## 2 Experiments
### Experimental Methods  
A STA449F3 device as a thermo-gravimetric analyzer was adopted for the experiment. The samples were put in an Al\({}_{2}\)O\({}_{3}\) container with a continuous gas flow, and heated from 50 to 950 \({}^{\circ}\)C. The co-firing experiment for sludge and coal was carried out in two atmospheres: one was an O\({}_{2}\)/N\({}_{2}\) atmosphere and the other was an O\({}_{2}\)/CO\({}_{2}\) atmosphere. The experimental device is shown in Figure 1.  
The co-combustion characteristics of diverse blending rates of brewery wastewater sludge are presented and compared. The effects of the physical properties of N\({}_{2}\) and CO\({}_{2}\) gas on the TG/DTG curve were explored. The effects of different oxygen concentrations on the ignition, burnout, and Comprehensive Combustion Index (CCI) characteristics of the samples under the O\({}_{2}\)/CO\({}_{2}\) atmosphere were investigated. The CCI indicates the ignition and burnout performance of fuel. The larger the ignition and burnout index, the better the comprehensive combustion behavior. Table 2 shows the experimental cases for this study. There are two main indexes for experimental sample combustion: ignition temperature and burnout temperature, which are important parameters to characterize combustion characteristics. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Items**} & \multicolumn{3}{c}{**Proximate Analysis (w/\%)**} & \multicolumn{3}{c}{**Ultimate Analysis (w/\%)**} & \multirow{2}{*}{**O\({}_{\text{net, ad}}\)/(MJ \(\times\) kg\({}^{-1}\))**} \\ \cline{2-2} \cline{5-8}  & **M\({}_{\text{ad}}\)** & **A\({}_{\text{ad}}\)** & **V\({}_{\text{ad}}\)** & **FC\({}_{\text{ad}}\)** & **C\({}_{\text{ad}}\)** & **H\({}_{\text{ad}}\)** & **N\({}_{\text{ad}}\)** \\ \hline BC & 4.78 & 44.66 & 6.78 & 43.78 & 42.26 & 2.12 & 0.52 & 17.12 \\ SD & 2.33 & 59.86 & 37.72 & 0.09 & 17.6 & 2.93 & 2.41 & 6.56 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Proximate and ultimate analysis of the sludge and coal. Figure 1: The thermo-gravimetric analyzer. \begin{table}
\begin{tabular}{c c c} \hline \hline \multicolumn{1}{c}{**Experimental Items**} & **Atmosphere** & **Heating Rate (\({}^{\circ}\)C/min)** \\ \hline SD, BC & 21\% O\({}_{2}\)/79\% N\({}_{2}\) & 20 \\
85\% BC + 15\% SD & 21\% O\({}_{2}\)/79\% CO\({}_{2}\) & 20 \\
75\% BC + 25\% SD & 21\% O\({}_{2}\)/79\% CO\({}_{2}\) & 20 \\ \hline
15\% SD + 85\% BC & 21\% O\({}_{2}\)/79\% CO\({}_{2}\) & 20 \\
30\% O\({}_{2}\)/70\% CO\({}_{2}\) & 20 \\
40\% O\({}_{2}\)/60\% CO\({}_{2}\) & 20 \\ \hline
15\% SD + 85\% BC & 21\% O\({}_{2}\)/79\% N\({}_{2}\) & 10 \\
21\% O\({}_{2}\)/79\% N\({}_{2}\) & 20 \\
21\% O\({}_{2}\)/79\% N\({}_{2}\) & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental cases. The ignition and burnout temperature can be confirmed by the thermo-gravimetric curve, such as the DTG weight loss rate method, the DTG curve demarcation point method, the tangent method, and so on [16; 17; 18; 19; 20]. The ignition temperature refers to the value at which the sample begins to ignite and the ignition temperature can better characterize the difficulty of igniting the fuel. In this study, the tangent method was adopted to determine the ignition temperature of these samples and the first point of a high weight loss rate on the DTG curve was put to use as a vertical line. The TG curve and vertical line have intersection points. The tangent line of the TG curve is made through the intersection point and the temperature corresponding to the intersection point of the tangent line and the smooth baseline after the fuel is dehydrated and dried is determined to be the ignition temperature, \(T_{\rm i}\). The burnout temperature refers to the point at which TG and DTG no longer undergo significant mass changes. \(T_{\rm b}\) is defined by the DTG weight loss rate method: the temperature corresponding to the time when the DTG curve reaches \(-1\) wt%/min at the end of the reaction is defined as the burnout temperature of \(T_{\rm b}\).