# A Review of the Water Desalination Technologies
## 3 Statistics on Desalination
On the contrary, exergy also represents the minimal energy required by a system to achieve a desired condition, starting from the environmental state, and adopting only reversible processes. In this optic, the efficiency analysis performed according to the Second Thermodynamic Law is a successful tool for suggesting solutions to improve the energy efficiency of the existing desalination technologies. A detailed exergy analysis is reported in [89], where each component is firstly modelled and then analyzed. In the case of desalination plants requiring a mechanical energy input (or electricity), the exergy efficiency is evaluated by Equation (3), defining \(W_{least}^{min}\) as the least work of separation required for an infinitesimal recovery ratio (RR, defined in the previous Equation (2)). \[\eta_{ex}=\frac{W_{least}^{min}}{W_{Sep}}=\frac{W_{least}^{min}}{W_{least}^{ min}+\tau_{0}S_{gen}^{TDS}}=\frac{W_{least}^{min}}{W_{least}+\tau_{0}S_{gen}^{RDS}} \tag{3}\]  
\(W_{sep}\) is the work required by the real desalination plant, which can be expressed as the sum of the least work, plus the total entropy generation \(S_{gen}^{TDS}\) (referred to as the Total Dead State), multiplied by the absolute environmental temperature \(\tau_{0}\). According to the definition of \(W_{least}^{min}\), this value is achievable if all processes are reversible and the freshwater production is infinitesimal. As a real process is designed to produce a significant amount of freshwater, the least work demand is introduced \(W_{least}\). This term has a greater value than \(W_{least}^{min}\), as it includes the entropy generation associated with the condition RR > 0. The remaining entropy generation \(S_{gen}^{RDS}\) (related to the Restricted Dead State) is associated only to the irreversibility of the adopted technologies (finite thermal differences, pressure drops, etc.). The trend of \(W_{least}\) is reported in Figure 36, as a function of the recovery ratio and the salinity concentration of freshwater and feed water. As introduced before, \(W_{least}^{min}\) is equal to \(W_{least}\) if the recovery ratio is equal to zero. In the case of seawater (salinity 35 g/kg), zero salinity in produced freshwater and environmental temperature fixed to 25 \({}^{\circ}\)C, \(W_{least}^{min}\) is equal to 2.71 kJ/kg (of freshwater) [89; 95]. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Technology**} & \multirow{2}{*}{**Average Capacity**} & \multirow{2}{*}{**Input**} & \multirow{2}{*}{**Recovery**} & \multirow{2}{*}{**Water Quality**} & \multicolumn{2}{c}{**Energy Consumption**} & \multirow{2}{*}{**Water Cost**} \\  & & & & & **[ppm]** & & **Electrical** & **Thermal** \\  & & & & & **[kWh/m3]** & [k/kg] & \\ \hline MED & 0.6–30 & SW & 0.25 & 10 & 1.5–2.5 & 230–390 & 0.52–1.5 \\ TVC & 10–35 & SW & 0.25 & 10 & 1.5–2.5 & 145–390 & 0.87–0.95 \\ MSF & 50–70 & SW & 0.22 & 10 & 4–6 & 190–390 & 0.56–1.75 \\ MVC & 0.1–3 & SW & & 10 & 6–12 & no & 2.0–2.6 \\ SWRO & 1–320 & SW & 0.42 & 400–500 & 3–6 & no & 0.45–1.72 \\ BWRO & Up to 98 & BW & 0.65 & 200–500 & 1.5–2.5 & no & 0.26–1.33 \\ ED & Up to 145 & BW & 0.9 & 150–500 & 2.64–5.5 & no & 0.6–1.05 \\ \hline \hline \end{tabular} Note: SW is the abbreviation of Seawater; BW brackish water.  
\end{table} 
Table 1: The state of the art of commercial desalination technologies. In the case of desalination plants supplied by thermal energy, Equation (5) can be adopted, where \(Q_{least}^{min}\) is the least thermal energy required with an infinitesimal recovery ratio. This term depends also on the temperature of the thermal source \(\tau_{H}\), introducing the Carnot factor \(\left(1-\frac{\tau_{0}}{\tau_{H}}\right)\), which physically represents the ratio of heat that can be converted into exergy, using a reversible thermal machine. \[Q_{least}^{min}=W_{least}^{min}\left(1-\frac{\tau_{0}}{\tau_{H}}\right)^{-1} \tag{4}\]  
So, the exergy efficiency can be evaluated by Equation (5), defining \(Q_{sep}\) as the thermal requirement for the real plant.