## 3 Results and Discussion  
The monthly potential, \(E\), and current density, \(j\), histories of an industrial electrolyser between 2008 and 2016 are shown in Figure 2.  
During the studied period, two sets of membranes and two sets of electrodes were inserted in the electrolyser. Chronologically, the data collection began in 2008, at the middle age of the electrodes (69 months) and with fresh membranes. At instant corresponding to an age equal to 117 months of the electrodes and equal to 48 months of the membranes, both electrodes and membranes were replaced and the time counting of the electrodes and membranes, respectively \(t_{\text{e}}\) and \(t_{\text{mi}}\), was reset to 0--cf. Figure 2. The first set of membranes was named #m1 and the second #m2; likewise, the first and second set of electrodes were named #e1 and #e2, respectively--cf. Figure 2. For each month in Figure 2, parameters \(E_{0}\) and \(k\)-factor were calculated by the Equation (11), which are plotted in Figure 3.  
Typically, \(E_{0}\) takes a value between 2.20 and 2.60 V and \(k\)-factor between 0.05 and 0.15 V\(\cdot\)kA\({}^{-1}\cdot\)m\({}^{2}\), when the membrane surface area is equal to 1.5 m\({}^{2}\), according to good operating principals for the chlor-alkali industry [22]. For a membrane area of 5.4 m\({}^{2}\), \(E_{0}\) should be between 2.40 and 2.80 V and the \(k\)-factor between 0.15 and 0.25 V\(\cdot\)kA\({}^{-1}\cdot\)m\({}^{2}\). For the investigated bipolar membrane electrolyser, electrodes display a surface area around 3 m\({}^{2}\). The first sets of electrodes and membranes (#e1 and #m1) display \(E_{0}\) values between 2.49 and 2.60 V and \(k\)-factor between 0.14 and 0.19 V\(\cdot\)kA\({}^{-1}\cdot\)m\({}^{2}\)--cf. Figure 2: Potential (\(\blacklozenge\)), \(E\), and current density (-), \(j\), as a function of the electrode and membrane service times, respectively \(t_{\text{e}}\) and \(t_{\text{mi}}\). Figure 3. After their replacement (corresponded to #e2 and #m2 period), \(E_{0}\) values are between 2.46 and 2.56 V and \(k\)-factor between 0.13 and 0.18 V\(\cdot\)kA\({}^{-1}\cdot\)m\({}^{2}\)--cf. Figure 3. These results are within the reported normal range of \(k\)-factor. In this period, the \(k\)-factor values are smaller, which indicates a smaller ohmic resistance related to the use of different type of membranes. Figure 4 shows the normalized potential, \(E_{ij,0}\) and the correspondent ohmic resistance, equal to \((E\)-\(E_{0})\cdot j^{-1}\), as a function of the respective electrode service time, \(t_{\text{e}}\), and membrane service time, \(t_{\text{mi}}\). Figure 4 shows that \(E_{j,0}\) starts at 3.22 V and increases ca. 200 mV over the 2012-2016 period, for the set #e2 and #m2 and for the set#e1 and #m1, over the 2008-2012 period, the initial value of the normalized potential is about the same (\(E_{j,0}=3.25\) V) but, the potential increase is smaller, approximately 100 mV. Comparing Figures 2 and 4, it can be observed that the potential normalization methodology allows for smoothing the production peaks and determining the effective progression of the potential over time due degradation of the elements of the electrolyser. Between the 79 and 95 months of the electrode service time, the ohmic resistance displays various peaks. These peaks are related to an experimental period to the maintenance of the membrane procedure that was discontinued, and no other peaks are observed afterwards. After the 95 months of the electrode service time, the normalized potential remains to increase slowly but, the ohmic resistances sharp growth. In this case, the electrodes contribution for the ohmic resistance was not negligible due to a significant deactivation, as assigned in Equation (13); the timely replacement or recoating of the electrodes prevented an expectable exponential growth of the potential [6; 9]. Figure 5 plots the activation and ohmic overpotentials (\(\eta_{\text{act}}\)\({}^{\prime}\) and \(\eta_{\text{C,I}}\)\({}^{\prime}\)) obtained from Equations (16) and (17).