## 2 Methodology
### Plant Performance Indicators  
To assess the performance in terms of efficiency and emissions of the different H\({}_{2}\)-power production processes, several indicators are defined in this section. The H\({}_{2}\)-power production plant can be envisaged as represented in Figure 11, attending to the products and by-products derived from it. The H\({}_{2}\) efficiency \(\eta_{H_{2}}\) in Equation (8) is determined as the relation between the heating value output of the H\({}_{2}\) stream and the heating value of the natural gas feed. However, this plant metric falls short to evaluate the electricity and steam demand or production that may take place in each of the plants. To fully account for these items, the equivalent natural gas feed \(\dot{m}_{NG,eq}\) is calculated by subtracting (or adding) to the original feed the corresponding amount that would be required to generate the same quantity of steam or electricity as the current plant is exporting or importing, given a predefined benchmark efficiency for such production, as represented in Equation (9). In this way, a homogenous or equivalent efficiency \(\eta_{H_{2},eq}\) is defined in Equation (10). In previous works [22], it was shown that GSR H\({}_{2}\) concepts are reliant on electricity imports. On the other hand, it is frequent that substantial LP steam is produced as well. On some occasions, this steam can be utilized by other processes, and is accounted for in the equivalent efficiency calculation. However, it may be the case that there is no useful application for this steam, therefore the equivalent efficiency is recalculated accounting only for the electricity by-product (or import thereof), and denoted by a superscript in Equations (11) and (12). \[\eta_{H_{2}}=\frac{\dot{m}_{H_{2}}LHV_{H_{2}}}{\dot{m}_{NG}LHV_{NG}} \tag{8}\]  
\[\dot{m}_{NG,eq}=\left(\dot{m}_{NG}LHV_{NG}-\frac{\dot{W}_{el}}{\eta_{el}}- \frac{\dot{Q}_{th}}{\eta_{th}}\right)/LHV_{NG} \tag{9}\]  
\[\eta_{H_{2},eq}=\frac{\dot{m}_{H_{2}}LHV_{H_{2}}}{\dot{m}_{NG,eq}LHV_{NG}} \tag{10}\]  
Figure 11: Simplified layout of the H\({}_{2}\)-power plant. \[\dot{m}_{NG,eq}^{\prime}=\left(\dot{m}_{NG}LHV_{NG}-\frac{\dot{W}_{e}}{\eta_{e}} \right)/LHV_{NG} \tag{11}\]  
\[\eta_{H_{2},eq}^{\prime}=\frac{\dot{m}_{H_{2}}LHV_{H_{2}}}{\dot{m}_{NG,eq}^{ \prime}LHV_{NG}}. \tag{12}\]  
In terms of CO\({}_{2}\) emissions performance, a similar approach is followed. The specific emissions \(E_{CO_{2}}\) calculated by Equation (13) are given in g of CO\({}_{2}\) per MJ of H\({}_{2}\) product. Alongside this, the capture ratio CC is the relation of the mass flow rate of CO\({}_{2}\) that is captured divided by the CO\({}_{2}\) intensity of the fuel \(E_{NG}\) as shown in Equation (16). When considering equivalent emissions \(E_{CO_{2},eq}\), the corresponding intensity of emissions avoided, derived from an alternative benchmark process for steam \(E_{th}\) and electricity production \(E_{el}\), are accounted for and presented in Equation (14). The CO\({}_{2}\) avoidance is consequently defined by Equations (17) and (18) when steam is or is not considered as a useful product, respectively. Finally, the Specific Primary Energy Consumption of CO\({}_{2}\) Avoided (\(SPECCA\)) of every concept with CO\({}_{2}\) capture is calculated using the equivalent efficiency and emissions of the unabated SMR process as reference plant, as shown in Equation (19). This parameter gives an indication of the original fuel heating value that must be invested due to the integration of a CO\({}_{2}\) capture technology in the plant.