## 3 Results and Discussion
### Effect of Heat Pump Set-Point Temperature  
Firstly, the impact of the heat pump set-point on the production of water was investigated. A vacuum scenario of 0.26 bar absolute pressure (\(\Delta\)p = 0.75 bar) was selected to investigate the impact of the temperature considered as the set-point. The heat pump operates to produce the required thermal load to heat the brine at the heat pump's condenser. The target temperature (set-point) constitutes the condensation temperature of the heat pump, operating until the brine reaches this temperature before it enters the flash tank. If the brine reaches this temperature, the heat pump stops its operation. The recirculation ratio (Equation (1)) defines the fraction of the brine that recirculates. A high recirculation ratio indicates that only a small fraction of the brine comes from the RO unit with a lower temperature, while the largest fraction has a temperature close to the set-point of the heat pump (due to recirculation); thus, the heat pump is mostly needed to operate to fully heat up the amount of brine that comes from RO (in addition to some heat losses to the environment of the recirculating amount that are also taken into account). For that reason, high recirculating ratios demonstrate lower energy consumption. At low recirculation ratios, the heat pump does not always reach the desired set-point temperature, since the required heating load happens to be higher than the heat pump capacity in some conditions. Figure 4: Validation of the current model compared with commercial software for the heat capacity and COP estimation at the evaporation temperature of 32 \({}^{\circ}\)C.  
Figure 5 shows the water production from the flash evaporation as the recirculation ratio increases from 70 up to 98%. Figure 5a presents the produced water in m\({}^{3}\)/h, while Figure 5b shows the percentage of water that is recovered from the initial feed brine. It is observed that, as the recirculation ratio increases, the water production increases up to 0.2 m\({}^{3}\)/h when the set-point for the temperature is 85 \({}^{\circ}\)C and the recirculation ratio is 95%, while for a higher recirculation ratio, this production decreases. When the recirculation ratio is too high, there is only a small flow of brine coming from RO to substitute the rejected brine to the sea. Therefore, the recirculating brine presents high salinity and the vapor production in the flash tank needs extra pressure difference from the vacuum pump, leading to reduced water production. The water production experiences the same behavior when the set-point is at 80 \({}^{\circ}\)C. In the case that the temperature is set at 75 \({}^{\circ}\)C, the water production remains relatively stable, around 0.128 m\({}^{3}\)/h, when the recirculation ratio is higher than 85% and exibits a slight decrease after 97%. For the water recovery, it is clear that it increases with the recirculation ratio and also when the set-point temperature increases. Figure 6 demonstrates the mean concentration in salinity of the liquid brine that flows out of the tank. It was noticed that the salinity increases as the recirculation ratio and the set-point temperature increases. This can be explained by the higher water production, which means that a higher fraction is vaporized and in turn, the remaining brine presents higher salinity. The thermodynamic properties of the model do not present the appropriate accuracy for salinity higher than 12%, but the results are presented to show the trend. Figure 7 illustrates the electric power consumption for the respective water production for each set-point of the heat pump.