## 4 Results and Discussion
### Case of Study  
An application case where the designed thermal storage system was used is studied. This case consists of an electric power generation plant for an off-grid pumping system in the mining industry, as shown in Figure 4. It controls water infiltration from a dam of tailings to groundwater by implementing a battery of wells to intercept the infiltration flow generated by decantation. This flow control is necessary to comply with environmental regulations, highlighting regulatory decree No. 86/60 regulated by [45]. The plant and the pumping system have an estimated useful life of 30 [years] and a capacity to dispatch 18 [kWe]. The main components are six submersible pumps, a solar concentration tower with its respective receiver located around a heliostat matrix, and a commercial container that houses two thermal storage tanks by structured thermocline, six Stirling engines, a piping system, electromagnetic pumps, flow meters, transmitters, valves, controllers, among others. Figure 3: Comparison of dimensionless temperature distribution after 2.5 [h] of loading between different time steps. The plant location was determined using the availability of maps of tailings deposits in Chile [46]. The only active tailings dam in the Commune of Pica was selected due to the high potential in solar resources for said geographical location (Figure 5). Subsequently, it was necessary to determine the potential for solar energy generation through concentration systems. According to the geographical location of the case study, through the Solar Explorer of the Ministry of Energy [48], the values of Direct Normal Radiation (DNI) expressed in a daily cycle are obtained as observed in Figure 6a,b, through which the energy needed for CSP was determined. Figure 4: Thermal storage system designed as part of a comprehensive TES + CSP solution. Figure 5: Extract from the tailings distribution map, Commune of Pica, Region of Tarapacá, Chile [47]. Based on these results, the primary heat transfer circuit transports the thermal energy from the receiver to the thermal storage system and the power block. This thermal energy produced by radiation depends on time, and its fluctuation is represented by the normalized DNI [49], assuming that the collector or solar concentration field has a constant optical efficiency. First, the DNI representative annual average for each characteristic hour of a daily cycle was calculated. Second, the normalized values based on the maximum DNI value were obtained within the standards. Therefore, using the procedures described by [50], the power that must be supplied to the power block corresponds to that of six Stirling engines divided by their thermal efficiency, a magnitude equivalent to 59.2 [kW]. Therefore, the maximum power required by the primary heat transfer circuit from the solar receiver is equivalent to 153.4 [kW], as shown in Figure 7. In this project, the type of receiver used was external, made up of tube panels positioned to resemble the defined outer circumference [50]. This configuration is simple in construction, minimizes the required surface area, and limits radiation losses. So, in the case of the study, an energy flux density corresponding to 0.14 [MW/m\({}^{2}\)] was taken as a reference. Therefore, for the required power of 153.4 [kW], a cylindrical (lateral) surface area of 1.095 [m\({}^{2}\)] is obtained. With this, a height and diameter of 0.60 [m] are selected, forming an _H/D_ ratio equivalent to 1. Additionally, the operational temperature and all the remaining parameters concerning implementing a concentrating solar tower, such as the number of heliostats and tower dimensions, were determined. The open-access software System Advisor Model (SAM) was used to model the concentrated solar power plant for electricity generation in all its configurations [51]. Its creation comes from the National Renewable Energy Laboratory in the United States (NREL) and is updated yearly in different and better versions.