## 2 Materials and Methods
### System Modeling  
The simulation of the integrated co-gasification system of MSW and BC in CO\({}_{2}\)/O\({}_{2}\) atmosphere is developed by using the Aspen plus software, and the detailed flowchart is displayed in Figure 2. In the ASU subsystem, a standard double column process is utilized in the O\({}_{2}\) production, which is also widely used by the ASU manufacturers [29]. After three-stage centrifugal compression, the feeding air is first purified by the molecular sieve adsorber (MSA) and is then divided into two streams. One stream directly enters into the low distillation column (LDC) after heat exchanger (EX-1), and another stream first enters into the expander and then enters the high distillation column (HDC). The separation of air is achieved in these two distillation columns, and finally the oxygen discharged from the HDC is re-heated in EX-1 exchanger and sent to the co-gasification chamber. By the calculation and analysis of power consumption in the ASU, the energy consumption of unit produced oxygen is 0.324 kWh/Nm\({}^{3}\) when the mole fraction of oxygen is 95%; approximate result obtained from literature [21]. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Samples** & \multicolumn{4}{c}{**Ultimate Analyses (wt%)**} & \multicolumn{4}{c}{**Proximate Analyses (wt%)**} \\ \hline MSW & C\({}_{\text{d}}\) & \(H_{\text{d}}\) & \(O_{\text{d}}\) & \(N_{\text{d}}\) & \(S_{\text{d}}\) & \(Cl_{\text{d}}\) & \(M_{\text{ar}}\) & \(V_{\text{d}}\) & \(FC_{\text{d}}\) & \(A_{\text{d}}\) & HHV (MJ/kg) \\ [23] & 34.62 & 4.87 & 23.63 & 1.29 & 0.31 & 0.67 & 48 & 57.77 & 7.62 & 34.61 & 14.687 \\ \hline BC & \(C_{\text{ad}}\) & \(H_{\text{ad}}\) & \(O_{\text{ad}}\) & \(N_{\text{ad}}\) & \(S_{\text{ad}}\) & \(Cl_{\text{ad}}\) & \(M_{\text{ad}}\) & \(V_{\text{ad}}\) & \(FC_{\text{ad}}\) & \(A_{\text{ad}}\) & LHV (MJ/kg) \\ [24] & 71.86 & 4.15 & 11.05 & 0.88 & 0.36 & 0 & 6.9 & 32.79 & 55.51 & 4.80 & 27.68 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The proximate and the ultimate analyses of raw municipal solid waste (MSW) and bituminous coal. \begin{table}
\begin{tabular}{l l l l} \hline \hline
**ID** & **Chemical Reaction** & \multicolumn{2}{c}{**Reaction Heat**} \\  & & & **(AH)** & **Reaction Name** \\ \hline R1 & MSW/coal \(\rightarrow\) Dried MSW/coal + H\({}_{2}\)O & – & Drying \\ R2 & Dried MSW/coal \(\rightarrow\) Char + CO + H\({}_{2}\) + CO\({}_{2}\) + H\({}_{2}\)O + H\({}_{2}\)S + N\({}_{2}\) + CH\({}_{4}\) + Tar & – \\ R3 & C + 0.5O\({}_{2}\)\(\leftrightarrow\) CO & – & \(-\)111 MJ/kmol & Partial oxidation \\ R4 & C + CO\({}_{2}\)\(\leftrightarrow\) ZCO & +172 MJ/kmol & Boudouard \\ R5 & C + H\({}_{2}\)O \(\leftrightarrow\) CO + H\({}_{2}\) & +131 MJ/kmol & Steam reforming \\ R6 & C + 2H\({}_{2}\)\(\leftrightarrow\) CH\({}_{4}\) & –74 MJ/kmol & Methanation \\ R7 & H + 0.5O\({}_{2}\)\(\leftrightarrow\) H\({}_{2}\)O & –484 MJ/kmol & H\({}_{2}\) oxidation \\ R8 & CO + 0.5O\({}_{2}\)\(\leftrightarrow\) CO\({}_{2}\) & –284 MJ/kmol & CO combustion \\ R9 & CO + H\({}_{2}\)O \(\leftrightarrow\) CO\({}_{2}\) + H\({}_{2}\) & –41 MJ/kmol & Water gas shift \\ R10 & CH\({}_{4}\) + H\({}_{2}\)O \(\leftrightarrow\) CO + 3H\({}_{2}\) & +206 MJ/kmol & Methane-steam reforming \\ R11 & CH\({}_{4}\) + CO\({}_{2}\)\(\leftrightarrow\) ZCO + 2H\({}_{2}\) & +247 MJ/kmol & Methane-CO\({}_{2}\) reforming \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Chemical reactions in the co-gasification process of MSW and bituminous coal (BC) [25; 26; 27; 28]. In the co-gasification subsystem of MSW and BC, a total of 100 kg/h blends of feed fuels are used in all cases. The MSW and BC first are dried in the RYield block, and the released H\({}_{2}\)O component is directly sent to the gasification unit. The gasification process is modeled by the RYield and RGIBBS blocks. The devolatilization process of MSW/BC is achieved by this RYIELD block, which is used to model a reactor when the reaction stoichiometry and kinetics are unknown [30].