# Reverse Electrodialysis: Potential Reduction in Energy and Emissions of Desalination
## 2 Methods
### Estimation of RED's Technical Performance: Net Power and Specific Energy  
We assessed the performance of the up-scaled RED system--i.e., the net power production and net energy recovery of the RED plant--in every scenario, in the process simulation software Aspen Plus(r) V11 (AspenTech, Bedford, MA, USA) [60], importing a custom RED stack model implemented in Aspen Custom Modeler(r) V11 (AspenTech) [61]. All simulations refer to a commercial RED unit (Fumatech GmbH(r), St. Ingbert, Germany) with an assumed number of cell pairs (cp) representative of industrial-scale stacks reported in the literature (Table 2) [20; 62]. We developed a RED system mathematical model, fully descriived in [PERSON] et al. [24] and [PERSON] et al. [63], and extensively validated it in several works of our research group [19; 24; 25; 64] to predict RED performance in a wide range of working conditions at different descriptive extents from cell pair to plant scale [63]. We estimated the SGE recovery potential in every scenario according to (i) the maximum work attainable (thermodynamic limit), which reduces to the Gibbs free energy of mixing, Equation (A1); and (ii) the net specific energy (net energy per cubic meter of desalted water), and net power density (net power per membrane pair effective area) of the RED system under net power optimal working conditions--diluate concentration, diluate and concentrate flowrate and electric current (Table 3)--of the RED stack. We performed parametric evaluations in Aspen Plus to identify the optimal working conditions in each location [63]. Assuming:  
* High-pressure (HP) RO pass' concentrate effluent was fully and evenly fed to the high-saline compartments of the RED units;
* Equal temperature--set according to location--for both concentrate and diluate streams;
* Unlimited diluate feed volume for energy conversion. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Number of cell pairs, N\({}_{\text{cp}}\) (-) & 1000 \\ Channel size, b (m) \(\times\) L (m) & 0.383 \(\times\) 0.456 \\
**Spacers** & \\ Thickness, \(\delta_{\text{SP}}\) (\(\mu\)m) & 270 1 \\ Porosity, \(\varepsilon\) (-) & 82.5\% \\
**Reference properties: fumasep® CEM (FKS-50)/AEM (FAS-50)** \\ Areal resistance, R\({}_{\text{IEM0}}\) (\(\Omega\) cm\({}^{2}\)) & 1.8/0.6 2 \\ Permselectivity, \(\alpha_{\text{IEM0}}\) (-) & 0.97/0.92 3 \\ Thickness dry, \(\delta_{\text{IEM}}\) (\(\mu\)m) & 50 \\ Active area, A\({}_{\text{m,eff}}=\) b \(\times\) L (m\({}^{2}\)) & 0.175 \\ \hline \hline \end{tabular} \({}^{1}\) Equal to inter-membrane distance—i.e., height of the high- or low-salinity (HC or LC) channels. 2 Measured in 0.5 M NaCl at 25 \({}^{\circ}\)C. 3 Measured in 0.5 M NaCl at 25 \({}^{\circ}\)C.  
\end{table} 
Table 2: Parameters of the commercial RED stack (Fumatatech GmbH®, Germany). The RED plant layout combines series and parallel arrangements of the RED units (Figure 2) to even out the power output and energy yield of the whole system; however, the salinity gradient--i.e., the driving force--declines through the downstream series units, thus undermining the net power density of the RED plant. Hence, to quantify the highest power density and energy yield attainable in each scenario, we computed the RED plant's supply under optimal net power conditions for two hydraulic configurations of the RED units: a multi-stage (series) and a single-stage (parallel) arrangement (Figure 2). The series layout provides the maximum specific energy, since it recovers a larger fraction of the SGE for conversion, while the parallel layout offers the highest power density, as all the RED units process the largest concentration gradient.