## 3 Results and Discussion
### Compensating for ICP Losses  
In this section, we compare the performance of three versions of the solution-diffusion model: the ideal model, a model that considers ICP, and a model that considers ICP plus rotational kinetic energy. As we are not considering the effects of other phenomena like external concentration polarization (ECP), the simulated values obtained for water flow and power density are overestimated when compared with experimental results in spiral-wound modules from works like [19; 20], but it is considered that the results are coherent for the simulated conditions.  
Figure 4 shows how increasing the angular velocity \(\omega\) for the system under ICP conditions increments its water flow to match the ideal model water flow. For this simulation, \(\Delta P\) is set to reach the ideal maximum power for the given concentration. For a PRO system working near the maximum power operating point, it would be possible to actively compensate for water flow losses over time that are intrinsic to PRO operation.  
Figure 5 presents the required angular velocity needed to compensate for ICP losses with a fixed concentration difference of approximately 35 g/kg for different values of draw solution concentration. From these results, it could be inferred that even if the \(\Delta\Pi\) is the same, for higher concentrations of the feed and draw solutions, the angular velocity needed to compensate for the water flow losses will increase in a non-linear fashion.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Mechanism radius (\(r_{M}\)) & 0.5 m \\ Angular velocity (\(\omega\)) & 0–2700 rev/min \\ Membrane water permeability (\(A\)) & 1.763 \(\times\) 10\({}^{-12}\) [m/s Pa] \\ Membrane solute permeability (\(B\)) & 1.17 \(\times\) 10\({}^{-7}\) [m/s] \\ Solute resistivity (\(K\)) & 3.38 \(\times\) 10\({}^{5}\) [s/m] \\ Temperature (\(T\)) & 25 [\({}^{\circ}\)] \\ Atmospheric pressure (\(P\)) & 0.101325 [MPa] \\ Draw solution concentration (\(C_{2}\)) & 35 g/kg \\ Draw solution flow rate (\(Q_{\!f\!\!Figure 6 illustrates how ICP losses can be compensated for various \(\Delta\Pi\) values. The results indicate that the angular velocity \(\omega\) does not increase significantly, even when \(\Delta\Pi\) is doubled. Since the theoretical extractable energy rises with \(\Delta\Pi\), this suggests that in a PRO system utilizing rotational kinetic energy, the net available energy--after accounting for ICP losses--will be higher for greater \(\Delta\Pi\) values. In other words, the proportion of rotational kinetic energy required to offset ICP losses will decrease as the salinity gradient increases.  
Figure 7 shows the water flow under variations of the applied hydraulic pressure \(P_{D}\). A fixed value of \(\omega\) was used to bring the system from ICP levels to the ideal model level. Similarly, Figure 8 presents the power density variation for the three models due to variation in the applied \(P_{D}\).  
Figure 5: ICP losses compensated for different draw solution concentrations and a fixed concentration difference.  
Figure 6: ICP losses compensated for some concentration differences.