# Techno-Economic Potential of Plasma-Based CO\({}_{2}\) Splitting in Power-to-Liquid Plants
## 3 Methodology
### Boundary Conditions
The cost functions chosen for the plasma reactors (DBD and GA) should only apply to system sizes of 3 MW and above. Below this limit, we assumed the EUR/kW value of 3 MW, which was EUR 1.300/kW for DBD. This coincided well with the cost of a reactor calculated by [PERSON] et al. [34]. To create a cost function (\(CF=f(P,...)\)) for the plasma reactors, NREL's 2019 publication of manufacturing costs for PEM electrolyzers was used [50]. Since the reactor systems must first be manufactured, costs for the equipment needed for this were included. The costs of the PEM-EL systems considered there were not only composed of direct and indirect costs. The model used in the publication considered:  
The diagram in accordance with the study, shown in Figure 8, reflects how the capital costs for the production facilities and ancillary costs for buildings, labor, etc., decreased when increasing the produced system power. Furthermore, as system power increased, material costs and balance of the plant (BOP) costs also decreased. The data were used to estimate DBD and GA reactor cost functions. Since there was no water cycle involved in the plasma reactors, this part of the BOP was omitted. In addition, cooling cycles were  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  
modeled and simulated separately in the model, so these costs were also omitted. Since the considered GA-plasma reactor was made of other materials due to a higher temperature level, the material costs in the cost function were increased from EUR 200 to EUR 400. The GDE cost function assumptions result from calculations with alkaline electrolysis parameters, voltage, and current density, in combination with specific electrolysis system costs [6]. To calculate the direct \(OPEX\), the specific costs are listed in Table 5. The specific cost of CO\({}_{2}\) arises from the use of a carbon capture system to clean exhaust gas from a cement plant [50]. The initially assumed electricity costs resulted from averaged market prices from 2018. Later, these costs were again varied based on studies that formulated outlook. In Table 6, factors are listed thatwere used for the calculation of the indirect \(OPEX\). For the methodology, the study by [PERSON] et al. and the book on plant design and economics were used [12; 47]. The indirect \(OPEX\) was then calculated according to  
\[OPEX,ind=\sum_{k=1}^{8}OPEX,ind,k \tag{18}\]  
from the sum of the individual quantities. Figure 8: Specific manufacturing costs over system-power of PEM electrolysis systems in accordance with the study of the NREL in 2019 [50]. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Expense/Revenue** & **Specific Cost** & **Reference** \\ \hline Carbon dioxide (CO\({}_{2}\)) & EUR 63/t & [50] \\ Oxygen (O\({}_{2}\)) & EUR 30/t & [34] \\ Water (H\({}_{2}\)O) & EUR 1/t & BEnViVer \\ Cooling water & EUR 0.004/m\({}^{3}\) & BEnViVer \\ Waste water & EUR 3.8/m\({}^{3}\) & BEnViVer \\ Steam & EUR 16.17/t & BEnViVer \\ electricity & EUR 50/MWh & [51] \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Specific costs of expenses and revenues for OPEX calculations.