## 2 Materials and Methods
### Methodology Adaptations for the Circular Index (Circulability Model)
#### 2.2.1 Energy Material Equivalents  
Energy consumption values have to be converted into material equivalents, as mentioned in Table 1. The methodology to do so was developed by Enel [22] and is briefly explained below.  
The energy-to-material conversion is based on three main assumptions:  
* The material equivalent of a given amount of energy represents the amount of resources consumed to produce it.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Product** & **Scenario** & **System Description** & **Source** \\ \hline Wood vinegar & 4 & Wood vinegar from unspecified wood biomass. Wood dust disposed of as waste. NCG and biocrude oil are used to produce heat. Biochar and surplus biocrude oil are outputs & \\ \hline \multirow{4}{*}{Spent mushroom substrate} & 1 & Spent mushroom substrate from _garicus bisporus_, produced in Mediterranean Europe & \\  & 2 & Spent mushroom substrate from _garicus bisporus_, produced in central Europe & [28] \\ \cline{1-1} \cline{2-4}  & 3 & Spent mushroom substrate from _garicus bisporus_, produced in northern Europe & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._* For calculation purposes, material consumption from non-renewable energy sources is not considered. While these sources do involve material use during the construction of infrastructure and technology, it is assumed that, strictly speaking, their material consumption during the electricity generation phase is negligible. Therefore, their material equivalent is set to zero.
* Thermal and nuclear energy material equivalents are obtained through the gross calorific value (GCV) for fossil fuels and the uranium yield for nuclear.  
By following these assumptions, an electric conversion factor (ECF) can be obtained and used to convert any electricity consumption into a material equivalent, following the relevant national electricity mix.  
To obtain the ECF, the national electricity production of a given year has to be disaggregated into the specific energy sources (e.g., wind, solar PV, biomass, hydro, geothermal, nuclear, coal, natural gas, petroleum, other fuels, etc.). Each one of these items consists of a value in energy units (GWh, for instance). Then, the GCV and yields presented in Table 3 are used to obtain an assumed amount of material needed to produce such electricity.  
The annual electricity production per source can thus be divided by the values contained in Table 3, resulting in material amounts. The next step is to divide the total material needs by the total annual electricity production--including those from renewable sources--which results in the ECF, in mass/energy units (e.g., kg/GWh). Figure 2 illustrates the calculation process.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Energy Vector** & **GCV/Yield (GWh/kg)** & **Source** \\ \hline Coal & 6.67 \(\times\) 10\({}^{-6}\) & [46] \\ \hline Natural gas & 1.54 \(\times\) 10\({}^{-5}\) & [47] \\ \hline Uranium & 0.43 & [48] \\ \hline Petroleum naphtha & 1.34 \(\times\) 10\({}^{-5}\) & [49] \\ \hline Heavy fuel oil & 1.16 \(\times\) 10\({}^{-5}\) & [49] \\ \hline \hline \end{tabular}
\end{table}
Table 3: Gross calorific values and yield values used for obtaining the electric conversion factor for a specific country’s electricity mix.  
Figure 2: Calculation process of the electric conversion factor used for obtaining the CI. Adapted from Enel [22].  
Finally, the electricity consumptions reported in the LCI are multiplied by the ECF, resulting in the corresponding material equivalent in mass units (e.g., kg).