# Furniture Wood Waste Management Towards the Circular Economy
## 2 Materials and Methods
### Circularity Indicator
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Symbol** & **Definition** & & & \\ \hline \multirow{2}{*}{_WO_} & Mass of unrecoverable waste through a product material going into landfill, waste to energy and any other type of process where the materials are no longer recoverable & \\ \hline \multirow{2}{*}{_WC_} & Mass of unrecoverable waste generated in the process of recycling parts of a product & \\ \hline \multirow{2}{*}{_WF_} & Mass of unrecoverable waste generated when producing recycled feedstock for a product & \\ \hline \multirow{2}{*}{_LFI_} & Linear Flow Index & & \\ \hline \multirow{2}{*}{_F(X)_} & Utility factor built as a function of the utility X of a product & \\ \hline \multirow{2}{*}{_X_} & Utility of a product & & \\ \hline \multirow{2}{*}{_L_} & Actual average lifetime of a product & & \\ \hline \multirow{2}{*}{_Law_} & Average lifetime of an industry-average product of the same type & & \\ \hline \multirow{2}{*}{_ER_} & Recovery energy & & \\ \hline \multirow{2}{*}{_HHV_} & Higher heating value & & \\ \hline \multirow{2}{*}{_MB_} & Mass of biological material & & \\ \hline \multirow{2}{*}{_U_} & Actual average number of functional units achieved during the use phase of a product & & \\ \hline \multirow{2}{*}{_Uav_} & Average number of functional units achieved during the use phase of an industry-aveerge product of the same type & \\ \hline \multirow{2}{*}{_MClp_} & Material Circularity Indicator of a product & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._ \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Input Data for MCI**} \\ \hline
**Factor** & **Unity** & **MDF** & **MDP** & **Brick** \\ \hline M & kg & 690 & 630 & 1 \\ \hline FR & \% & 0.172 & 0.170 & 0.1045 \\ \hline FU & \% & 0.00 & 0.00 & 0.00 \\ \hline FS & \% & 0.688 & 0.680 & 0.00 \\ \hline Cc & \% & 0.00 & 0.00 & 0.00 \\ \hline CE & \% & 0.05 & 0.05 & 0.12 \\ \hline CR & \% & 0.95 & 0.95 & 1.00 \\ \hline CU & \% & 0.00 & 0.00 & 0.00 \\ \hline EC & Factor & 0.95 & 0.95 & 0.95 \\ \hline EF & Factor & 0.95 & 0.95 & 0.95 \\ \hline Bc & \% & 0.45 & 0.45 & 0.00 \\ \hline MB & kg & 593.4 & 535.5 & 0.110 \\ \hline F(x) & Factor & 0.9 & 0.9 & 0.9 \\ \hline L & years & 20 & 20 & 40 \\ \hline LAV & years & 20 & 20 & 40 \\ \hline U & qtt & 0.80 & 0.80 & 1.00 \\ \hline UAV & qtt & 0.80 & 0.80 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Input data for computing the circularity indicator from Scenarios 1–3. Equation (1) of the LFI quantifies how much material comes from virgin raw material and ends as irrecoverable waste. LFI presents a value between 0 and 1, in which 0 is a circular flow and 1 is totally linear. The same is calculated using the following equation:  
\[LFI=\frac{V+W}{2M+\frac{W/-Wc}{2}} \tag{1}\]  
Equation (2) of the MCI considers the LFI and an F(X) factor, which is constructed as an F function with X utility. It is calculated using the following equation:  
\[\textbf{{MCI}}=\textbf{1}-\textbf{{LFI}}\cdot\textbf{{F}}(\textbf{{X}}) \tag{2}\]  
The data collected for the LCA studies conducted in Scenarios 1 to 3 in [PERSON] et al. [8] served as the basis for composing the input parameters for calculating the MCI, which are presented in Table 2. The mass (M) represents the weight of each finished product, while FR represents the percentage of wood waste incorporated into MDF, MDP, and ceramic brick. FS denotes the fraction of biological raw material originating from sustainable sources. In the panels, FR and the FS were calculated considering only the final wood incorporated. It was possible to exclude the value of other raw materials contained in the product; thus, V = 148.35 kg for MDF and V = 113.40 kg for MDP. The values of 108.33 kg (20% \(w/w\)) and 433.32 kg (80% \(w/w\)) are associated with MDF, respectively, for FR and FS. Regarding MDP, 113.4 kg (20% \(w/w\)) is related to FR and 413.28 kg (80% \(w/w\)) to FS. The FR of the ceramic brick corresponds to 0.111 kg (11% \(w/w\)).