Energy, exergy and thermoeconomic analysis of an industrial solar pond

1 Energy, exergy and thermoeconomic analysis of an industrial solar pond M. Montalà1,2, K. Ganesan1,2, O. Casal1,2, J.L. Cortina2,3, M. Santarelli4, C. Valderrama1,2,3,* 1 Barcelona School of Industrial Engineering, ETSEIB, UPC•BarcelonaTECH 2 Chemical Engineering Department, UPC•BarcelonaTECH 3 Barcelona Research Center for Multiscale Science and Engineering, 08930 Barcelona, Spain 4 Department of Energy, Politecnico di Torino, C.so Duca Degli Abruzzi 24, Turin, 10129, Italy *Correspondence should be addressed to: César Valderrama Departament d’Enginyeria Química, Universitat Politècnica de Catalunya-Barcelona TECH C/ Eduard Maristany, 10-14 (Campus Diagonal-Besòs), 08930 Barcelona, Spain Tel.: 93 4011818 Email: [email protected] Abstract This study evaluates the viability of an industrial salinity gradient solar pond during two operating seasons (2014 and 2015). The Granada solar pond was built to supply low-temperature heat (up to 60°C) to satisfy the temperature requirements of the flotation unit in a mineral processing plant (Solvay Minerales in Granada (Spain)). Energy analysis indicates that the non-convective zone (NCZ) and the upper convective zone (UCZ) have low efficiencies because these zones have a low capacity to store heat, and no heat extractions are carried out from these zones. In contrast, heat extraction in the lower convective zone (LCZ) has a positive impact on the system because it increases the capacity of the solar pond to store energy. Higher efficiencies were achieved in the second operation period in the LCZ, since higher amount of heat was extracted during this period. The overall exergy efficiency of the LCZ after the first and second operation periods was 1.6% and 2.3%, respectively. The solar pond works at temperatures Unmarked Revised Manuscript for Publication Click here to view linked References 2 close to room temperature and thus the exergetic efficiency decreases significantly. Regarding the thermoeconomic analysis, the cost of exergy stored is studied in this work, using two different approaches, by estimating the minimum price for exergy stored or the minimum surface area that ensure the thermoeconomic viability. The price of the stored exergy tends to decrease inversely to the price of fuel oil. Thus, the cost of the stored exergy must be four to five times higher than the price of fuel oil for the solar pond system to be feasible. On the other hand, solar pond technology is affected by economies of scale; the larger the solar pond, the higher the inflation rates and the lower the cost reduction rates that can be accommodated. This implies that estimating the cost of the stored exergy is complex due to the variability of the processes involved and can lead to erroneous interpretations when evaluating the viability of a solar pond from a thermoeconomic perspective. Keywords: Solar energy; energy storage; salinity gradient solar pond; mineral processing; flotation unit Nomenclature Parameters Greek Symbols 𝐼 Solar radiation 𝜃𝑖 Angle of incidence 𝑄 Energy flux 𝜃𝑟 Refraction angle 𝐸/𝐸 Exergy flux ∅ Latitude 𝑍 Annual capital cost 𝛿 Declination angle of the sun 𝑄𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟 Energy stored in a certain layer 𝜔 Hour angle 𝐸𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟 Exergy stored in a certain layer 𝜆 Reflectivity of the bottom of the solar pond 𝑄𝑖𝑛𝑙𝑎𝑦𝑒𝑟 Input energy in a certain layer 𝜂 Energy efficiency 𝐸𝑖𝑛𝑙𝑎𝑦𝑒𝑟 Input exergy in a certain layer 𝜓 Exergy efficiency 𝑄𝑜𝑢𝑡𝑙𝑎𝑦𝑒𝑟 Output energy in a certain layer 𝛼 Thermal expansion coefficient 𝐸𝑜𝑢𝑡𝑙𝑎𝑦𝑒𝑟 Output exergy in a certain layer 𝛽 Salinity expansion coefficient 3 𝑄𝑠𝑜𝑢𝑡 Outlet solar radiation inlet 𝑀 Aggregated exergy fluxes 𝐸𝑠𝑖𝑛 Inlet solar radiation exergy Subscripts 𝐸𝑠𝑜𝑢𝑡 Outlet solar radiation exergy i Layer 𝑄𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟 Energy absorbed by a layer t Time 𝐸𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟 Exergy absorbed by a layer B Bottom 𝑄𝑖𝑛𝑙𝑎𝑦𝑒𝑟→𝑙𝑎𝑦𝑒𝑟 Energy transmitted from one layer to another T Net Temperature 𝐸𝑖𝑛𝑙𝑎𝑦𝑒𝑟→𝑙𝑎𝑦𝑒𝑟 Exergy transmitted from one layer to another CI Investment cost 𝑄𝑒𝑥𝑡 Energy extracted from the system OM Operation & Maintenance Cost 𝐸𝑒𝑥𝑡 Exergy extracted from the system ch Chemical 𝑄𝑙𝑜𝑠𝑠𝑙𝑎𝑦𝑒𝑟 Energy lost from a certain layer ph Physical 𝐸𝑢𝑠𝑒𝑙𝑒𝑠𝑠𝑙𝑎𝑦𝑒𝑟 Exergy lost and destroyed in a certain layer Abbreviations 𝑐𝑒𝑥𝑡 Cost of the extracted exergy flux 𝑆𝐺𝑆𝑃 Salinity Gradient Solar Pond 𝑐𝑠𝑡𝑜𝑟𝑒𝑑 Cost of the stored exergy 𝑆𝑃 Solar Pond 𝑐𝑠𝑜𝑙𝑎𝑟 Cost of the solar exergy 𝑈𝐶𝑍 Upper convective zone 𝑚𝑙𝑎𝑦𝑒𝑟 Water mass of a certain layer 𝑁𝐶𝑍 Non convective zone 𝐶𝑝𝑙𝑎𝑦𝑒𝑟 Heat capacity of a certain layer 𝐿𝐶𝑍 Lower convective zone 𝑇𝑙𝑎𝑦𝑒𝑟 Temperature of a certain layer 𝐹𝑟 Froude number 𝑚 𝑒𝑥𝑡 Mass flow rate through the heat exchanger to extract heat 𝐶𝐴𝑃𝐸𝑋 Capital expenditures 𝐶𝑝 Heat capacity of water used to extract heat 𝑂𝑃𝐸𝑋 Operating expense 4 𝑇𝑖𝑛 Water temperature before the heat exchanger 𝐿𝑆𝑇𝑀 Local Standard Time Meridian 𝑇𝑒𝑥𝑡 Water temperature after the heat exchanger 𝐿𝑇 Local Time 𝑅 Fraction of the solar radiation directly reflected to the environment 𝐺𝑀𝑇 Greenwich Mean Time 𝐿 Total depth of the solar pond 𝐸𝑜𝑇 Equation of Time 𝑅𝑐𝑜𝑛𝑑 Conductive resistance 𝑇𝐶𝐹 Time correction factor ∆𝑧 Thickness of contact zone 𝐿𝑆𝑇 Local Solar Time 𝐴 Area 𝐾 Thermal conductivity 𝐸 Static stability 𝑖𝑟 Economy inflation 𝑛𝑦 Lifetime of the solar pond 𝐼𝑛𝑣. 𝐶𝑜𝑠𝑡 Investment cost of the solar pond 𝑥𝑖 Molar fraction e0x,ch Standard molar chemical exergy 𝐶𝑝 Heat capacity of water used to extract heat 1. Introduction Solar energy is an abundant, clean and inexhaustible source of energy that can reduce the impact of the climate crisis caused by the use of fossil fuels. However, the use of solar thermal energy is associated with significant challenges due to its low energy density and its intermittent characteristics. The salinity gradient solar pond technology provides a solution using a large area of land that allows energy to be 5 collected and stored [1, 2]. A solar pond is a system capable of storing part of the received solar radiation for a long period of time and providing heat to an external system. The salinity gradient solar pond (SGSP) system generally consists of three zones, namely the upper convective zone (UCZ), non-convective zone (NCZ) and lower convective zone (LCZ). The UCZ, which is the thinnest layer, has a temperature close to room temperature and possesses the lowest salinity concentration (5‒10%). The middle zone of the SGSP is called the NCZ or gradient zone, where the temperature and the degree of salinity increase with depth. The salinity gradient in the NCZ provides a transparent insulating layer under various climatic conditions to store solar energy at the bottom of the pond [3]. The LCZ is the storage zone, which has the highest salinity concentration (15‒30%) [4]. The efficiency of solar ponds is low due to the lack of retention of solar radiation that is absorbed by the lower convective zone, which is the main reservoir for stored energy in solar ponds [4]. The thermal efficiency of solar ponds has been commonly defined and evaluated based on their energy storage capacity or the quantum of heat extracted from them. It is worth mentioning that the operation of the solar pond is a continuous process of charging, storage and discharge [5] [6]. For heat extraction from solar ponds, there are two methods [7]: first is to circulate hot LCZ water through an external heat exchanger, and second is to install heat exchangers within the LCZ through which a suitable working fluid flows [8]. An appreciable portion of heat energy stored inside the lower convective zone (LCZ) gets conducted to the ground below as waste, which can be recovered by installing heat exchangers inside the ground can enhance the output of solar ponds quite significantly [9]. The amount of heat extraction from the solar pond depends on the level of demand for the heating process, which implies that the amount of energy extracted can be greater or less than the energy stored in the solar pond. During certain periods, there may be no heat extraction, which doesn’t mean that the efficiency of the solar pond can be assigned as zero. This is because the absorbed energy is still being stored by the pond during this period [10]. The unused part of the available energy undergoes a quality degradation termed exergy destruction that causes the system to deviate from its expected ideal 6 operating state. Verma and Das [11] reported that the rate of exergy destruction caused by the operation of the pond (heat extraction) is underestimated by the assumption of an infinite heat transfer coefficient that does not affect the stability of the pond. For instance, the energy available in a system that has reached an equilibrium with its surroundings is no longer suitable for use. Furthermore, the exergetic analysis preserves the energy conservation principle by introducing the quality degradation of energy caused by the entropy generation in real system transformations [12] [13]. Different authors have suggested theoretical models or lab scale analysis to study both the energy and exergetic performance of solar pond technology [14]. Bozkurt and Karakilcik [15] evaluated the exergetic performance of a cylindrical solar pond (1.6 m of diameter) integrated with four flat plate collectors. Authors concluded that exergy analysis allows to identify the heat losses and to improve the performance of the system. The influence of the geometry on the solar pond performance was also evaluated from the exergy perspective by Dehghan et al. [16]. Two small solar ponds (square and circular cross sections) with a surface area of 3 m2 were evaluated using the experimental data collected during 10 months. The energy and exergy efficiency reported for circular solar pond were higher than for square solar pond at the LCZ. Authors concluded that storage capacity is higher in the circular solar pond. The influence of shading walls on storage capacity of small solar pond (4 m2 circular and square crosssection) was evaluated by Khalilian [17, 18]. Numerical analysis of energy and exergy efficiencies was carried out by author considering the shadows effect and concluded that exergy efficiency was one order of magnitude lower than the energy efficiency. Njoku et al. [19] critically reviewed the aforementioned studies, highlighting that the temperature stratifications in the NCZ were not accounted for when calculating the exergies, using the average temperatures of the gradient leading to significant errors in the computed exergies. A 1-D transient numerical model was proposed, including temperature stratification within the SGSP as well as heat extraction from the LCZ. Authors concluded that the largest exergy destructions occurred in the LCZ. Therefore it was suggested that in formulating measures for enhancing SGSP performance. Heat extraction process was also evaluated in terms of transient thermal 7 performance of solar pond. Extraction at different rates at the LCZ and at the NCZ were considered as well as simultaneous extraction from both zones using a finite difference method. Results indicated that maximum exergy efficiency was obtained extracting heat from the LCZ only [20]. Recently, Cardoso et al. [21] reported a numerical analysis of the potential performance of a 1 ha solar pond located on Caota Beach, in Benguela, Angola. Authors concluded that heat losses at the LCZ penalize the useful energy extracted from this zone and lead to a very low energy and exergy efficiencies of the pond. Namin et al. [22] described the potential of solar pond technology in recent years, despite the low exergetic efficiency of a SGSP due to the immense irreversibilities in all regions of the system, when integrated with hybrid energy systems (especially in systems power and desalination). It is worth to mention the evaluation of construction of SGSP refrigeration system [23], the enhanced design of a large scale SGSP power plant using ORC systems and two-phase closed thermosyphons to generate electricity [24, 25], the hydrogen production by flat-plate collectors assisted by a solar pond [26], the feasibility design of a SGSPhumidification‒dehumidification desalination system for producing freshwater [4, 27]. In most of aforementioned studies [20-27] the solar pond formulation is simplified to the heat collection efficiency assuming mathematical relations obtained in previous studies. Only the study by Zeynali et al [28], when evaluating the power generation using organic Rankine cycles (ORC) and trilateral modified flash cycles (TFC) assisted by a solar pond, reported a detailed description of each zone, however, how the temperature of the gradient is considered in NCZ analysis is not mentioned. To the best of our knowledge, the performance evaluation of industrial solar ponds using energy and exergy analysis has not been reported. The present study evaluates the efficiency of a 500 m2 industrial solar pond built in Spain to supply heat to a flotation unit in a mine facility. Energy and exergetic efficiencies are detailed analysed for each zone of the solar pond and the overall efficiencies of the system are estimated. Finally, a thermoeconomic analysis is also performed in order to assess the feasibility of the Granada solar by quantifying the cost of the exergy stored in the solar pond during two operating seasons. 8 2. Materials and Methods 2.1 Description of the Granada solar pond The solar pond was constructed in the Solvay Minerales facilities in Granada (South Spain) in 2014. Details of the design, construction and operation were reported in Alcaraz et al. [3]. The solar pond was installed in a mine facility producing celestine (SrSO4(s)). The processed rock, with a celestine content of 30‒50%, is milled and then concentrated up to a content of 90% by using a flotation stage. The solar pond was constructed to deliver the heat needed to preheat the water (> 60 °C) used in the mineral flotation unit. The total area of the pond is 500 m2 (20 × 25 m) and it has a depth of 2.2 m. The LCZ was designed to be 0.6 m thick, the NCZ was 1.4 m thick, and the UCZ was 0.2 m thick. The main climatological parameters of the solar pond’s location [29] are listed in Table 2. Table 1. Location and climatological parameters at Solvay Minerales mining facilities in Granada (Spain). Coordinates 37° 3′ 0″ N, 3° 45′ 0″ W Altitude (m) 929 Wind average speed (m/s) 2.3 Summer maxim temperature (°C) 33.0 Winter minimal temperature (°C) -7.0 January February March April May June July August September October November December Average monthly temperatu re (°C) 3.10 4.20 7.30 10.0 13.3 18.1 21.9 21.4 18.0 12.0 7.2 4.1 Solar radiation (MJ/m2 month) 283 346 496 618 734 813 838 748 565 400 275 227 Table 1. Location and weather parameters at the Solvay Minerales facilities (Granada, Spain). The bottom and the walls were insulated using a synthetic insulation material, ChovAFOAM 300-M50 (thermal conductivity = 0.034 W/mK; thickness = 50 mm; maximum pressure = 300 kPa; maximum temperature = 65 °C) in order to prevent heat losses. Expanded clay pellets (Arlita) were laid on the base of the pond to a total height of 50 mm. The remainder of the wall, not covered with Arlita, was laid with a geotextile (non-woven polyester GTXnw PS NTL, Atarfil, Spain). In addition, a secondary (PE) liner was used to prevent 1 leakage in the system (thickness = 2 mm). To control the stability of the salinity gradient, samples are taken every 10 cm from the bottom area through a PVC pipe (6 mm in diameter with a height of 3 m) to determine the density, pH, and turbidity 9 of the system over its entire height. A DMA 35 portable density meter (Anton Par; accuracy of ±0.001 g/cm3) is used to measure the density. The pH and turbidity are measured by a portable pH meter (Crison pH25, accuracy of ±0.01 pH) and a portable turbidity meter (Hanna HI93703C, accuracy of ±0.5 NTU), respectively. The temperature measurement at different heights is performed by 42 sensors (thermoresistances, PT100 type, Abco, Spain) uniformly distributed at intervals of 5 cm, starting 0.5 cm from the bottom and installed in plastic supports. The temperature is measured every 2 s and the average after 10 min as well as the hourly and daily average is recorded. The monthly average temperature of each zone is determined by averaging the values recorded daily. The weather parameters are measured by means of an automatic weather station, the CR1000 Measurement and Control System (Campbell Scientific, Barcelona, Spain). Before the installation of the solar pond, water was heated using a boiler fed with gasoil. After starting its operation, a degradation in the salinity gradient was detected through monitoring the density profile, and in April 2015 the salinity gradient was considered technically destroyed. In September 2015 the solar pond was refilled and its operation restarted. No problems were detected until April 2016 when the salinity gradient started to deteriorate again. In this study, energy and exergy analyses are detailed for the two operation seasons. 2.2 Energy analysis In this section, all the energy fluxes found in the system are detailed as depicted in Figure 1. a b 16 affects the overall operation of the solar pond technology. In this case, the input energy/exergy also contains internal gains. An instantaneous efficiency analysis can be considered as suggested by Date et al. [33]; however, it has important shortcomings. First, the instantaneous efficiency in periods when the solar pond is storing energy is not representative of the global efficiency of the system. Second, the heat extracted in a given period is not a result of the instantaneous solar radiation but rather the result of previously stored solar radiation. Third, in periods when the solar pond is not storing energy/exergy and when no heat extractions take place, an efficiency of 0% would be obtained, which is not representative. These shortcomings may be overcome by considering longer periods. Alcaraz et al. [3] suggested that the overall efficiency of the system could be determined as the average of all monthly efficiencies. As previously said, the heat stored at a given period of time may be used some months later. For that reason, a cumulative model is suggested in this work. Hence, the energy and exergy efficiencies at the end of a period consider all events that have occurred since the beginning of the operation period. Thus, the energy and exergy efficiencies of each layer are determined through Eq. 18 and 19, respectively: 𝜂= ∑[𝑄𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝑄𝑒𝑥𝑡𝑡] 𝑡0 ∑[𝑄𝑆𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝑄𝑖𝑛𝑡𝑙𝑎𝑦𝑒𝑟𝑖+1,𝑡→𝑙𝑎𝑦𝑒𝑟𝑖.𝑡+𝑄𝑖𝑛𝑡𝑙𝑎𝑦𝑒𝑟𝑖−1,𝑡→𝑙𝑎𝑦𝑒𝑟𝑖,𝑡] 𝑡0 (18) 𝜓= ∑[𝐸𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝐸𝑒𝑥𝑡𝑡] 𝑡0 ∑[𝐸𝑆𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝐸𝑖𝑛𝑡𝑙𝑎𝑦𝑒𝑟𝑖+1→𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝐸𝑖𝑛𝑡𝑙𝑎𝑦𝑒𝑟𝑖−1,t→𝑙𝑎𝑦𝑒𝑟𝑖,𝑡] 𝑡0 (19) The overall efficiencies of a solar pond are determined considering all the layers of the system. Additionally, when the whole system is analysed the internal heat transfers are compensated. Eq. 20 and 21 are used to determine the overall energy and exergy efficiency of the system: 𝜂=∑ ∑ [𝑄𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝑄𝑒𝑥𝑡𝑡] 𝑡0 𝑖=𝐿𝑇𝑂𝑇 0∑ ∑ [𝑄𝑆𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟𝑖,𝑡] 𝑡0 𝑖=𝐿𝑇𝑂𝑇 0 (20) 17 𝜓=∑ ∑ [𝐸𝑠𝑡𝑜𝑟𝑒𝑑𝑙𝑎𝑦𝑒𝑟𝑖,𝑡+𝐸𝑒𝑥𝑡𝑡] 𝑡0 𝑖=𝐿𝑇𝑂𝑇 0∑ ∑ [𝐸𝑆𝑎𝑏𝑠𝑙𝑎𝑦𝑒𝑟𝑖,𝑡] 𝑡0 𝑖=𝐿𝑇𝑂𝑇 0 (21) 2.5 Thermoeconomic analysis Thermoeconomics is an important branch of engineering that combines the theories and methodologies of thermodynamics and economics [38]. The exergy associated with the different variables that intervene in the system are taken as the basis for the allocation of economic costs between the different input and output flows. Mathematically, a thermoeconomic analysis may be described by Eq. 22 as proposed by Oliviera et al. [39]: ∑𝛱 𝑖𝑘+𝑍 =∑𝛱 𝑜𝑙 𝑙𝑘 (22) where 𝛱 𝑖𝑘 is the economic value of the input exergy fluxes to the system, 𝑍 is the total capital costs including the investment and operation and maintenance costs, and 𝛱 𝑜𝑙⁡is the economic value of the output exergy fluxes from the system. In turn, 𝛱 may be calculated through Eq. 23: 𝛱 =𝑐·𝐸 (23) where 𝑐 is the price associated with the exergy flux and 𝐸 is the corresponding exergy flux. The solar pond is a complex system because part of the input flux is stored in the system for a long period of time. Hence, there is no balance between the input and output fluxes. In the literature, none of the existing solar ponds, industrial or pilot plants have been analysed from the thermoeconomic point of view. In that context, an exhaustive literature review was carried out to identify thermoeconomic analyses that have been applied in different technologies and that may be useful to develop a methodology to analyse a solar pond technology. The methodology developed by Kazim et al. [40] to thermoeconomically evaluate a fuel cell may have a certain parallelism with the solar pond. 18 First, the fuel cell was analysed as a black box, i.e., the system was studied as a whole and the different elements were not independently analysed. The solar pond analysis follows the same principle and it is analysed as a whole. However, the fuel cell charge‒discharge cycles were relatively short. Hence, the authors considered hydrogen and air as inputs, and water, air and electricity as outputs. The analysis omitted the time variable for the energy stored in the fuel cell. In a solar pond, part of the heat stored in the system will not be extracted. Once the system starts its operation, the temperature inside the LCZ will never return to its initial value. Despite part of the heat stored never being used, this part of the heat has an economic value for the owner of the facility because it is an important reserve that may be used in case of necessity. In that context, the model suggested to analyse a solar pond from the thermoeconomic point of view can be determined using Eq. 24: 𝑐𝑠𝑜𝑙𝑎𝑟𝐸 𝑠+𝑍 𝑆𝑃=𝑐𝑒𝑥𝑡𝐸 𝑒𝑥𝑡+𝑐𝑠𝑡𝑜𝑟𝑒𝑑𝐸 𝑠𝑡𝑜𝑟𝑒𝑑 (24) where 𝑐𝑠𝑜𝑙𝑎𝑟 is the exergy cost of the solar exergy (𝐸 𝑠), 𝑐𝑒𝑥𝑡 is the exergy cost of the exergy extracted from the system (𝐸 𝑒𝑥𝑡), 𝑐𝑠𝑡𝑜𝑟𝑒𝑑 is the exergy cost of the exergy stored in the system (𝐸 𝑠𝑡𝑜𝑟𝑒𝑑) and 𝑍 𝑆𝑃 is the annual cost of the system, which includes a proportional part of the investment cost and the operation and maintenance costs, which can be determined according to Eq. 25: 𝑍 𝑆𝑃=𝑍 𝐶𝐼+𝑍 𝑂𝑀 (25) where 𝑍 𝐶𝐼 is the annual investment cost and 𝑍 𝑂𝑀 the annual operation and maintenance cost. Although the investment cost is paid during the construction of the solar pond, the annual capital cost is considered. The annual capital cost considers both the investment cost and economic inflation. Thus, the annual capital cost may be determined through Eq. 26: 𝑍𝐶𝐼=𝐼𝑛𝑣.𝐶𝑜𝑠𝑡· 𝑖𝑟(1+𝑖𝑟)𝑛𝑦 (1+𝑖𝑟)𝑛𝑦−1 (26) 19 where 𝐼𝑛𝑣.𝐶𝑜𝑠𝑡 is the investment cost, 𝑖𝑟 is the inflation rate and 𝑛𝑦 is the lifetime of the system. The annual operation and maintenance cost, 𝑍 𝑂𝑀, is determined as a percentage of the investment cost. 3. Results and discussion 3.1. Energy and exergy efficiencies The solar pond in Granada started its operation in July 2014. The density in the LCZ was kept almost constant for 10 months with an average value of 1203 kg/m3 and the temperature evolved according to the weather conditions. The initial temperature in the LCZ recorded in the solar pond once the salinity gradient was established was 42.7 °C. Thanks to the high solar radiation during the first month, the temperature in the LCZ increased by 1.5 °C per day on average, reaching a maximum temperature of 89 °C at the end of August 2014 as can be seen in Figure 2. The degradation of the salinity gradient was detected by the density profile monitoring as the height to the UCZ increases from 0.3 m in July 2014 to 0.8 m in April 2014. Although the same trend was observed in the evolution of the temperature profile, the average monthly temperature of the LCZ not decreased below 40 °C (Figure 2). After a second refilling process in 2016, the Granada solar pond operated successfully until March 2020, when the mine facility restricted its operation due to the pandemic situation. 0 2000 4000 6000 8000 10000 12000 14000 16000 0 10 20 30 40 50 60 70 80 90 100 10/07/14 18/10/14 26/01/15 06/05/15 14/08/15 22/11/15 01/03/16 09/06/16 MJ ºCTlcz OPERATION PERIOD 1 Tlcz OPERATION PERIOD 2 DAILY SOLAR RADIATION Solar radiation trend line MAX Temp REFILLING PROCESS 20 Figure 2. Evolution of the LCZ average temperature along the first and second operation periods of the Granada solar pond. The Granada solar pond is evaluated from the energy point of view. Figure 3 represents the energy analysis of the three zones of the system. As can be seen in Figure 3a, the UCZ cannot store energy; almost all the solar radiation absorbed by this zone is lost through the surface, evaporative and convective losses, and the walls. The efficiency of this zone is not analysed because there is no storage or heat extraction. The NCZ (Figure 3b) has a small capacity to store part of the solar radiation, especially in the first months. The main aim of the NCZ is to prevent heat stored in the LCZ from escaping, i.e. it works as an insulator. Thus, the isolation of the lowest sublayers of the NCZ results in a notable capacity of the system to store heat. The low temperature of the water during the filling and the high ambient temperature and solar radiation in summer resulted in an increase in the energy stored in the NCZ. However, in winter, the system was not capable of retaining the heat stored in the NCZ. The system started to store again in the NCZ when the environmental conditions were notably better. The energy stored in the zone has a direct impact on the energetic efficiency. The NCZ reported an efficiency of almost 60% in the first month of operation that decreased to 0% in the winter months because of the heat losses. As this work considered a cumulative analysis of the system, the efficiency obtained at the end of the operation period is the overall efficiency of the zone. This efficiency considers all the environmental events that occurred since the operation started. Thus, the NCZ has an overall efficiency of 3.4% and 5.9% in the first and second operation periods, respectively. The large capacity and potential of the system to store heat is clearly represented in Figure 3c, which contains the analysis of the LCZ. The LCZ is the zone in the solar pond that provides heat to an external application, in this case the flotation stage at Solvay Minerales facilities. In the first operation period, the fraction of stored energy increased abruptly in the first months of operation, due to the good environmental conditions and due to the large capacity of the system, thereby increasing its temperature. 21 In September, the system started to lose part of the energy stored. However, the LCZ always kept a significant amount of stored heat, even under adverse environmental conditions. In March 2014, due to the improvement in environmental conditions the LCZ started to increase the stored energy, thereby increasing its temperature. Throughout the year, even in the winter months, a significant amount of energy was extracted from the system. As a result, the LCZ, when independently analysed, shows high efficiency. The large capacity of the system to store energy at the beginning of the operation period resulted in efficiencies of 57.8% and 46.6% after the first and second month of operation, respectively. The lowest energy efficiency registered in the LCZ was 19.6%, when the first six months of operation were considered. After one year of operation, the overall efficiency of this zone was 23.1%. 22 23 Figure 3. Energy fluxes and efficiency of: a) UCZ, b) NCZ and c) LZC during the first and second operation periods of the Granada solar pond (blue line indicates efficiency). In the second operation period, despite starting the operation in September 2015, the system was able to increase the stored energy and provide heat to the flotation stage. The amount of heat stored in the pond started to decrease from November 2015 to February 2016, when the stored heat increased again. In the second period of operation, a greater amount of heat was extracted from the system. Heat extraction has a positive impact on the system because it increases the capacity of the solar pond to store energy. As a result, higher efficiencies were achieved in the second operation period. The efficiency after the first and second months of operation was 66.0% and 52.7%, respectively. The lowest efficiency in this operation period was 36.4% registered in January 2016. The overall efficiency at the end of the second operation period was 39.6%. 24 Considering the energy analysis, the UCZ and the NCZ are essential in the system to ensure the proper operation of the solar pond. In this sense, maximizing heat extraction will increase the energy and exergetic efficiency of the solar pond by increasing the storage capacity; this can be achieved by optimizing the operation of the flotation unit that allows increasing the mineral treatment during the months of high radiation. However, the LCZ is the part of the system that produced an energetic value due to its capacity to store and provide heat. Thus, the exergy analysis is focused on the LCZ and is compared with the energy analysis. All the energy and exergy fluxes of the LCZ are shown in Figure 4. Exergy analysis is less favourable than energy analysis because not all energy is always useful. The greater the difference between the temperature of the energy flux and the ambient air temperature, the greater the exergy, i.e., the more useful is the energy flux. The internal heat transfers and the heat stored decreased notably due to the small difference between the LCZ temperature and the ambient air temperature. The maximum and minimum monthly mean differences were 55.5ºC in August 2014 and 29.8ºC in January 2015, respectively, during the first operation period, and 55.9ºC in April 2016 and 33.0ºC in September 2015, respectively, during the second operation period. The efficiency of the heat exchanger installed at the bottom of the pond resulted in a lower temperature of the water inside the heat exchanger than the LCZ temperature. As a consequence, the heat extraction is the variable with the smallest difference between its temperature range and the ambient temperature. Hence, the exergy of the heat extracted is much lower than the energy of this heat flux. The heat stored and heat extracted were much lower in percentage than the solar radiation in the exergy analysis. As a consequence, the values obtained for the exergy efficiency are clearly much lower than for the energy analysis as has been reported in previous studies [15-20]. The overall exergy efficiency of the LCZ after the first and second operation periods was 1.6% and 2.3%, respectively. 25 As in the energy analysis, increasing the amount of heat extracted from the system improves the exergy efficiency. As a result, the exergy efficiency was significantly higher in the second operation period. Figure 4. Energy and exergy fluxes and efficiencies of the LCZ during the first and second operation periods of the Granada solar pond. Finally, the overall energy and exergy performance of the Granada solar pond is compared in Figure 5. As for the energy analysis, the energy efficiency is less favourable when the whole system is considered than when the LCZ is independently analysed as a consequence of the whole system being influenced by the low efficiencies of the NCZ and the UCZ. As has been said, the NCZ and the UCZ have low efficiencies because these zones have a low capacity to store heat and no heat extractions are carried out. However, thanks to the UCZ and the NCZ, the LCZ has a large capacity to store heat and consequently a large efficiency. At the end of the first operation period the overall efficiency of the system 32 under different surfaces is calculated proportional to the exergy stored and extracted under the current solar pond (500 m2). The minimum surface area needed to make the solar pond technology feasible is determined under different scenarios involving cost reduction and economic inflation as shown in Figure 8. The analysis evaluates 5 different inflation rates (1%, 2%, 3%, 4% and 5%) and under a range of cost reductions between 51 and 80%. A minimum cost reduction of 51% is considered because below this percentage the technology is not feasible under any inflation rate. Figure 8. Minimum surface to ensure the thermoeconomic feasibility of the Granada solar pond under different inflation and cost reduction rates. As shown in Figure 8, by setting the inflation rate, the surface can be reduced by increasing cost reductions. For a fixed percentage of cost reduction, the solar pond can be a feasible technology with a minimal footprint by lowering the inflation rate. In addition, at higher inflation rates, higher cost reduction rates are needed to make the solar pond feasible; that is, with inflation below 2%, a minimum cost 1% 2% 3% 4% 5% 00 5,000 10,000 15,000 20,000 51% 53% 55%57%59%61%63% 65% 67% 69% 71% 73% 75% 77% 79% Inflation rate (%) Minimum surface (m2) Cost reduction (%) 33 reduction of 55% is necessary. The larger the solar pond, the higher the inflation rates and lower the cost reduction rates that can be accommodated, as has also been reported by Valderrama et al. [42]. It is worth mentioning that this analysis is carried out assuming that the energy stored as a fuel oil deposit and this may lead to an unrealistic interpretation of the behavior of the solar pond from a thermoeconomic point of view. The objective was to consider evaluating the exergy cost of the energy stored in the solar pond, which is variable over time, to determine the thermoeconomic viability of the Granada solar pond, estimating either the minimum cost of stored exergy or the minimum area to ensure such feasibility. The results indicate that this depends largely on the fluctuation of the replaced fossil fuel market, the amount of heat extracted, which is also variable, and the capacity of the solar pond to store exergy in the LCZ, highly dependent on the heat extracted, environmental conditions, and its maintenance and operation. This first attempt to estimate the thermoeconomic viability of an industrial solar pond reveals that it is more complex than other energy storage systems described in the literature due to the variability of some of the processes involved. Future work should therefore consider new approaches to reduce uncertainty in the modeling of the system. 4. Conclusions The overall energy efficiencies of the Granada solar pond were 5.79% and 8.98% after the first and second operation period, respectively. The exergy analysis reported overall efficiencies of 0.34% and 0.43%, respectively. This significant difference between the energy and exergy analysis is due to the fact that the exergy considers the useful part of the energy flux. It is also observed that heat extraction plays an important role in the efficiency of the solar pond, by increasing the amount of heat extracted, it also increases the storage capacity and consequently the energy and exergetic efficiency of the system increases. The thermoeconomic analysis of the Granada solar pond indicated that this installation is not feasible with the current investment, maintenance costs, and considering the amount of fossil fuel savings. Estimating the cost of the stored exergy is the main source of uncertainty due to the variability of the processes involved and it can lead to erroneous interpretations when evaluating the viability of a 34 solar pond from a thermoeconomic perspective. According to assumption considered in the current study, to be feasible, the cost of the exergy stored in the system must be between 4 and 5 times higher than the cost of fuel oil, in addition to providing economic incentives or tax reductions. In addition, the minimum surface area required to make the system feasible under different scenarios was estimated (between 10000 and 20000 m2). 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