## 2 Materials and Methods
### Process Model Description
#### 2.2.3 GTM Process Model Description
The combination of the synthesis gas stream and the flash drum recycling stream raises the synthesis gas stream temperature from 209 \({}^{\circ}\)C to 270 \({}^{\circ}\)C. The methanol synthesis reactor is a plug flow reactor (PFR) (see Figure 7). Every reaction occurring in the reactor, including hydrogenation of carbon monoxide and carbon dioxide, and water gas shift, is exothermic and modelled as a heterogeneous catalytic reaction. The raw methanol (vapour product) at 250 \({}^{\circ}\)C and 8000 kPa pressure from the methanol synthesis reactor (plug flow reactor) is flashed in the flash drum (V-100), and the streams from this device are at 30 \({}^{\circ}\)C and 8000 kPa pressure. After flashing, V-100 vapour is recycled to maintain a chemically inactive rate inside the circuit. The liquid product from \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Reaction** & \(\Delta\)**H (k/mol)** & \(\Delta\)**G (k/mol)** & \(\Delta\)**S (J/kmol)** & \(\mathbf{T_{Camot}}\) (\({}^{\circ}\)C)** \\ \hline
1 & C\({}_{2}\)H\({}_{6}\) + 2H\({}_{2}\)O \(\rightarrow\) 2 CO + 5H\({}_{2}\) & 348 & 216 & 441.8 & 514 \\
2 & C\({}_{3}\)H\({}_{6}\) + 3H\({}_{2}\)O \(\rightarrow\) 3 CO + 7H\({}_{2}\) & 522 & 283 & 802.5 & 377 \\
3 & n-C\({}_{4}\)H\({}_{10}\) + 4H\({}_{2}\)O \(\rightarrow\) 4 CO + 9H\({}_{2}\) & 677 & 366 & 1042.3 & 376 \\
4 & CH\({}_{4}\) + H\({}_{2}\)O \(\leftrightarrow\) CO + 3H\({}_{2}\) & 207 & 143 & 215.44 & 687 \\
6 & CO + H\({}_{2}\)O \(\leftrightarrow\) H\({}_{2}\) + CO\({}_{2}\) & \(-\)42 & \(-\)29 & \(-\)42.87 & 706 \\ \hline \end{tabular}
\end{table} 
Table 2: Pre-reforming reactions [25]. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Reaction** & \(\Delta\)**H (k/mol)** & \(\Delta\)**G (k/mol)** & \(\Delta\)**S (J/kmol)** & \(\mathbf{T_{Camot}}\) (\({}^{\circ}\)C)** \\ \hline
1 & CH\({}_{4}\) + 1.5O\({}_{2}\)\(\leftrightarrow\) CO + 2H\({}_{2}\)O & \(-\)522 & \(-\)546 & 81.52 & \(-\)6670 \\
2 & CH\({}_{4}\) + H\({}_{2}\)O \(\leftrightarrow\) CO + 3H\({}_{2}\) & 207 & 143 & 215.44 & 687 \\
3 & CO + H\({}_{2}\)O \(\leftrightarrow\) H\({}_{2}\) + CO\({}_{2}\) & \(-\)43 & \(-\)30 & \(-\)43.93 & 705 \\ \hline \end{tabular}
\end{table} 
Table 3: Autothermal reforming reactions [25]. V-100, predominantly methanol and water, is then sent to the distillation column. Table 4 shows the methanol synthesis reaction. Here, a CuO/ZnO/Al\({}_{2}\)O\({}_{3}\) was chosen due to its selectivity of 99%. Table 5 gives the design requirements and catalyst details for the industrial methanol reactor. The reaction rate constants together with the equilibrium rate constants provide ample information on methanol synthesis kinetics. Table 1 (see Appendix A) displays the constants of the reaction rate, adsorption equilibrium, and reaction equilibrium that appear in kinetic expressions. Methanol purification--A distillation column is used in the purification of methanol. The distillation unit's column comprises 20 stages, and the condenser and reboiler pressures are 90 kPa and 7400 kPa, respectively. The bottom streams are made up of 99% water, and 99.5% pure methanol is released at 20 \({}^{\circ}\)C and 90 kPa pressure. \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Reaction** & **\(\Delta\)H (kJ/mol)** & **\(\Delta\)G (kJ/mol)** & **\(\Delta\)S (J/kmol)** & **T\({}_{\text{C}\text{a}nt}\)**(\({}^{\circ}\)C)** \\ \hline
1 & CO + 2H\({}_{2}\leftrightarrow\) CH\({}_{3}\)OH & \(-92\) & \(-27\) & \(-222.6\) & 140 \\
2 & CO + 3H\({}_{2}\leftrightarrow\) CH\({}_{3}\)OH + H\({}_{2}\)O & \(-50\) & \(4\) & \(-179.13\) & 6 \\
3 & CO\({}_{2}\) + H\({}_{2}\leftrightarrow\) H\({}_{2}\)O + CO & +43 & \(29\) & 43.89 & 706 \\ \hline \end{tabular}
\end{table} 
Table 4: Methanol synthesis reactions [25].