## 3 Results and Discussion  
Figures 3 and 4 show the different SOWs considering the different BWRO configurations (1:0, 2:0...) and two different \(C_{\rm f}\) (1.2 and 5.8 g L\({}^{-1}\), respectively). The irregularities in the contours of the surfaces are due to the \(p_{\rm f}\) and \(Q_{\rm f}\) steps. It can be observed that with lower \(C_{\rm f}\) there is greater separation along the x-axis between the different SOWs. This is because low osmotic pressure of the  
Figure 2: Inputs and outputs of the calculation algorithm. feed solution allows water production with low \(P_{\text{in}}\), which can result in SWMMs operating outside their recommended range (in terms of \(Q_{\text{r-min}}\)) due to the very high permeate production of the first SWMMs. Figure 3 shows a possible operating range for the 1.0 configuration at very low \(P_{\text{in}}\). However, the 2:0, 3:0 and 3:1 configurations can be discarded, as higher permeate productions can be attained with the 2:1 and 3:2 configurations with the same \(P_{\text{in}}\). The same occurs when considering higher \(C_{\text{f}}\) (Figure 4), although in this case the operating range of configuration 1:0 is shorter. Having higher \(C_{\text{f}}\) means higher osmotic pressure and a lower number of operating points that are outside the recommended range. This is because the first SWMMs do not produce a high amount of permeate due to osmotic pressure, resulting in the subsequent SWMMs remaining within the recommended range since, as we move along the PV, the SWMMs produce less permeate flow. For the solution with higher \(C_{\text{f}}\), operating conditions with higher \(P_{\text{in}}\) were found to be suitable as higher osmotic pressure allows the BWRO system to remain within the SOW. However, the energy required is also higher and production is decreased compared to the case with lower \(C_{\text{f}}\). It can be appreciated how permeate production of more than 700 m\({}^{3}\) d\({}^{-1}\) can be obtained with sample 20 as feed solution (Figure 3), whereas, with sample 11 as feed solution, permeate production is below 600 m\({}^{3}\) d\({}^{-1}\) and more energy is required. The SOWs are affected by SWMM characteristics such as \(S_{\text{m}}\) or permeability coefficients. As a result of changes in these characteristics, there is a shift in the SOWS and, consequently, in the optimal operating points. Figure 3: Permeate production for different BWRO configurations using sample 20 (Table 1) as \(C_{\text{f}}\). Figures 5 and 6 show the \(R\) for the most relevant BWRO system configurations (1:0, 2:1 and 3:2), considering the \(C_{\rm f}\) of samples 20 and 11, respectively. A wider operating range can be observed for configuration 3:2. This is due to the higher number of SWMMs allowing more possible operating points without exceeding the membrane manufacturer constraints. Higher \(R\) values were obtained for the configurations with two stages as more SWMMS are arranged in series in this sort of configuration. While the highest \(R\) can be attained with both the 2:1 and 3:2 configurations, the 2:1 configuration requires less input power but has a lower production than the 3:2 configuration (Figure 3). The highest \(R\) value attained with a single-stage configuration was around 60%. Considering as \(C_{\rm f}\) a feed solution with higher \(TDS_{\rm f}\) (5.82 g L\({}^{-1}\)), the surfaces of the three configurations considered are closer together, as observed previously (Figure 4). The change in feedwater inorganic composition results in a decrease in \(R_{\rm max}\). With higher \(TDS_{\rm f}\), the difference in terms of \(R\) between the single- and two-stage configurations is lower. It should be mentioned that, in terms of production, the 2-stage configurations outperform the others as more SWMMs are arranged in series and so more elements are producing permeate. The influence of \(TDS_{\rm f}\) (and therefore of \(\pi\)) can be observed by comparing Figures 5 and 6.