# Plant Design for the Conversion of Plastic Waste into Valuable Chemicals (Alkyl Aromatics)
## 3 Results and Discussion
### Absorption Column  
The material and energy balance of the absorption column is an important tool for understanding the performance of the column. Table 25 summarizes the mass and energy flowing into and out of the column. The table also shows the heat of adsorption and the heat losses from the column. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{\begin{tabular}{c} **Molar Mass** \\ **(kg/mol)** \\ \end{tabular} } & \multirow{2}{*}{**Composition**} & \multirow{2}{*}{\begin{tabular}{c} **Mass Flow** \\ **Rate (kg/hr)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Molar Flow** \\ **Rate (mol/hr)** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **\(\Delta\)C\_AT** \\ **(kJ/kg)** \\ \end{tabular} } & \multirow{2}{*}{**H (kJ/hr)**} \\ \hline Polyethylene & S1 & & & & Input & & \\  & & 3500 & 1 & 5000 & 1.428571429 & 100.75 & 503,750 \\  & Total & & 1 & 5000 & 1.428571429 & — & 503,750 \\ \hline \multirow{4}{*}{\
\begin{tabular}{c} Gases \\ \end{tabular} } & S2 & & & Output & & & \\  & Total & 182.2 & 1 & 750 & 4.116355653 & — & 390,000 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} Alkylbenzene \\ Tetalin \\ Alkyl naphthalene \\ Naphthene \\ Cycloalkane \\ Unreacted polyethylene \\ Total \\ \end{tabular} } & 106.16 & 0.258823529 & 1100 & 10.36171816 & 130 & 143,000 \\  & 160.25 & 0.188235294 & 800 & 4.992199688 & 195 & 156,000 \\  & 156.22 & 0.094117647 & 400 & 2.560491614 & 260 & 104,000 \\  & 152.28 & 0.117647059 & 500 & 3.283425269 & 325 & 162,500 \\  & 112.21 & 0.2 & 850 & 7.575082435 & 390 & 331,500 \\ \cline{1-1}  & 3500 & 0.141176471 & 600 & 0.171428571 & 455 & 273,000 \\ \cline{1-1}  & Total & & 1 & 4250 & 28.94434574 & — & 1,170,000 \\ \hline \hline \end{tabular}
\end{table} 
Table 24: Material and energy balance of the reactor. Figure 6 shows that as the weight of the catalyst increases, the conversion rate of the reaction increases because the number of active sites available for the reaction also increases. Likewise, Figure 7 shows that as the volume of the reactor increases, the conversion rate of the reaction increases because the number of active sites available for the reaction also increases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multicolumn{2}{c}{**Molar Mass**} & \multirow{2}{*}{**Composition**} & \multicolumn{2}{c}{**Mass Flow Rate**} & \multirow{2}{*}{**Molar Flow Rate**} \\  & & **(kg/mol)** & & **(kg/hr)** & **(mol/hr)** \\ \hline \multicolumn{4}{c}{S4} & \multicolumn{2}{c}{Input} \\ Alkylbenzene & 106.16 & 0.285714286 & 1100 & 10.36171816 \\ Tetralin & 160.25 & 0.207792208 & 800 & 4.992199688 \\ Naphthene & 152.28 & 0.12987013 & 500 & 3.283425269 \\ Cycloalkane & 112.21 & 0.220779221 & 850 & 7.575082435 \\ Unreacted polyethylene & 3500 & 0.155844156 & 600 & 0.171428571 \\ Total & & 1 & 3850 & 26.38385412 \\ \hline \multicolumn{4}{c}{Top} & \multicolumn{2}{c}{Output} \\ Naphthene & 152.28 & 0.99 & 439.5175847 & 2.886246288 \\ Alkylbenzene & 106.16 & 0.01 & 0.212776885 & 0.002004304 \\ Total & & 1 & 439.7303615 & 2.888250591 \\ \hline \multicolumn{4}{c}{Bottom} & \multicolumn{2}{c}{Output} \\ Alkylbenzene & 106.16 & 0.029218651 & 18.21152166 & 0.171547868 \\ Unreacted polyethylene & 3500 & 0.029198332 & 600 & 0.171428571 \\ Tetralin & 160.25 & 0.850289435 & 800 & 4.992199688 \\ Naphthene & 152.28 & 0.009543607 & 8.532584189 & 0.056032205 \\ Cycloalkane & 112.21 & 0.081749975 & 53.85727285 & 0.479968567 \\ Total & & 1 & 1480.601379 & 5.871176899 \\ \hline \multicolumn{4}{c}{Heat duty of condenser = Qc = 13,009.42 kW; Heat duty of boiler = Qb = 19,565.42 kW.} \\ \end{tabular}
\end{table} 
Table 26: Material and energy balance of the distillation column.