# A Review of the Water Desalination Technologies
## 3 Statistics on Desalination
\[\eta_{ex}=\frac{Q_{least}^{min}}{Q_{sep}}=\frac{Q_{least}^{min}}{Q_{least}^{ min}+\tau_{0}S_{gen}^{TDS}\left(1-\frac{\tau_{0}}{\tau_{H}}\right)^{-1}}=\frac{Q_{ least}^{min}}{Q_{least}+\tau_{0}S_{gen}^{RDS}\left(1-\frac{\tau_{0}}{\tau_{H}} \right)^{-1}} \tag{5}\]  
Similarly, the term \(Q_{least}\) is introduced, representing the least thermal input requirement, assuming significant freshwater production (RR > 0). [PERSON] et al. analyzed the energy performances of developed desalination technologies, obtaining the results reported in Figure 37 (based on data reported in [89]). The graph reports the exergy efficiency according to Equation (3) for technologies requiring mechanical (or electrical) energy and Equation (5) in case of thermally supplied technologies. The authors considered a seawater salinity equal to 4.2% in case of MED and MSF units, and 3.5% (common seawater) in the other cases. The graph emphasizes the high exergy efficiency of RO and the low value of DC-MD; but the result is contrary if entropy generation is considered as indicator [89]. In the case of MED units, the high entropy generation is essentially related to the finite temperature differences between fluids. In fact, considering a simple unit with 6 effects, [PERSON] et al. demonstrated that entropy generation is essentially related to the effects (56.5%), the feed heaters (12.3%) and the condenser (21.8%). Figure 36: Least work as function of recovery ratio and salinity of feedwater and freshwater. Reproduced from [95] (CC BY-NC-SA 3.0). It is significant to underline that a significant amount of energy is irreversibly wasted as the produced brine and freshwater have a higher temperature than the environmental conditions. Due to the limited temperature differences between the fluids and the environments, the entropy generation is only the 6.2% [89]. MSF unit are also affected by the thermal gradient between fluids. It is evaluated that the entropy is mainly generated by feed heaters (73.9%) and brine heater (12.5%), where the temperature difference is higher. The temperature disequilibrium between produced freshwater and brine affects also MSF, causing an entropy generation equal to 10% [89]. The only solution to improve the exergy efficiency of thermally driven desalination processes is the increasing of the sizes or the number of heat exchangers in order to reduce the temperature difference between primary and secondary fluids. However, this approach is limited by the fact that increasing the sizes of the heat exchangers raises the initial investment of the plant that which may not be counterbalanced by the economic value of the energy saving [90]. The direct contact membrane distillation is a very energy consuming process. As shown in Figure 37, the exergy efficiency is equal to 1%, with an entropy generation equal to 925.4 J/(kg-K). The entropy is essentially generated by four items: pressure drop through the module (34.5%), temperature difference in the heater (26.3%), temperature disequilibrium between feedwater, freshwater and brine (22.9%) and temperature difference inside the regenerator (16.3%). In the case of MVC units, the entropy is essentially generated by the finite temperature difference inside the evaporator-condenser (57.2%), the irreversibility of the mechanical compressor (28.1%) and the temperature difference in the regenerator (10.9%). To improve the exergy efficiency, the main solution is the reduction of the temperature difference between the condensing steam and the evaporating brine inside the evaporator-compressor. Therefore, the irreversibility from the heat transfer and the mechanical compressor are both reduced, thanks to the reduction of the compression work. On the other side, the cost for the desalination unit is increased [14]. According to data above reported, the RO unit represents the most efficient technology for desalination, if the energy recovery system is adopted. The exergy efficiency is equal to 31.9% in the case reported by [PERSON] et al. [89].