# Techno-Economic Potential of Plasma-Based CO\({}_{2}\) Splitting in Power-to-Liquid Plants
## 3 Methodology
### Methodology of Techno-Economic Analysis  
The technical evaluation of the overall process was carried out via the process efficiency:  
\[\eta_{PTL}=\frac{\dot{m}_{product}\cdot LHV_{product}}{P_{e,tot}} \tag{9}\]  
This relates the mass of the product produced together with its lower heating value to the total electrical power input:  
\[P_{e,tot}=P_{Plasma}+P_{EL}+P_{GDE}+\sum P_{pump}+\sum P_{c}+\sum P_{t} \tag{10}\]  
\(P_{Plasma}\): Power of plasma-based CO\({}_{2}\) splitting;  
\(P_{EL}\): Power of electrolysis system;  
\(P_{GDE}\): Power of gas diffusion electrode;  
\(P_{pump}\): Power of water pump;  
\(P_{c}\): Power of a compressor;  
\(P_{t}\): Power of a turbine. The techno-economic analysis focused on the calculation of the fuel costs incurred. The calculation methodology presented by [PERSON] et al. was applied in a modified form [12]. Using the technically proven components represented in the industry, a deviation of \(+/-30\%\) can be assumed for this type of cost estimation. Due to the inclusion of new components, such as the plasma reactor and the GDE, further deviations are to be expected. However, it is sufficient for a first estimation. In the process, equipment costs were first calculated using variables that arose in the individual components, which led to the capital costs \(CAPEX\) via various factors. In addition to \(CAPEX\), operating costs \(OPEX\) were determined, which were divided into indirect and direct costs. In addition, labor costs were determined. The equipment costs:  
\[EC_{i}=CF_{i}\cdot\left(\frac{CEPCI}{CEPCI_{ref}}\right)\cdot F_{mat}\cdot F_{ press} \tag{11}\]  
Consist of the cost functions \(CF_{i}\), which determines the cost dimension of the device from technical quantities, the chemical engineering plant cost index (\(CEPCI\)), which includes the time of the determination of the cost function, and factors due to higher requirements regarding material and pressure. After that, the fixed capital investment for each component was calculated through:  
\[FCI_{i}=EC_{i}\cdot\left(1+\sum_{j=1}^{10}F_{j}\right)\cdot\left(1+\sum_{j=11} ^{12}F_{j}\right) \tag{12}\]  
Considering additional costs represented as factors \(F_{j}\), these additional costs incurred were divided by [PERSON] et al. into twelve areas or relationship factors. \(F_{1}\) considers installation costs, \(F_{2}\) instrumentation costs, \(F_{3}\) necessary piping, \(F_{4}\) electrical to be installed, \(F_{5}\) building costs, \(F_{6}\) site improvements, and \(F_{7}\) installed service facilities. Factors \(F_{8}\), \(F_{9}\), and \(F_{10}\) consider indirect plant costs such as engineering, supervision, construction costs, and legal fees. \(F_{11}\) and \(F_{12}\) consider contractor fees and contingencies, and random events [12]. For the whole capital expenditure, a capital factor of 0.9 was used. For amortization of the \(CAPEX\), over a plant lifetime \(y\) in years, the annual capital costs \(ACC\) are calculated with the annuity factor \(AF\) and the interest rate \(IR\). \[CAPEX=\frac{\sum FCI_{i}}{0.9} \tag{13}\]  
\[ACC=CAPEX\cdot\left(0.9\cdot AF+0.1\cdot IR\right) \tag{14}\]  
\[AAF=\left(1+IR\right)^{y}\cdot\frac{IR}{\left(1+IR\right)^{y}-1} \tag{15}\]  
In addition to capital costs, operating costs also play a role in the production costs of fuels. These operational expenditures (\(OPEX\)) can be divided into direct and indirect costs. Direct operating costs  
\[OPEX_{dir}=\sum\dot{m}_{i}\cdot c_{i}+\sum P_{j}\cdot c_{e}+\sum\dot{Q}_{i} \cdot c_{Q} \tag{16}\]  
include costs through expenses and revenues and refer to specific market prices \(c_{i}\). Direct operating costs thus refer to raw materials required, and by-products produced \(\dot{m}_{i}\) (\(c_{i}\)), as well as outputs \(P_{j}\) (\(c_{e}\)) and heat flows \(\dot{Q}\) (\(c_{Q}\)). In our model, no heat flows were drawn externally due to heat integration, so this term was omitted. Indirect operating costs \(OPEX\) include accruing maintenance costs, operating material costs, and laboratory fees.