# Mathematics-Driven Analysis of Offshore Green Hydrogen Stations
## 3 Results
when \(\alpha_{solar\_elevation}\) is at its highest throughout the different days of the year, which occurs during the local summer months. However, in both Figure 5a,b, it can be observed that the average density of reflected solar radiation, \(I_{n\_reflected}\), reaches its minimum when \(\alpha_{solar\_elevation}\) is at its maximum, at 12 p.m. This situation can be explained by considering that, according to [PERSON]'s law, \(I_{n\_reflected}\) depends on \(\alpha_{incident}\), which increases when \(\alpha_{solar\_elevation}\) is lower, at sunrise and sunset. As expressed in equation (Equation (27)), the total radiation density (\(I_{n\_total}\)) is the sum of direct radiation (\(I_{n\_direct}\)) and reflected radiation (\(I_{n\_reflected}\)). The contribution \(I_{n\_reflected}\) becomes more significant during periods of low \(\alpha_{solar\_elevation}\). In the case under analysis, the contribution of \(I_{n\_reflected}\) leads to an average increase of 18.2% in the \(I_{n\_total}\) received--when averaged over the hours of a typical day--and 10.54% when averaged over the days of the year. A vertical axis of symmetry is observed in both Figure 5a,b, centered around the position of the maximum value. The subsequent step in the mathematics-driven analysis process involves estimating the average energy consumption of the station's electrolyzer and adiabatic compressor. (Equation (41)). To this end, it is necessary to configure the model input parameters related to the electrolyzer and the adiabatic compressor, which are summarized in Table 3.  
In this way, the produced and stored hydrogen flow rate (\(\frac{\text{mol}_{H_{2}}}{\text{s}\times\text{m}^{2}}\)) and (\(\frac{\text{kg}_{H_{2}}}{\text{s}\times\text{m}^{2}}\)), as well as the amount of water consumed (\(\frac{\text{kg}_{H_{2}}}{\text{s}\times\text{m}^{2}}\)), are obtained. Figure 6a,b present the results represented in a day-year format. Additionally, the results for both electrolyzer models  
\begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Value** \\ \hline Number of moles \((N_{mol})\): & 1 \\ Electrolyzer type (i): & ALK, PEM \\ Selected heating value constant (\(HV\)): & LHV \\ Conversion efficiency of both electrolyzer types \((K_{electrolyte\_i})\): & PEM = 0.7 \\  & \(K_{electrolyte\_i}\)\(=K_{electrolyte\_DEM}\times R_{ALK\_DEM}\) \\  & (Equation (32)) \\  & 0.7 \\  & Operating ambient temperature \((T_{in})\): & 12.5 \({}^{\circ}\)C \\  & \\  & \(\text{}\text{}\text{}\text{}\text{}\are included. Depending on the relationship \(R_{ALK\_DEM}\) and the pressures \(P_{ALK}\) and \(P_{PEM}\), different outcomes are obtained. As observed in all the graphs in Figure 6, the maximum values obtained using the PEM electrolyzer are slightly lower than those obtained with the ALK electrolyzer simulation conducted for the year 2025. In any case, as previously mentioned, the relationship \(R_{ALK\_DEM}\) is a parameter dependent on the year (_year_) in which this study is conducted. In the case under study, the superior performance of ALK technology over PEM--quantified using the \(R_{ALK\_DEM}\) ratio applicable to the year 2025--results in a 4.19% increase in the green hydrogen output rate, expressed in both \(\frac{\text{mol}_{\text{H}_{2}}}{\text{s}\times\text{m}^{2}}\) and \(\frac{\text{kg}_{\text{H}_{2}}}{\text{s}\times\text{m}^{2}}\), for an equivalent level of received total \(I_{n\_total}\). This performance difference between the two technologies is expected to diminish over time as their respective efficiencies progressively converge. Figure 7 shows the amount of water (\(l\)) consumed per second (\(s\)) in relation to the available solar panel surface area, expressed in square meters (m\({}^{2}\)). The 4.19% increase in green hydrogen production is proportionally reflected in the amount of water required at the input of the electrolyzer.