of 0.33 [46]. 5 The gross heat of combustion of the natural gas was calculated for a gas composition (percentage by volume) of 85 % methane, 6 % Ethane, 4 % Propane, and 5 % Nitrogen. 3.3. Layout of the CSP th Central Tower and energy balance of the CSP th Hybrid-CT system The CSP th Central Tower was designed using SolarPILOT. This software provides layout, characterization, parametric simulation, and optimization capabilities [47]. Two layouts for each scenario were generated to evaluate the effect of the solar multiple. The solar multiple (S.M.) is the ratio between the energy delivered by the system when it operates at design conditions and the nominal energy demand. The CSP th Central Tower layouts were generated for the noon of the spring equinox (March 20) and a value of 950 W/m 2 was selected for the design DNI. The general procedure to generate every layout was as follow: 1. Selection of a design thermal power. 1 2. Generation of a coarse layout. 3. Optimization of the solar field based on the system’s performance. 1 For each off-gas scenario, the energy for air preheating “E x ” was weighted by the thermal losses of the CSP th Hybrid-CT system to calculate the design thermal power. The thermal losses are described forwards in this section. The energy balance of the Thermal Energy Storage system was calculated using equation (13). (dTES dt )i =(hin dmin dt )i −(hout dmout dt )i −(dQloss dt )i (13) Kolb [48] estimates a thermal energy loss of 1 MW th for a TES system of 5,000 MWh; this represents an hourly loss of 0.02 %. For this work, the hourly energy loss of the TES system was assumed to be the same, 0.02 % of the stored energy. (dQloss dt )i =0.0002 TESi−1(14) Equations (15) to (18) were used to calculate the charging and discharging process of the TES system. EGrossX= (EAPx/ η HE)(15) (hin dmin dt )i ={ESolari SU− (TESi−1−EGross) ;TESi−1+ESolari−EGrossX≤SU ;TESi−1+ESolari−EGrossX>SU (16) (hout dmout dt )i =⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ 0;TESi−1+(hin dmin dt )i ≤SL ETES Airi;TESi−1+(hin dmin dt )i >SL (17) ETES Airi=⎧ ⎪ ⎨ ⎪ ⎩ EGrossX TESi−1+(hin dmin dt )i −SL ;TESi−1+(hin dmin dt )i −EGrossX≥SL ;TESi−1+(hin dmin dt )i −EGrossX<SL (18) E APx : energy that the smelting process demand for air preheating. E GrossX : energy that the CSP Central Tower must supply. η HE : efficiency of the heat exchanger between molten salt and air. S U and S L : upper and lower charging limits of the TES system. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 6 There isnt a work that reports the study of a heat exchanger between molten salt and air. In the absence of data, the efficiency of such heat exchanger was assumed similar to the efficiency of a steam coil air heater, though they might show a different behavior. The energy efficiency of steam coil air heaters has been reported to be up to 98 % [49]; however, with a conservative approximation, the paper assumes a value of 90 % for the heat exchanger. The fuel consumption for the backup system was calculated using equations (19) and (20). FCi=⎧ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎩ Ex/ η B;(hout dmout dt )i =0 EF−Airi;(hout dmout dt )i >0 (19) EF−Airi=⎧ ⎪ ⎨ ⎪ ⎩ 0 (Ex− η HE(hout dmout dt )i)/ η B ;(hout dmout dt )i =EGrossX ;(hout dmout dt )i <EGrossX (20) η B : efficiency of the backup system. Commercial fuel-based boilers for heating molten salt have not been found. However, the project Solar Two [50] is a precedent that this can be possible; in that project, both molten salt and the hot tank of the TES system were heated using a propane-fired chest and flue gases. As an approximation, the paper assumes a similar system for the backup system, with an efficiency similar to a medium-level of efficiency boiler for steam production (71 %) [51]. 3.4. Economic evaluation Two alternatives were analyzed in this work: carrying out the reactions without using high-temperature air and carrying out the reactions using high-temperature air. For the second alternative, air is preheated using a CSP th Hybrid-CT system. The two alternatives aim to obtain the same products; however, the only measure of difference between the two alternatives is the equivalent energy consumption of the reactions, which can be expressed in terms of costs. For this reason, the economic evaluation can only indicate which is the most cost-effective solution. In this context, the Present Value is the most suitable measure to evaluate and compare the economic viability of these two alternatives. The Present Value indicates the equivalent value at time 0 of a set of cash flows. This measure is easy to use because of the sign convention for cash flows: positive cash flows represent revenues, while negative cash flows represent costs. The Present Value was calculated using equation (21). Since all cash flows are costs, the Present Value is negative; therefore, the most cost-effective solution is the one that shows the minor absolute value. PVcosts =CAPEX +∑ N n=1 Costsn (1+r)n(21) CAPEX: capital expenditure. Costs n : annual costs incurred at year “n”. r: discount rate. N: system’s lifespan. The capital expenditure for the CSP th Hybrid-CT systems was calculated considering direct and indirect costs (equation (22)). The direct costs include the costs of the main components of the CSP th Hybrid-CT system (equation (23)), while the indirect costs include the owner’s costs, planning and contracting costs, engineering and construction management, and contingency costs [52]. CAPEX =DC +IC (22) DC = (HFC+TC+RC+TESC+HEC+BC)(23) HF C : heliostats field cost. T C : tower cost. R c : receiver cost. TES c : thermal energy storage system cost. HE c : heat exchanger cost. B c : backup system cost. Table 1 shows the reference data that was used to calculate the CAPEX of the CSP th Hybrid-CT systems. The heliostat field cost was calculated by multiplying the heliostat field area by a solar field price; the most recent reference in Table 1 was used, 145 $USD/m 2 (2020). The TES system cost was calculated by multiplying the TES capacity by 24 $USD/kW th (2020). The tower cost was calculated with an exponential function, equation (24). There isnt prior data about the cost of a heat exchanger that works with molten salt and air; therefore, the cost of this equipment was assumed similar to a steam generation system (SGS). The same situation occurs with the backup system; the cost of this system was assumed similar to a fuel-based boiler. The receiver cost, the steam generation system cost, and the Fuel-Based boiler cost were calculated using a capacity function. Finally, the indirect costs were assumed to be 15 % of the direct costs. T cost =CRes*H(24) Cx=CR(I2019/IR)(Sx/SR)s(25) C x : estimated cost of the equipment of size “S x ”. C R : estimated cost of the equipment of size “S R ”. H: tower’s height. s: scaling exponent. The scaling exponents were 0.0113 for the tower, 0.7 for the receiver, and 0.8 for both the steam generation system and the FuelBased boiler [53]. The reference costs in Table 1 were actualized for equation (25). The actualizations were carried out using the Chemical Engineering Plant Cost Index 2019 (CEPCI 2019), equation (26). CR=C(I2019/IR)(26) C: reference cost at year of reference. I 2019 : Index CEPCI2019. I R : Index CEPCIyear of reference. Table 2 shows reference data for the calculation of the annual costs; they comprise three concepts: operation and maintenance expenses “O&M”, insurance, and annual expenses due to the equivalent energy Table 1 Reference data for the calculation of Capital Expenditure. Equipment Reference Cost (year) References Solar Field 130 – 217 $USD/m 2 [19,54–58,59–60] Tower 3,170,000 e 0.0113H (2010) [53] Receiver 97,020,000 USD; Size: 1,571 m 2 (2010) [53] Storage 14–33 $USD/kWh th [55–57,59–61] Heat exchanger molten saltair (steam generation system) 29,000,000 USD; Size: 260 MW th (2011) [56] Backup system (fuel-based boiler) 4,200,000 USD; Size: 26.6 MW th (2015) [63] Indirect Cost 15–17 ( % of D.C.) [55,59,61] Table 2 Reference data for the calculation of annual costs. Reference value References Values used in this work O&M ( % of CAPEX) 1–2.5 % [19,56,65–67,68–70] 2 % Insurance ( % of CAPEX) 0.5–1 % [19,55,56,62,63,65–68,70] 0.5 % I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 7 consumption “AE EEC ”. The value “AE EEC ” was calculated by multiplying a reference fuel price by the annual equivalent energy consumption “EEC” that does not come from the solar source. The value “EEC” was calculated with equation (27). EEC =OIEE +FFREE +FFPEE (27) OI EE : annual equivalent energy consumption due to industrial oxygen. FFR EE : annual equivalent energy consumption due to fossil fuel in reactions. FFP EE : annual equivalent energy consumption due to fossil fuel for air preheating. For the theoretical baseline cases (no air preheating), the annual costs consist just in the value of “AE EEC ”. For this work, the natural gas price was chosen as the reference fuel price. The natural gas price was assumed to be 7 USD/MMBTU, which was the price of U.S. LNG exports to Chile in 2021 [64]. The Present Value was calculated with the annual costs at constant value. Finally, a real rate of 8 % was used to discount the annual costs. 4. Results and discussions This section presents the results that were obtained using the methodology of Section 3. First, the section shows the results corresponding to one off-gas scenario to describe the implementation of the CSP th Hybrid-CT system. Then, the section presents the annual energy consumption for the five off-gas scenarios; the analysis includes the results for CSP th Hybrid systems designed with solar multiples of 1 and 2.5. Finally, the section shows the CO 2 emissions for all the cases and the results of the economic evaluation. Fig. 4 shows the equivalent energy consumption of the chemical reactions and the operation of the CSP th Hybrid-CT system; the results correspond to the off-gas scenario of 1,728 kg of off-gas per ton of copper concentrates, and the performance of the CSP th Hybrid-CT system corresponds to December 21. As mentioned before, the copper smelting rate was set in 50 tons of concentrates per hour; therefore, the energy values of Fig. 4 corresponds to this smelting rate. The equivalent energy consumption of the reactions without using high-temperature air is 89.2 GJ per hour (black line): 69.5 % of this energy corresponds to the fuel consumption in reactions and 30.5 % corresponds to the industrial oxygen consumption. For a process that uses high-temperature air, the equivalent energy that the reactions consume corresponds to a steady stream of industrial oxygen (8.1 GJ – blue line), a steady stream of fossil fuel (18.45 GJ – red line), and a steady stream of preheated air (39.6 GJ – purple line). However, the actual energy consumption for air preheating depends on the performance of the CSP th Hybrid-CT system. Air is preheated with fossil fuel and solar thermal energy; these sources are complementary: fuel (green line) is consumed when the solar energy (yellow line) is not enough to fulfill the thermal demand for air preheating. Due to the efficiencies of the backup system, every unit of Fig. 4. Energy consumption of the chemical reactions and operation of the CSP Hybrid-CT system. Off-gas scenario: 1,728 kg/ton of concentrates. Evaluation day of the CSP Hybrid-CT system: 355. Fig. 5. Off-gas production and mass of blast. Off-gas scenario: 1,728 kg/ton of concentrates. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 8 energy for air preheating demands more equivalent energy if this energy comes from the fuel source; this fact is clearly seen from the 00:00 to the 05:00 h and from the 18:00 to the 23:00 h. As seen in Fig. 4, the equivalent energy consumption of the reactions using high-temperature air (orange line) is lower than the equivalent energy consumption of the reactions in the scheme that doesnt use hightemperature air (black line); the equivalent energy consumption decreases due to an improvement of the reactions. Desulfurization of concentrates requires certain amount of oxygen to get a specific copper content in matte. If the energy demand of the reactions is complemented by burning fossil fuel and not by preheating the air, the oxygen demand increases considerably. This increment in the oxygen supply, either by consuming more air or more industrial oxygen, also increases the equivalent energy consumption of the chemical reactions. Two possible concerns of using high-temperature air are the burner’s performance and the operation of the off-gas handling system, particularly the operation of the acid plant. A change in the velocity and composition of the blast (mass of industrial oxygen +mass of air) can affect the burner’s performance, whereas a change in the sulfur dioxide content in the off-gas can diminish the efficiency of the acid plant. In this sense, Fig. 5 shows the off-gas production and the mass of blast for the two process schemes: the process without air preheating and the process using air preheating. The results in this figure correspond to the same off-gas scenario: 1,728 kg of off-gas per ton of concentrates. As seen in Fig. 5, the off-gas production and the sulfur dioxide content remain constant for the two schemes: 86.4 tons of off-gas per hour and 31.2 tons of SO 2 per hour. The blast rate increases from 70.4 tons per hour (process without air preheating) to 71.3 tons per hour (using air preheating); for these blast rates, the air content is 91.2 % and 97.4 %, respectively. These changes in the rate and composition of the blast are not significant; however, the high-temperature air produces a higher blast volume, which in turn leads to a higher blast velocity. The effect of higher blast velocities on the burner’s performance should be further evaluated using fluid dynamic techniques; however, that evaluation is not within the scope of this work. It is worth noting that, in industrial practice, steam or flue gases have been used to preheat air at temperatures up to 300 ◦C; and, for reverberatory furnaces, air has been preheated to higher temperatures [22]. The annual equivalent energy consumption corresponding to the two process schemes was calculated for this off-gas scenario. For the scheme where the reactions use high-temperature air, the industrial oxygen consumption represents 70,956 GJ in the annual equivalent energy consumption, whereas the fuel consumption in reactions represents 161,622 GJ; the equivalent energy consumption for air preheating was calculated after an annual evaluation of the performance of the CSP th Hybrid-CT system. For this specific off-gas scenario, the CSP th Central Towers layout was designed with a design thermal power of 12.18 MW. With this layout, the CSP th Hybrid-CT system delivers an annual value of 117,863 GJ of solar energy for air preheating and burns an annual amount of 357,721 GJ of fossil fuel for air preheating. In sum, for the scheme where the reactions use high-temperature air, the reactions consume 708,162 GJ annually. For the scheme where the reactions do not use high-temperature air (theoretical baseline case), the reactions consume 781,392 GJ annually: 30.5 % by industrial oxygen consumption and 69.5 % by burning fossil fuels in the reactions. These results indicate a reduction of 9.37 % in the annual equivalent energy consumption if the reactions are carried out using high-temperature air; for this case, the air is preheated to an approximate temperature of 550 ◦C. The same analysis was carried out for the other four off-gas scenarios. Fig. 6 shows the annual equivalent energy consumption for the five off-gas scenarios. The CSP th Hybrid-CT systems were designed with solar multiples of 1, and the results correspond to the first year of operation of the system. The chemical reactions require less energy at lower values of off-gas production; this is related to the industrial oxygen consumption. When the reactions depend on ambient-temperature air to obtain most of the oxygen supply, the fossil fuel must deliver enough energy for the reactions and enough energy to increase the nitrogen’s temperature. When the reactions are carried out with ambienttemperature air, increasing the industrial oxygen content in the blast reduces the air demand, the nitrogen income, the need for burning fossil fuel, the blast rate, and, in consequence, the off-gas production. Given these correlations, the scenarios with high off-gas production rates require low or no industrial oxygen consumption and demand more energy. If the reactions use high-temperature air, there is a reduction in the annual equivalent energy consumption; the cause of this reduction was already explained using Fig. 4. These reductions represent 7.97 %, Fig. 6. Annual equivalent energy consumption of the reactions. CSP th Hybrid systems S.M. 1. (First year of operation). I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 9 9.28 %, 9.37 %, 9.44 %, and 6.4 % of the annual equivalent energy consumption for the off-gas scenarios of 1328, 1528, 1728, 1928, and 2128 kg/ton of concentrates, respectively. These results indicate that using high-temperature air results in a significant advantage regarding the reactions’ energy consumption. However, for CSP th Hybrid-CT systems designed with solar multiples of 1, burning fossil fuel is the main source (75 %) of the equivalent energy consumption for air preheating. In order to increase the solar energy contribution (solar fraction), the CSP th Hybrid-CT systems were designed with solar multiples of 2.5; the increment in the solar multiple also requires the inclusion of a thermal energy storage (TES) system. After an economic analysis, a TES system of 13 h was chosen for these CSP th Hybrid-CT systems. Fig. 7 shows the annual equivalent energy consumption for the five off-gas scenarios; the results correspond to CSP th Hybrid-CT systems (S. M. 2.5) with 13 h of thermal energy storage for the first year of operation. For these cases, burning fossil fuel represents about 20 % of the equivalent energy for air preheating, while solar energy represents 80 %. This increase in the solar fraction also reduces the annual equivalent energy consumption: as mentioned before, every unit of energy for air preheating demands more equivalent energy if this energy comes from the fuel source. Now, compared with the scheme that doesn’t use hightemperature air, the scheme that use high-temperature air shows reductions of 19.03 %, 22.05 %, 22.45 %, 22.61 %, and 15.22 % in the annual equivalent energy consumption for the off-gas scenarios of 1328, 1528, 1728, 1928, and 2128 kg/ton of concentrates, respectively. The ultimate goal of using a CSP th Hybrid-CT system to deliver hightemperature air to the reactions is to reduce CO 2 emissions. The annual CO 2 emissions were calculated by multiplying the emission factor of the natural gas, 56.1 kg of CO 2 /GJ [59], and the annual equivalent energy consumption that does not come from the solar source; this calculation was made for every case and off-gas scenario. Table 3 shows the annual CO 2 emissions and the annual avoided CO 2 emissions for the two schemes and the five off-gas scenarios; the table presents the results of using the CSP th Hybrid-CT systems designed with the solar multiples of 1 and 2.5 for the first year of operation. Compared with the process that doesn’t use high-temperature air, the process that uses it shows a significant reduction in the annual CO 2 emissions. Regarding the off-gas scenario, the reductions of CO 2 emissions vary between 14.5 % and 22 % if using a CSP th Hybrid-CT system designed with a solar multiple of 1, and between 41 % and 61.4 % if using a CSP th Hybrid-CT system designed with a solar multiple of 2.5. This can represent a significant advance towards the decarbonization of the copper smelting process: for example, for the off-gas scenario of 1,928 kg/ton of concentrates with an annual process rate of 438,000 tons of concentrates, the avoided emissions are 28,399 tons of CO 2 if using a CSP th Hybrid-CT system S.M. 2.5 to preheat air. Using high-temperature air has a positive effect in terms of avoiding CO 2 emissions; moreover, the reduction of CO 2 emissions becomes more significant if the air is primarily preheated with solar energy. Given the way that emissions were calculated, a reduction of CO 2 emissions means a reduction of the annual equivalent energy consumption, which means Fig. 7. Annual equivalent energy consumption of the reactions. CSPth Hybrid systems S.M. 2.5 with 13 h of thermal energy storage. (First year of operation). Table 3 Annual CO2 emissions of the schemes. (First year of operation). Off-Gas Scenario (kg of off-gas/ton of concentrates) 1,328 1,528 1,728 1,928 2,128 Tons of CO 2 Process without using high-temperature air (Alternative 1) Emissions 30,402 35,682 40,936 46,216 51,471 Alternative 2 - using high-temperature air: CSP th Hybrid-CT system S.M. 1 Emissions 25,125 28,444 32,374 36,015 44,002 Avoided emissions 5277 (17.3 %) 7238 (20.3 %) 8562 (20.9 %) 10,201 (22 %) 7469 (14.5 %) Alternative 3 - using high-temperature air: CSP th Hybrid-CT system S.M. 2.5 Emissions 15,404 15,082 16,487 17,817 30,340 Avoided emissions 14,998 (49.3 %) 20,600 (57.7 %) 24,449 (59.7 %) 28,399 (61.4 %) 21,131 (41 %) I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 16 kW/m 2 . This assumption was based on the receiver’s performance of the Solar Two project [79]. The thermal losses (radiative, convective, and conductive combined) of the Solar Two’s receiver were measured and calculated as function of the wind speed; with a molten salt outlet temperature of 550 ◦C, the results indicated thermal losses between 2.7 MW and 3 MW for the receiver of 99 m 2 operating under wind speeds between 5 mph and 20 mph. This indicates a combined thermal loss between 27.27 kW/m 2 and 30.3 kW/m 2 . Since Q R-Loss was assumed constant, “E Solari ” can be negative for low DNI values and low solar fields efficiencies; in those cases, “E Solari ” was changed by zero. Appendix D. Capital expenditure for the CSP th Hybrid Central Tower systems and performance of the CSP th Central Tower layouts See Table D1 and Figs. D1–D5. Fig. C1. Efficiency of the CSP th Central Tower layout at 144 evaluated sun positions. Design thermal power 12.18 kW th Solar Multiple 1). Fig. C2. Assignation of efficiency for non-evaluated sun positions. (X1 =B1, and X2 =B2). I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 17 Table D1 Cost of the CSP th Hybrid Central Tower systems. Systems: 7.46 kW th 10.33 kW th 12.18 kW th 13.97 kW th 10.56 kW th Solar Multiple 1 Heliostats field ($USD) 1,936,750 2,716,230 3,166,310 3,645,650 2,747,740 Receiver ($USD) 5,255,060 5,830,400 6,576,630 7,035,180 6,129,460 Tower ($USD) 5,901,650 5,577,450 6,607,670 6,244,690 5,577,450 Backup system ($USD) 2,504,520 3,249,480 3,707,250 4,137,060 3,307,240 Heat exchanger ($USD) 2,053,580 2,664,410 3,039,760 3,392,180 2,711,770 Subtotal ($USD) 17,651,560 20,037,970 23,097,620 24,454,760 20,473,660 Indirect costs ($USD) 2,647,734 3,005,696 3,464,643 3,668,214 3,071,049 Total ($USD) 20,299,294 23,043,666 26,562,263 28,122,974 23,544,709 Solar Multiple 2.5 Heliostats field ($USD) 4,957,910 6,825,460 8,030,550 9,215,390 6,952,050 Receiver ($USD) 8,909,670 11,491,100 12,546,300 13,452,000 11,862,700 Tower ($USD) 6,607,670 7,398,160 7,828,190 8,283,220 7,398,160 TES system ($USD) 2,327,250 3,222,960 3,800,160 4,358,640 3,294,720 Backup system ($USD) 2,504,520 3,249,480 3,707,250 4,137,060 3,307,240 Heat exchanger ($USD) 2,053,580 2,664,410 3,039,760 3,392,180 2,711,770 Subtotal ($USD) 27,360,600 34,851,570 38,952,210 42,838,490 35,526,640 Indirect costs ($USD) 4,104,090 5,227,736 5,842,832 6,425,774 5,328,996 Total ($USD) 31,464,690 40,079,306 44,795,042 49,264,264 40,855,636 Fig. D1. Configuration of CSP th Central Tower layouts (SM 1 Left; SM 2.5 Right) and energy transferred to the heat transfer fluid (monthly data). Off-gas scenario 1328 kg/ton of con. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 18 Fig. D2. Configuration of CSP th Central Tower layouts (SM 1 Left; SM 2.5 Right) and energy transferred to the heat transfer fluid (monthly data). Off-gas scenario 1528 kg/ton of con. Fig. D3. Configuration of CSP th Central Tower layouts (SM 1 Left; SM 2.5 Right) and energy transferred to the heat transfer fluid (monthly data). Off-gas scenario 1728 kg/ton of con. I. Cruz-Robles et al. Applied Thermal Engineering 226 (2023) 120270 19 References [1] International Copper Study Group, The World Copper Factbook 2016, Available Online: https://www.rockstone-research.com/images/PDF/ICSG_CopperFactboo k2016.pdf (accessed on January 8, 2023). 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