## 3 Thermodynamic Behavior of the ORC-TER System
(**a**) Thermal efficiency as a function of the boiler saturation temperature at different efficiency of the turbine. (**b**) Exergetic efficiency of the ORC-TES system at a fixed pinch temperature of 10 \({}^{\circ}\)C with Therminol LT (thermal point No. 1). Solid-black line corresponds to benchmark case, solid green-line corresponds to C1, and dashed green-line to C2. system optimization, as selecting a boiler temperature in proximity to this minimum allows for a balanced design that reduces equipment size while maintaining efficient operation. Once the working fluid flow rates are characterized, it becomes essential to compare them with the thermal oil flows, which constitutes a critical design parameter for the boiler. Figure 6a-c illustrates the mass flow rates of the thermal oils, while Figure 6d-f presents the corresponding volumetric flow rates as functions of the working fluid saturation temperature, under three different pinch-point temperature conditions. In all mass flow cases, C2 exhibits higher flow rates compared to the configuration that follows the working fluid temperature profile. A similar behavior is observed in the volumetric flows, where the thermophysical properties of each oil influence the slope and magnitude of the curves. For instance, Oil 2 displays limited thermal expansion across the evaluated pinch-point temperature range. Additionally, a notable variation in flow behavior is observed at higher working fluid temperatures (above approximately 80 \({}^{\circ}\)C), where flow rates either significantly increase or decrease depending on the configuration. This effect must be considered in the design of heat exchangers. Although C2 achieves superior efficiency, it also demands higher flow rates, which in turn increases the required heat transfer surface and equipment size. Therefore, while elevated working fluid temperatures enhance system efficiency, their impact on the physical dimensions and overall feasibility of the thermal equipment must be carefully balanced during the design phase. Figure 7 provides a general overview of the thermodynamic behavior of the cycle in the absence of the thermal oil heating system. Although the behaviors are independent of the thermal oil configuration, the analysis offers valuable insights into the internal heat distribution and phase change characteristics. In Figure 7a, the black bold line represents the total heat input to the boiler, while the crimson line denotes the heat distribution between the boiler and the heater. An inverse trend is observed: as the boiler temperature approaches the critical point of the working fluid, the heat in the boiler decreases, whereas the heat absorbed in the heater increases. Despite the differing heat transfer mechanisms, the total energy input remains almost constant, maintaining thermal balance and aiding in equipment sizing. Additionally, Figure 7b presents the vapor fraction at the boiler outlet. As shown, increasing the boiler temperature results in a higher proportion of liquid phase at the outlet. However, the vapor fraction remains below 0.90 in all cases, ensuring stable operation within the design specifications. Figure 5: Working fluid flow rates as a function of turbomachinery characteristics and boiler temperature. (**a**) Mass flow rate. (**b**) Volumetric flow rate. The previous analysis indicates that the design and operational parameters converge to favorable values around 80 \({}^{\circ}\)C for R134a, the working fluid under study. Therefore, a detailed discussion of system performance at the aforementioned temperature is warranted to elucidate its behavior near optimal operating conditions. This evaluation should account for the fact that the system performance is not affected by the presence of a significant amount of noise. Figure 6: Mass (**a**–**c**) and volumetric (**d**–**f**) flow rates of the thermal oils under study. Solid lines represent C1, while dashed lines correspond to C2. Blue, green, and crimson lines indicate pinch-point temperatures of 5, 10, and 15 \({}^{\circ}\)C, respectively.