## 3 Results and Discussion
### Effect of Operating Under Supercritical Conditions  
The industrial application of processes involving pressures and temperatures above the critical point of water (374 \({}^{\circ}\)C, 221 bar) presents major difficulties from a technical and economic point of view due to the severe conditions that the process must comply with and because of a number of problems related to the insolubility of the salts and the occurrence of corrosion, among others [34]. However, in this section, our aim is to ascertain whether obtaining high DR values using shorter reaction times can justify the use of hydrothermal treatments under supercritical conditions.  
For this purpose, two tests were carried out at 400 \({}^{\circ}\)C temperature (P11 and P12) and at a pressure of about 240 bar. Both experiments were carried out without stirring and using a reaction time of 35 min. For the P11 test, pure deionized water (Milli-Q) was used as solvent, while in the P12 test, an aqueous solution of 5 wt.% IPA with 0.1 M KOH as catalyst was used.  
The DRs obtained from these tests are shown in Figure 7. The graph displays the DRs according to each experimental temperature and reaction time, and a clear difference can be seen between the experiments where a catalyst was used (solid columns) and those where no catalyst was used (striped columns). Thus, the DR values achieved in P11 and P12 were 94% and 98%, respectively. The graph also shows the results that correspond to the tests that were carried out under subcritical conditions (300 \({}^{\circ}\)C, 100-130 bar) so that they can be compared against those obtained under supercritical conditions.  
Figure 6: Decomposition rates obtained when varying the solvent volume/composite mass ratio at 300 \({}^{\circ}\)C, 130 bar, 60 rpm, 80 min, IPA 5 wt.%, KOH 0.1 M.  
Table 2 presents the severity factor (SF) as determined according to Equation (3) for the different temperature levels and reaction times that were studied. Generally, a lower SF means lower temperature and reaction time, that is, lower technical and economical requirements to carry out a thermochemical process. It can be observed that the tests under supercritical conditions (400 \({}^{\circ}\)C) present a higher SF (10.38) than the subcritical tests (SF between 7.43 and 7.97 at 300 \({}^{\circ}\)C) despite the significant differences between reaction times [35; 36]. A value of SF = 7.97 is better than a value of 10.38, because a lower value of SF indicates a better combination of temperature and reaction time; that is, it means that the conditions are milder. At 300 \({}^{\circ}\)C, the best reaction time is clearly 120 min, because it provides a considerable increase in DR, while the SF at 300 \({}^{\circ}\)C and different reaction times shows a very small increase. The two tests conducted under supercritical conditions achieved high DR values, the highest (98%) being reached by the tests that were performed at 400 \({}^{\circ}\)C using KOH 0.1 M as catalyst and IPA 5 wt.% as solvent. This particular test required just 35 min reaction time to reach a DR comparable to those obtained under subcritical conditions (300 \({}^{\circ}\)C) using reaction times nearly four times longer (120 min). Nonetheless, despite the longer time required, because of the lower demands with regard to their pressure and temperature conditions (lower SF), the subcritical hydrothermal processes were deemed more appropriate for a potential scaling up.  
\[SF=log\bigg{[}t\cdot\exp\bigg{(}\frac{T-100}{14.75}\bigg{)}\bigg{]}, \tag{3}\]