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Energies 2021, 14, 365 6 of 13 arose as the most influencing parameters, and they were considered for the correlations and the correction factors. Then, the outputs from the simplified computational tool (X, Y) involve a close connec- tion to some technical and design parameters (PCM mass, system volume, temperatures of flue gases outlet, temperature of the air stream outlet, charging and discharging periods, investment costs). These relationships may be linear, polynomial, logarithmic, potential, etc. The selection of proper correlations consists of finding a strong correlation, that is, high squared-correlation coefficient (R2), and minimising the deviation of the relationship calcu- lated compared with the detailed simulation results. An example of a possible correlation is presented in Equation (4): Xi = a · MRPb·xi (4) where a and b are the correlation coefficients and the MRP. For instance, in order to determine the solidification and the melting periods, the MRPs chosen were the system storage capacity and the PCM thermal conductivity. Other correlations follow the structure represented in Equation (5): Yi =ci +MRPi·di (5) ci and di being coefficients for the linear equation and the MRPi applicable to the specific “i” output equation. For instance, this correlation type was applied to calculate the investment cost of the PCM-TES system in function of the VPCM that needed to be introduced in the PCM-TES and the operating temperature from which the heat was going to be recovered. 2.4. Multicriteria Approach A multicriteria approach was applied to evaluate energy, economic, and environmental savings. From the energy perspective, the heat that was recovered and able to be reused was the most valuable input, along with the PCM-TES system performance indicators defined in the above section. The modelling results consider that the heat sources were available for full charging or discharging of the PCM-TES system. In the economic assessment, the techno-economic indicators and costs incurred for a furnace including a PCM-TES system were calculated for the viability assessment. Namely, the net savings (k€/yr) were considered to calculate the net savings, similar to a net present value (NPV) with no interest rate, and the ratio €saved/€invested presents an estimation of the profitability of the PCM-TES as WHR strategy. The investment cost of the PCM-TES system was calculated considering both the costs of the storage core material (the PCM itself) and the costs of the storage system infrastructure. This cost followed the linear correlation in Equation (5) as a fixed cost (ci) in addition to a ratio in function of the PCM volume to be stored (VPCM) as one of the MRP. This ratio (di) was higher when the operational temperature of the flue gases and the PCM melting temperature were at very high levels (>700 ◦C), since the material costs rise considerably. With this information, it was also possible to calculate the latent storage capacity cost (€/kWh) of the different PCM-TES systems analysed as the ratio of the total investment costs for a system and the total amount of thermal energy [kWh] that this system stores and recovers during its lifetime. During charging, there was not any saving in comparison to the initial operating mode of the furnace. However, significant fossil fuel savings (NGsaved in economic terms) were obtained annually when the PCM-TES system discharged the accumulated heat according to Equation (6). NGsaved = Esaved · nocycles· ndays ·LHVNG · ρNG · cNG (6) Esaved being the energy saved per one cycle of operation, nocycles the number of daily cycles that the PCM-TES could perform as maximum depending on the discharge+charge periods, and ndays is the number of working days considered per year (260 days). The considerations assumed for the natural gas (NG) are: lower heating value (LHV) = 15.75 kWh/kg; densityPDF Image | Latent Heat Storage for Waste Heat Recovery in the Energy Industry
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