# Design of Pyrolysis Plant for Waste Methyl Ethyl Ketone from the Polarizer Manufacturing Process
## 2 Materials and Methods
### Detection and Computational Detail  
The product gas was analyzed using Nondispersive infrared gas detectors (NDIR, Molecular Analysis 6000i), Fourier-transform infrared spectrometer (FTIR, Jasco FTIR-6700), and Gas Chromatography (GC, Agilent 7890B). Fuel gas yield (mmole/g) was defined as the mass ratio of the sum of H\({}_{2}\), CO, CH\({}_{4}\), and C\({}_{2}\)H\({}_{4}\) produced in the pyrolysis reactor. This study does not consider the potential deviation of H and O resulting from the glue due to its negligible amount. The carbon ratio was determined through weight comparison to check against the theoretical reaction equation. The amount of carbon formed was measured by extracting samples from the reactors in each experiment to validate the equation. The fraction of gas mixtures was defined using the ideal gas principle and the following equations. \[\mathrm{H_{2}~{}yield~{}(Y_{H_{2}})}=\frac{\mathrm{H_{2}~{}yield~{}in~{}the~{} reactor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{1}\]  
\[\mathrm{CO~{}yield~{}(Y_{CO})}=\frac{\mathrm{CO~{}yield~{}in~{}the~{} reactor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{2}\]  
\[\mathrm{CH_{4}~{}yield~{}(Y_{CH_{4}})}=\frac{\mathrm{CH_{4}~{}yield~{}in~{}the~{ }factor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{3}\]  
\[\mathrm{C_{2}H_{4}~{}yield~{}(Y_{C_{2}H_{4}})}=\frac{\mathrm{C_{2}H_{4}~{}yield~{} in~{}the~{}factor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{4}\]  
Fuel gas yield \((Y_{fuel})=\mathrm{H_{2}~{}yield~{}+~{}CO~{}yield~{}+~{}CH_{4}~{}yield~{}+~{} C_{2}H_{4}~{}yield}\)  
Figure 4: The 3D plant of fuelizing waste organic solvent system. \[\mathrm{Y_{H_{2}}}=\frac{\mathrm{F_{N_{2}}}}{1-\left(\mathrm{X_{CO}+X_{CO_{2}}+X_{ CH_{4}}+X_{C_{2}H_{4}}+X_{H_{2}}}\right)}\times\frac{\mathrm{X_{H_{2}}}}{\mathrm{F_{MEK} }\times\mathrm{\rho_{MEK}}}\times\frac{1000}{24.5} \tag{6}\]  
\[\mathrm{Y_{CO}}=\frac{\mathrm{F_{N_{2}}}}{1-\left(\mathrm{X_{CO}+X_{CO_{2}}+X_{ CH_{4}}+X_{C_{2}H_{4}}+X_{H_{2}}}\right)}\times\frac{\mathrm{X_{CO}}}{\mathrm{F_{MEK} }\times\mathrm{\rho_{MEK}}}\times\frac{1000}{24.5} \tag{7}\]  
\[\mathrm{Y_{CH_{4}}}=\frac{\mathrm{F_{N_{2}}}}{1-\left(\mathrm{X_{CO}+X_{CO_{2}}+ X_{CH_{4}}+X_{C_{2}H_{4}}+X_{H_{2}}}\right)}\times\frac{\mathrm{X_{CH_{4}}}}{ \mathrm{F_{MEK}}\times\mathrm{\rho_{MEK}}}\times\frac{1000}{24.5} \tag{8}\]  
\[\mathrm{Y_{C_{2}H_{4}}}=\frac{\mathrm{F_{N_{2}}}}{1-\left(\mathrm{X_{CO}+X_{ CO_{2}}+X_{CH_{4}}+X_{C_{2}H_{4}}+X_{H_{2}}}\right)}\times\frac{\mathrm{X_{C_{2}H_{4}}}}{ \mathrm{F_{MEK}}\times\mathrm{\rho_{MEK}}}\times\frac{1000}{24.5} \tag{9}\]  
\[\mathrm{Y_{i}}=\frac{\mathrm{F_{N_{2}}}}{1-\left(\mathrm{X_{CO}+X_{CO_{2}}+X_{ CH_{4}}+X_{C_{2}H_{4}}+X_{H_{2}}}\right)}\times\frac{\mathrm{X_{i}}}{\mathrm{F_{MEK} }\times\mathrm{\rho_{MEK}}}\times\frac{1000}{24.5} \tag{10}\]  
\[\mathrm{CO~{}yield~{}(Y_{CO})}=\frac{\mathrm{CO~{}yield~{}in~{}the~{} reactor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{2}\]0  
where Y (fuel gas) = Gas yield (mmole/g-MEK), Xi = The concentration of the exhaust gas (i = CO, CO\({}_{2}\), CH\({}_{4}\), C\({}_{2}\)H\({}_{4}\), H\({}_{2}\)), Y = The yield rate of the exhaust gas (i = CO, CO\({}_{2}\), CH\({}_{4}\), C\({}_{2}\)H\({}_{4}\), H\({}_{2}\)). As indicated by the equations above, the mixture amount was used to calculate the calorific value, which was evaluated using the following equation to determine the heat value burned by the burner. \[\mathrm{CO~{}yield~{}(Y_{CO})}=\frac{\mathrm{CO~{}yield~{}in~{}the~{} reactor~{}(mmole)}}{\mathrm{MEK~{}fed~{}to~{}the~{}system~{}(g)}} \tag{2}\]1  
MEK undergoes cracking into approximately four molecules per one MEK molecule in the first stage. This can be further multiplied by the gas expansion factor (\(f_{T}\)) to determine the effective volume flow rate. Subsequently, the residence times during the process can be calculated by dividing the volume flow rate in a fixed reaction zone using the following equations.