# Feasibility Analysis of Industrial High-Temperature Heat Pumps in Greece
## 2 Materials and Methods
### Followed Methodology  
This analysis is performed with a developed thermodynamic model which has been implemented in the Engineering Equation Solver [19]. The model includes the equations described in Section 2.2. The used tool solves all the non-linear equations together through iterations. Table 1 summarizes the input parameters of this work, while Table 2 presents the range of the parameters that are investigated parametrically in this analysis. For the capacity of the process heat, the nominal value is selected at 300 kW. For the case of the ambient source, an hourly-based model was considered to account for the yearly variation in the environmental temperature. The weather data of Athens in Greece (latitude 38\({}^{\circ}\), longitude 23.7\({}^{\circ}\)) were considered, and they were retrieved from Ref. [25]. Figure 2 depicts the ambient temperature variation for Athens.  
The system examined was compared to a conventional natural gas boiler (baseline scenario), aiming to determine economic and environmental benefits. The total boiler  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Value** \\ \hline Isentropic efficiency of the compressor & \(\eta_{\text{lis}}\) & 70\% \\ \hline Motor and shaft efficiency & \(\eta_{\text{motor}}\) & 90\% \\ \hline WHS mass flow rate & \(\text{m}_{\text{w}}\) & 10 kg/s \\ \hline Specific heat capacity of the WHS & \(\text{c}_{\text{p,w}}\) & 1.1 kJ/kgK \\ \hline Specific heat capacity of the thermal oil & \(\text{c}_{\text{p,s}}\) & 1.9 kJ/kgK \\ \hline Temperature difference of the thermal oil & \(\Delta\text{T}_{\text{s}}\) & 5 K \\ \hline Pinch point in the heat exchangers & PP & 5 K \\ \hline Default ambient temperature & \(\text{T}_{\text{am}}\) & 25 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 1: Basic input parameters in this work.  
\begin{table}
\begin{tabular}{c c c} \hline
**Parameter** & **Symbol** & **Range** \\ \hline Process heat capacity & \(\text{Q}_{\text{process}}\) & 100 to 500 kW \\ \hline Process heat temperature level & \(\text{T}_{\text{process}}\) & 100 to 180 \({}^{\circ}\)C \\ \hline WHS inlet temperature & \(\text{T}_{\text{win}}\) & 50 to 100 \({}^{\circ}\)C \\ \hline \end{tabular}
\end{table}
Table 2: Ranges of the variable parameters studied in this work.  
Figure 2: Ambient temperature variation during the year for Athens, Greece.  
efficiency was set at 70% [26], the natural gas cost at 0.06 EUR/kWh\({}_{\text{th}}\)[27] and the CO\({}_{2}\) specific emissions factor at 0.196 kgC\({}_{\text{O}2}\)/kWh [28]. The specific cost of the HTTP was set at 300 EUR/kWh [2], and the electricity cost at 0.15 EUR/kWh (a reasonable value for the Greek market [29; 30]). The yearly maintenance cost of a HTTP was considered to be 2% of the capital cost, and the same value in Euros was selected as the maintenance cost in the boiler scenario. The specific CO\({}_{2}\) emissions factor for the electricity was set at 0.252 kgC\({}_{\text{O}2}\)/kWh for Greece [31]. The economic analysis was conducted for a lifetime period of N = 25 years and for a discount factor of r = 3%. The life cycle costs of the unit with HTTP and with the boiler were calculated using the present methodology of Ref. [32], considering that the process heat is produced for 8760 h per year. Table 3 summarizes the aforementioned data.  
Finally, it should be stated that the present thermodynamic model of the HTTP was developed based on fundamental energy balance equations. The validation of this study relies on the authors' previous study [22; 32], which also involves high-temperature heat pumps. In particular, the study [22] includes validation evidence derived from the existing literature [24].