## 2 Materials and Methods
### Goal and Scope Definition
#### 2.1.7 Method for Estimating CO\({}_{2}\) Emissions  
The equation for calculating the CO\({}_{2}\) emission is shown in Equation (7). \[\text{E}_{\text{CO2}}=\text{E}_{1}+\text{E}_{2}+\text{E}_{3}+\text{E}_{4}+\text{ E}_{5}-\text{S}_{1}-\text{S}_{2}-\text{S}_{3}, \tag{7}\]  
where  
\(\text{E}_{\text{CO2}}=\text{Total annual CO}_{2}\) emissions for each case [t-CO\({}_{2}\)/Y]  
\(\text{E}_{1}=\text{Total annual CO}_{2}\) emissions from waste incineration [t-CO\({}_{2}\)/Y]  
\(\text{E}_{2}=\text{Total annual CO}_{2}\) emissions from electricity consumption of the waste incineration plant during suspension periods [t-CO\({}_{2}\)/Y]  
\(\text{E}_{3}=\text{Total annual CO}_{2}\) emissions from electricity consumption of biogas power generation facilities [t-CO\({}_{2}\)/Y]  
\(\text{E}_{4}=\text{Total annual CO}_{2}\) emissions generated during transportation [t-CO\({}_{2}\)/Y]  
\(\text{E}_{5}=\text{Total annual CO}_{2}\) emissions from N\({}_{2}\)O generated during waste incineration [t-CO\({}_{2}\)/Y]  
\(\text{S}_{1}=\text{Total annual CO}_{2}\) emissions reduced by waste power generation [t-CO\({}_{2}\)/Y]  
\(\text{S}_{2}=\text{Total annual CO}_{2}\) emissions reduced by biogas power generation [t-CO\({}_{2}\)/Y]  
\(\text{S}_{3}=\text{Total annual CO}_{2}\) emissions that could be reduced through in-house consumption or heat supply to neighboring facilities. [t-CO\({}_{2}\)/Y]. Equation (8) through Equation (20) show how to calculate the values required by Equation (7). In Equation (8), paper waste and food waste are excluded because they are carbon-neutral, and only plastic and other waste are included in the calculation. In addition, the annual waste disposal volume was calculated based on the waste volume input to the waste incineration shown in Figures 2 and 3 and the number of working days shown in Table 6. For Case 1 and Case 2, it was 145,600 [t-waste/Y], and for Case 3 and Case 4, it was 128,484 [t-waste/Y]. \[\text{E}_{1}=\text{V}_{\text{W}}\times\left(\gamma_{\text{p}}+\gamma_{\text{ o}}\right)\times\frac{\gamma_{\text{p}}\times\gamma_{\text{pc}}+\gamma_{\text{o}} \times\gamma_{\text{oc}}}{\gamma_{\text{p}}+\gamma_{\text{oc}}}\times\frac{ \gamma_{\text{pc}}\times\text{C}_{\text{p}}\times\gamma_{\text{p}}+\gamma_{ \text{oc}}\times\text{C}_{\text{o}}\times\gamma_{\text{o}}}{\gamma_{\text{pc}} \times\gamma_{\text{p}}+\gamma_{\text{oc}}\times\gamma_{\text{o}}}\times\frac {44}{12}, \tag{8}\]  
where  
\(\text{V}_{\text{W}}=\text{Annual waste disposal volume}=\text{145,600 or 128,484 [t-waste/Y]}\)  
\(\gamma_{\text{p}}=\text{Weight composition percentage of plastic = 13.7 or 15.5 [%]}\)  
\(\gamma_{\text{o}}=\text{Weight composition percentage of other waste}=\text{26.2 or 29.7 [%]}\)  
\(\gamma_{\text{pc}}=\text{Percentage of combustible content of plastic = 74 [%]}\)  
\(\gamma_{\text{oc}}=\text{Percentage of combustible content of other waste}=\text{51 [%]}\)  
\(\text{C}_{\text{p}}=\text{Percentage of carbon content in plastic = 74 [%]}\)  
\(\text{C}_{\text{o}}=\text{Percentage of carbon content in other waste}=\text{40 [%]}\). \begin{table}
\begin{tabular}{c c} \hline \hline
**Item** & **Value** \\ \hline Steam transportation distance (km) & 3 \\ Steam piping unit price (100 million Yen/km) & 13.95 \\ Piping heat loss (\%) & 20 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Setting conditions for using heat. In Equation (9), the waste incineration facility's power consumption was conditioned to be purchased from outside only when the incinerator was suspended. Therefore, we used 5.5 kWh/t-waste, which was the power consumption of waste incineration during suspension periods shown in Table 6[37]. \[\mathrm{E}_{2}=5.5\times\mathrm{V}_{\mathrm{W}}\times\mathrm{E}_{\mathrm{e}}, \tag{9}\]  
where  
\(\mathrm{E}_{\mathrm{e}}=\mathrm{Electric}\) power emission factor = 0.512 [kg-CO\({}_{2}\)/kWh]. In Equation (10), the power consumption of biogas power generation was calculated as the sum of the power required in mixing, digestion, dewatering, and incineration.